diff options
| author | gingerBill <bill@gingerbill.org> | 2021-04-01 11:12:40 +0100 |
|---|---|---|
| committer | gingerBill <bill@gingerbill.org> | 2021-04-01 11:12:40 +0100 |
| commit | 0fc04a939e56f269aeaff2e97ba248411cebcd10 (patch) | |
| tree | 5897d0aa6afc87bad2fd697e4bc5aad5f73d3fd4 /core/math | |
| parent | 3e1b4c17ac9a5fc17d57b4e886844092c0bec5be (diff) | |
Add `f16` support to core:math/linalg
Diffstat (limited to 'core/math')
| -rw-r--r-- | core/math/linalg/general.odin | 21 | ||||
| -rw-r--r-- | core/math/linalg/specific.odin | 831 | ||||
| -rw-r--r-- | core/math/linalg/specific_euler_angles.odin | 200 | ||||
| -rw-r--r-- | core/math/linalg/specific_euler_angles_f16.odin | 1356 |
4 files changed, 2284 insertions, 124 deletions
diff --git a/core/math/linalg/general.odin b/core/math/linalg/general.odin index 84001184f..10e557aec 100644 --- a/core/math/linalg/general.odin +++ b/core/math/linalg/general.odin @@ -47,6 +47,9 @@ vector_dot :: proc(a, b: $T/[$N]$E) -> (c: E) where IS_NUMERIC(E) { } return; } +quaternion64_dot :: proc(a, b: $T/quaternion64) -> (c: f16) { + return a.w*a.w + a.x*b.x + a.y*b.y + a.z*b.z; +} quaternion128_dot :: proc(a, b: $T/quaternion128) -> (c: f32) { return a.w*a.w + a.x*b.x + a.y*b.y + a.z*b.z; } @@ -54,7 +57,7 @@ quaternion256_dot :: proc(a, b: $T/quaternion256) -> (c: f64) { return a.w*a.w + a.x*b.x + a.y*b.y + a.z*b.z; } -dot :: proc{scalar_dot, vector_dot, quaternion128_dot, quaternion256_dot}; +dot :: proc{scalar_dot, vector_dot, quaternion64_dot, quaternion128_dot, quaternion256_dot}; inner_product :: dot; outer_product :: proc(a: $A/[$M]$E, b: $B/[$N]E) -> (out: [M][N]E) where IS_NUMERIC(E) { @@ -230,6 +233,16 @@ matrix_mul_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B) quaternion_mul_quaternion :: proc(q1, q2: $Q) -> Q where IS_QUATERNION(Q) { return q1 * q2; } + +quaternion64_mul_vector3 :: proc(q: $Q/quaternion64, v: $V/[3]$F/f16) -> V { + Raw_Quaternion :: struct {xyz: [3]f16, r: f16}; + + q := transmute(Raw_Quaternion)q; + v := transmute([3]f16)v; + + t := cross(2*q.xyz, v); + return V(v + q.r*t + cross(q.xyz, t)); +} quaternion128_mul_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V { Raw_Quaternion :: struct {xyz: [3]f32, r: f32}; @@ -239,7 +252,6 @@ quaternion128_mul_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V { t := cross(2*q.xyz, v); return V(v + q.r*t + cross(q.xyz, t)); } - quaternion256_mul_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V { Raw_Quaternion :: struct {xyz: [3]f64, r: f64}; @@ -249,12 +261,13 @@ quaternion256_mul_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V { t := cross(2*q.xyz, v); return V(v + q.r*t + cross(q.xyz, t)); } -quaternion_mul_vector3 :: proc{quaternion128_mul_vector3, quaternion256_mul_vector3}; +quaternion_mul_vector3 :: proc{quaternion64_mul_vector3, quaternion128_mul_vector3, quaternion256_mul_vector3}; mul :: proc{ matrix_mul, matrix_mul_differ, matrix_mul_vector, + quaternion64_mul_vector3, quaternion128_mul_vector3, quaternion256_mul_vector3, quaternion_mul_quaternion, @@ -347,7 +360,9 @@ to_u32 :: #force_inline proc(v: $A/[$N]$T) -> [N]u32 { return array_cast(v, u3 to_u64 :: #force_inline proc(v: $A/[$N]$T) -> [N]u64 { return array_cast(v, u64); } to_uint :: #force_inline proc(v: $A/[$N]$T) -> [N]uint { return array_cast(v, uint); } +to_complex32 :: #force_inline proc(v: $A/[$N]$T) -> [N]complex32 { return array_cast(v, complex32); } to_complex64 :: #force_inline proc(v: $A/[$N]$T) -> [N]complex64 { return array_cast(v, complex64); } to_complex128 :: #force_inline proc(v: $A/[$N]$T) -> [N]complex128 { return array_cast(v, complex128); } +to_quaternion64 :: #force_inline proc(v: $A/[$N]$T) -> [N]quaternion64 { return array_cast(v, quaternion64); } to_quaternion128 :: #force_inline proc(v: $A/[$N]$T) -> [N]quaternion128 { return array_cast(v, quaternion128); } to_quaternion256 :: #force_inline proc(v: $A/[$N]$T) -> [N]quaternion256 { return array_cast(v, quaternion256); } diff --git a/core/math/linalg/specific.odin b/core/math/linalg/specific.odin index f7b255961..3aa3b67f7 100644 --- a/core/math/linalg/specific.odin +++ b/core/math/linalg/specific.odin @@ -2,9 +2,39 @@ package linalg import "core:math" +F16_EPSILON :: 1e-3; F32_EPSILON :: 1e-7; F64_EPSILON :: 1e-15; +Vector2f16 :: distinct [2]f16; +Vector3f16 :: distinct [3]f16; +Vector4f16 :: distinct [4]f16; + +Matrix1x1f16 :: distinct [1][1]f16; +Matrix1x2f16 :: distinct [1][2]f16; +Matrix1x3f16 :: distinct [1][3]f16; +Matrix1x4f16 :: distinct [1][4]f16; + +Matrix2x1f16 :: distinct [2][1]f16; +Matrix2x2f16 :: distinct [2][2]f16; +Matrix2x3f16 :: distinct [2][3]f16; +Matrix2x4f16 :: distinct [2][4]f16; + +Matrix3x1f16 :: distinct [3][1]f16; +Matrix3x2f16 :: distinct [3][2]f16; +Matrix3x3f16 :: distinct [3][3]f16; +Matrix3x4f16 :: distinct [3][4]f16; + +Matrix4x1f16 :: distinct [4][1]f16; +Matrix4x2f16 :: distinct [4][2]f16; +Matrix4x3f16 :: distinct [4][3]f16; +Matrix4x4f16 :: distinct [4][4]f16; + +Matrix1f16 :: Matrix1x1f16; +Matrix2f16 :: Matrix2x2f16; +Matrix3f16 :: Matrix3x3f16; +Matrix4f16 :: Matrix4x4f16; + Vector2f32 :: distinct [2]f32; Vector3f32 :: distinct [3]f32; Vector4f32 :: distinct [4]f32; @@ -63,9 +93,15 @@ Matrix2f64 :: Matrix2x2f64; Matrix3f64 :: Matrix3x3f64; Matrix4f64 :: Matrix4x4f64; +Quaternionf16 :: distinct quaternion64; Quaternionf32 :: distinct quaternion128; Quaternionf64 :: distinct quaternion256; +MATRIX1F16_IDENTITY :: Matrix1f16{{1}}; +MATRIX2F16_IDENTITY :: Matrix2f16{{1, 0}, {0, 1}}; +MATRIX3F16_IDENTITY :: Matrix3f16{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}; +MATRIX4F16_IDENTITY :: Matrix4f16{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}; + MATRIX1F32_IDENTITY :: Matrix1f32{{1}}; MATRIX2F32_IDENTITY :: Matrix2f32{{1, 0}, {0, 1}}; MATRIX3F32_IDENTITY :: Matrix3f32{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}; @@ -76,9 +112,14 @@ MATRIX2F64_IDENTITY :: Matrix2f64{{1, 0}, {0, 1}}; MATRIX3F64_IDENTITY :: Matrix3f64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}; MATRIX4F64_IDENTITY :: Matrix4f64{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}; +QUATERNIONF16_IDENTITY :: Quaternionf16(1); QUATERNIONF32_IDENTITY :: Quaternionf32(1); QUATERNIONF64_IDENTITY :: Quaternionf64(1); +VECTOR3F16_X_AXIS :: Vector3f16{1, 0, 0}; +VECTOR3F16_Y_AXIS :: Vector3f16{0, 1, 0}; +VECTOR3F16_Z_AXIS :: Vector3f16{0, 0, 1}; + VECTOR3F32_X_AXIS :: Vector3f32{1, 0, 0}; VECTOR3F32_Y_AXIS :: Vector3f32{0, 1, 0}; VECTOR3F32_Z_AXIS :: Vector3f32{0, 0, 1}; @@ -118,7 +159,13 @@ orthogonal :: proc{vector2_orthogonal, vector3_orthogonal}; - +vector4_srgb_to_linear_f16 :: proc(col: Vector4f16) -> Vector4f16 { + r := math.pow(col.x, 2.2); + g := math.pow(col.y, 2.2); + b := math.pow(col.z, 2.2); + a := col.w; + return {r, g, b, a}; +} vector4_srgb_to_linear_f32 :: proc(col: Vector4f32) -> Vector4f32 { r := math.pow(col.x, 2.2); g := math.pow(col.y, 2.2); @@ -134,11 +181,33 @@ vector4_srgb_to_linear_f64 :: proc(col: Vector4f64) -> Vector4f64 { return {r, g, b, a}; } vector4_srgb_to_linear :: proc{ + vector4_srgb_to_linear_f16, vector4_srgb_to_linear_f32, vector4_srgb_to_linear_f64, }; +vector4_linear_to_srgb_f16 :: proc(col: Vector4f16) -> Vector4f16 { + a :: 2.51; + b :: 0.03; + c :: 2.43; + d :: 0.59; + e :: 0.14; + + x := col.x; + y := col.y; + z := col.z; + + x = (x * (a * x + b)) / (x * (c * x + d) + e); + y = (y * (a * y + b)) / (y * (c * y + d) + e); + z = (z * (a * z + b)) / (z * (c * z + d) + e); + + x = math.pow(clamp(x, 0, 1), 1.0 / 2.2); + y = math.pow(clamp(y, 0, 1), 1.0 / 2.2); + z = math.pow(clamp(z, 0, 1), 1.0 / 2.2); + + return {x, y, z, col.w}; +} vector4_linear_to_srgb_f32 :: proc(col: Vector4f32) -> Vector4f32 { a :: 2.51; b :: 0.03; @@ -182,12 +251,39 @@ vector4_linear_to_srgb_f64 :: proc(col: Vector4f64) -> Vector4f64 { return {x, y, z, col.w}; } vector4_linear_to_srgb :: proc{ + vector4_linear_to_srgb_f16, vector4_linear_to_srgb_f32, vector4_linear_to_srgb_f64, }; +vector4_hsl_to_rgb_f16 :: proc(h, s, l: f16, a: f16 = 1) -> Vector4f16 { + hue_to_rgb :: proc(p, q, t: f16) -> f16 { + t := t; + if t < 0 { t += 1; } + if t > 1 { t -= 1; } + switch { + case t < 1.0/6.0: return p + (q - p) * 6.0 * t; + case t < 1.0/2.0: return q; + case t < 2.0/3.0: return p + (q - p) * 6.0 * (2.0/3.0 - t); + } + return p; + } + r, g, b: f16; + if s == 0 { + r = l; + g = l; + b = l; + } else { + q := l * (1+s) if l < 0.5 else l+s - l*s; + p := 2*l - q; + r = hue_to_rgb(p, q, h + 1.0/3.0); + g = hue_to_rgb(p, q, h); + b = hue_to_rgb(p, q, h - 1.0/3.0); + } + return {r, g, b, a}; +} vector4_hsl_to_rgb_f32 :: proc(h, s, l: f32, a: f32 = 1) -> Vector4f32 { hue_to_rgb :: proc(p, q, t: f32) -> f32 { t := t; @@ -243,11 +339,41 @@ vector4_hsl_to_rgb_f64 :: proc(h, s, l: f64, a: f64 = 1) -> Vector4f64 { return {r, g, b, a}; } vector4_hsl_to_rgb :: proc{ + vector4_hsl_to_rgb_f16, vector4_hsl_to_rgb_f32, vector4_hsl_to_rgb_f64, }; +vector4_rgb_to_hsl_f16 :: proc(col: Vector4f16) -> Vector4f16 { + r := col.x; + g := col.y; + b := col.z; + a := col.w; + v_min := min(r, g, b); + v_max := max(r, g, b); + h, s, l: f16; + h = 0.0; + s = 0.0; + l = (v_min + v_max) * 0.5; + + if v_max != v_min { + d: = v_max - v_min; + s = d / (2.0 - v_max - v_min) if l > 0.5 else d / (v_max + v_min); + switch { + case v_max == r: + h = (g - b) / d + (6.0 if g < b else 0.0); + case v_max == g: + h = (b - r) / d + 2.0; + case v_max == b: + h = (r - g) / d + 4.0; + } + + h *= 1.0/6.0; + } + + return {h, s, l, a}; +} vector4_rgb_to_hsl_f32 :: proc(col: Vector4f32) -> Vector4f32 { r := col.x; g := col.y; @@ -277,7 +403,6 @@ vector4_rgb_to_hsl_f32 :: proc(col: Vector4f32) -> Vector4f32 { return {h, s, l, a}; } - vector4_rgb_to_hsl_f64 :: proc(col: Vector4f64) -> Vector4f64 { r := col.x; g := col.y; @@ -308,12 +433,22 @@ vector4_rgb_to_hsl_f64 :: proc(col: Vector4f64) -> Vector4f64 { return {h, s, l, a}; } vector4_rgb_to_hsl :: proc{ + vector4_rgb_to_hsl_f16, vector4_rgb_to_hsl_f32, vector4_rgb_to_hsl_f64, }; +quaternion_angle_axis_f16 :: proc(angle_radians: f16, axis: Vector3f16) -> (q: Quaternionf16) { + t := angle_radians*0.5; + v := normalize(axis) * math.sin(t); + q.x = v.x; + q.y = v.y; + q.z = v.z; + q.w = math.cos(t); + return; +} quaternion_angle_axis_f32 :: proc(angle_radians: f32, axis: Vector3f32) -> (q: Quaternionf32) { t := angle_radians*0.5; v := normalize(axis) * math.sin(t); @@ -333,11 +468,18 @@ quaternion_angle_axis_f64 :: proc(angle_radians: f64, axis: Vector3f64) -> (q: Q return; } quaternion_angle_axis :: proc{ + quaternion_angle_axis_f16, quaternion_angle_axis_f32, quaternion_angle_axis_f64, }; +angle_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 { + if abs(q.w) > math.SQRT_THREE*0.5 { + return math.asin(q.x*q.x + q.y*q.y + q.z*q.z) * 2; + } + return math.cos(q.x) * 2; +} angle_from_quaternion_f32 :: proc(q: Quaternionf32) -> f32 { if abs(q.w) > math.SQRT_THREE*0.5 { return math.asin(q.x*q.x + q.y*q.y + q.z*q.z) * 2; @@ -353,11 +495,19 @@ angle_from_quaternion_f64 :: proc(q: Quaternionf64) -> f64 { return math.cos(q.x) * 2; } angle_from_quaternion :: proc{ + angle_from_quaternion_f16, angle_from_quaternion_f32, angle_from_quaternion_f64, }; - +axis_from_quaternion_f16 :: proc(q: Quaternionf16) -> Vector3f16 { + t1 := 1 - q.w*q.w; + if t1 < 0 { + return {0, 0, 1}; + } + t2 := 1.0 / math.sqrt(t1); + return {q.x*t2, q.y*t2, q.z*t2}; +} axis_from_quaternion_f32 :: proc(q: Quaternionf32) -> Vector3f32 { t1 := 1 - q.w*q.w; if t1 < 0 { @@ -375,11 +525,17 @@ axis_from_quaternion_f64 :: proc(q: Quaternionf64) -> Vector3f64 { return {q.x*t2, q.y*t2, q.z*t2}; } axis_from_quaternion :: proc{ + axis_from_quaternion_f16, axis_from_quaternion_f32, axis_from_quaternion_f64, }; +angle_axis_from_quaternion_f16 :: proc(q: Quaternionf16) -> (angle: f16, axis: Vector3f16) { + angle = angle_from_quaternion(q); + axis = axis_from_quaternion(q); + return; +} angle_axis_from_quaternion_f32 :: proc(q: Quaternionf32) -> (angle: f32, axis: Vector3f32) { angle = angle_from_quaternion(q); axis = axis_from_quaternion(q); @@ -391,11 +547,55 @@ angle_axis_from_quaternion_f64 :: proc(q: Quaternionf64) -> (angle: f64, axis: V return; } angle_axis_from_quaternion :: proc { + angle_axis_from_quaternion_f16, angle_axis_from_quaternion_f32, angle_axis_from_quaternion_f64, }; +quaternion_from_forward_and_up_f16 :: proc(forward, up: Vector3f16) -> Quaternionf16 { + f := normalize(forward); + s := normalize(cross(f, up)); + u := cross(s, f); + m := Matrix3f16{ + {+s.x, +u.x, -f.x}, + {+s.y, +u.y, -f.y}, + {+s.z, +u.z, -f.z}, + }; + + tr := trace(m); + + q: Quaternionf16; + + switch { + case tr > 0: + S := 2 * math.sqrt(1 + tr); + q.w = 0.25 * S; + q.x = (m[2][1] - m[1][2]) / S; + q.y = (m[0][2] - m[2][0]) / S; + q.z = (m[1][0] - m[0][1]) / S; + case (m[0][0] > m[1][1]) && (m[0][0] > m[2][2]): + S := 2 * math.sqrt(1 + m[0][0] - m[1][1] - m[2][2]); + q.w = (m[2][1] - m[1][2]) / S; + q.x = 0.25 * S; + q.y = (m[0][1] + m[1][0]) / S; + q.z = (m[0][2] + m[2][0]) / S; + case m[1][1] > m[2][2]: + S := 2 * math.sqrt(1 + m[1][1] - m[0][0] - m[2][2]); + q.w = (m[0][2] - m[2][0]) / S; + q.x = (m[0][1] + m[1][0]) / S; + q.y = 0.25 * S; + q.z = (m[1][2] + m[2][1]) / S; + case: + S := 2 * math.sqrt(1 + m[2][2] - m[0][0] - m[1][1]); + q.w = (m[1][0] - m[0][1]) / S; + q.x = (m[0][2] - m[2][0]) / S; + q.y = (m[1][2] + m[2][1]) / S; + q.z = 0.25 * S; + } + + return normalize(q); +} quaternion_from_forward_and_up_f32 :: proc(forward, up: Vector3f32) -> Quaternionf32 { f := normalize(forward); s := normalize(cross(f, up)); @@ -483,11 +683,14 @@ quaternion_from_forward_and_up_f64 :: proc(forward, up: Vector3f64) -> Quaternio return normalize(q); } quaternion_from_forward_and_up :: proc{ + quaternion_from_forward_and_up_f16, quaternion_from_forward_and_up_f32, quaternion_from_forward_and_up_f64, }; - +quaternion_look_at_f16 :: proc(eye, centre: Vector3f16, up: Vector3f16) -> Quaternionf16 { + return quaternion_from_matrix3(matrix3_look_at(eye, centre, up)); +} quaternion_look_at_f32 :: proc(eye, centre: Vector3f32, up: Vector3f32) -> Quaternionf32 { return quaternion_from_matrix3(matrix3_look_at(eye, centre, up)); } @@ -495,13 +698,20 @@ quaternion_look_at_f64 :: proc(eye, centre: Vector3f64, up: Vector3f64) -> Quate return quaternion_from_matrix3(matrix3_look_at(eye, centre, up)); } quaternion_look_at :: proc{ + quaternion_look_at_f16, quaternion_look_at_f32, quaternion_look_at_f64, }; -quaternion_nlerp_f32 :: proc(a, b: Quaternionf32, t: f32) -> (c: Quaternionf32) { +quaternion_nlerp_f16 :: proc(a, b: Quaternionf16, t: f16) -> (c: Quaternionf16) { + c.x = a.x + (b.x-a.x)*t; + c.y = a.y + (b.y-a.y)*t; + c.z = a.z + (b.z-a.z)*t; + c.w = a.w + (b.w-a.w)*t; + return normalize(c); +}quaternion_nlerp_f32 :: proc(a, b: Quaternionf32, t: f32) -> (c: Quaternionf32) { c.x = a.x + (b.x-a.x)*t; c.y = a.y + (b.y-a.y)*t; c.z = a.z + (b.z-a.z)*t; @@ -516,12 +726,39 @@ quaternion_nlerp_f64 :: proc(a, b: Quaternionf64, t: f64) -> (c: Quaternionf64) return normalize(c); } quaternion_nlerp :: proc{ + quaternion_nlerp_f16, quaternion_nlerp_f32, quaternion_nlerp_f64, }; -quaternion_slerp_f32 :: proc(x, y: Quaternionf32, t: f32) -> (q: Quaternionf32) { +quaternion_slerp_f16 :: proc(x, y: Quaternionf16, t: f16) -> (q: Quaternionf16) { + a, b := x, y; + cos_angle := dot(a, b); + if cos_angle < 0 { + b = -b; + cos_angle = -cos_angle; + } + if cos_angle > 1 - F32_EPSILON { + q.x = a.x + (b.x-a.x)*t; + q.y = a.y + (b.y-a.y)*t; + q.z = a.z + (b.z-a.z)*t; + q.w = a.w + (b.w-a.w)*t; + return; + } + + angle := math.acos(cos_angle); + sin_angle := math.sin(angle); + factor_a := math.sin((1-t) * angle) / sin_angle; + factor_b := math.sin(t * angle) / sin_angle; + + + q.x = factor_a * a.x + factor_b * b.x; + q.y = factor_a * a.y + factor_b * b.y; + q.z = factor_a * a.z + factor_b * b.z; + q.w = factor_a * a.w + factor_b * b.w; + return; +}quaternion_slerp_f32 :: proc(x, y: Quaternionf32, t: f32) -> (q: Quaternionf32) { a, b := x, y; cos_angle := dot(a, b); if cos_angle < 0 { @@ -576,11 +813,16 @@ quaternion_slerp_f64 :: proc(x, y: Quaternionf64, t: f64) -> (q: Quaternionf64) return; } quaternion_slerp :: proc{ + quaternion_slerp_f16, quaternion_slerp_f32, quaternion_slerp_f64, }; +quaternion_squad_f16 :: proc(q1, q2, s1, s2: Quaternionf16, h: f16) -> Quaternionf16 { + slerp :: quaternion_slerp; + return slerp(slerp(q1, q2, h), slerp(s1, s2, h), 2 * (1 - h) * h); +} quaternion_squad_f32 :: proc(q1, q2, s1, s2: Quaternionf32, h: f32) -> Quaternionf32 { slerp :: quaternion_slerp; return slerp(slerp(q1, q2, h), slerp(s1, s2, h), 2 * (1 - h) * h); @@ -590,11 +832,19 @@ quaternion_squad_f64 :: proc(q1, q2, s1, s2: Quaternionf64, h: f64) -> Quaternio return slerp(slerp(q1, q2, h), slerp(s1, s2, h), 2 * (1 - h) * h); } quaternion_squad :: proc{ + quaternion_squad_f16, quaternion_squad_f32, quaternion_squad_f64, }; +quaternion_from_matrix4_f16 :: proc(m: Matrix4f16) -> (q: Quaternionf16) { + m3: Matrix3f16 = ---; + m3[0][0], m3[0][1], m3[0][2] = m[0][0], m[0][1], m[0][2]; + m3[1][0], m3[1][1], m3[1][2] = m[1][0], m[1][1], m[1][2]; + m3[2][0], m3[2][1], m3[2][2] = m[2][0], m[2][1], m[2][2]; + return quaternion_from_matrix3(m3); +} quaternion_from_matrix4_f32 :: proc(m: Matrix4f32) -> (q: Quaternionf32) { m3: Matrix3f32 = ---; m3[0][0], m3[0][1], m3[0][2] = m[0][0], m[0][1], m[0][2]; @@ -610,11 +860,61 @@ quaternion_from_matrix4_f64 :: proc(m: Matrix4f64) -> (q: Quaternionf64) { return quaternion_from_matrix3(m3); } quaternion_from_matrix4 :: proc{ + quaternion_from_matrix4_f16, quaternion_from_matrix4_f32, quaternion_from_matrix4_f64, }; +quaternion_from_matrix3_f16 :: proc(m: Matrix3f16) -> (q: Quaternionf16) { + four_x_squared_minus_1 := m[0][0] - m[1][1] - m[2][2]; + four_y_squared_minus_1 := m[1][1] - m[0][0] - m[2][2]; + four_z_squared_minus_1 := m[2][2] - m[0][0] - m[1][1]; + four_w_squared_minus_1 := m[0][0] + m[1][1] + m[2][2]; + + biggest_index := 0; + four_biggest_squared_minus_1 := four_w_squared_minus_1; + if four_x_squared_minus_1 > four_biggest_squared_minus_1 { + four_biggest_squared_minus_1 = four_x_squared_minus_1; + biggest_index = 1; + } + if four_y_squared_minus_1 > four_biggest_squared_minus_1 { + four_biggest_squared_minus_1 = four_y_squared_minus_1; + biggest_index = 2; + } + if four_z_squared_minus_1 > four_biggest_squared_minus_1 { + four_biggest_squared_minus_1 = four_z_squared_minus_1; + biggest_index = 3; + } + + biggest_val := math.sqrt(four_biggest_squared_minus_1 + 1) * 0.5; + mult := 0.25 / biggest_val; + + q = 1; + switch biggest_index { + case 0: + q.w = biggest_val; + q.x = (m[1][2] - m[2][1]) * mult; + q.y = (m[2][0] - m[0][2]) * mult; + q.z = (m[0][1] - m[1][0]) * mult; + case 1: + q.w = (m[1][2] - m[2][1]) * mult; + q.x = biggest_val; + q.y = (m[0][1] + m[1][0]) * mult; + q.z = (m[2][0] + m[0][2]) * mult; + case 2: + q.w = (m[2][0] - m[0][2]) * mult; + q.x = (m[0][1] + m[1][0]) * mult; + q.y = biggest_val; + q.z = (m[1][2] + m[2][1]) * mult; + case 3: + q.w = (m[0][1] - m[1][0]) * mult; + q.x = (m[2][0] + m[0][2]) * mult; + q.y = (m[1][2] + m[2][1]) * mult; + q.z = biggest_val; + } + return; +} quaternion_from_matrix3_f32 :: proc(m: Matrix3f32) -> (q: Quaternionf32) { four_x_squared_minus_1 := m[0][0] - m[1][1] - m[2][2]; four_y_squared_minus_1 := m[1][1] - m[0][0] - m[2][2]; @@ -714,11 +1014,33 @@ quaternion_from_matrix3_f64 :: proc(m: Matrix3f64) -> (q: Quaternionf64) { return; } quaternion_from_matrix3 :: proc{ + quaternion_from_matrix3_f16, quaternion_from_matrix3_f32, quaternion_from_matrix3_f64, }; +quaternion_between_two_vector3_f16 :: proc(from, to: Vector3f16) -> (q: Quaternionf16) { + x := normalize(from); + y := normalize(to); + + cos_theta := dot(x, y); + if abs(cos_theta + 1) < 2*F32_EPSILON { + v := vector3_orthogonal(x); + q.x = v.x; + q.y = v.y; + q.z = v.z; + q.w = 0; + return; + } + v := cross(x, y); + w := cos_theta + 1; + q.w = w; + q.x = v.x; + q.y = v.y; + q.z = v.z; + return normalize(q); +} quaternion_between_two_vector3_f32 :: proc(from, to: Vector3f32) -> (q: Quaternionf32) { x := normalize(from); y := normalize(to); @@ -762,11 +1084,21 @@ quaternion_between_two_vector3_f64 :: proc(from, to: Vector3f64) -> (q: Quaterni return normalize(q); } quaternion_between_two_vector3 :: proc{ + quaternion_between_two_vector3_f16, quaternion_between_two_vector3_f32, quaternion_between_two_vector3_f64, }; +matrix2_inverse_transpose_f16 :: proc(m: Matrix2f16) -> (c: Matrix2f16) { + d := m[0][0]*m[1][1] - m[1][0]*m[0][1]; + id := 1.0/d; + c[0][0] = +m[1][1] * id; + c[0][1] = -m[0][1] * id; + c[1][0] = -m[1][0] * id; + c[1][1] = +m[0][0] * id; + return c; +} matrix2_inverse_transpose_f32 :: proc(m: Matrix2f32) -> (c: Matrix2f32) { d := m[0][0]*m[1][1] - m[1][0]*m[0][1]; id := 1.0/d; @@ -786,11 +1118,15 @@ matrix2_inverse_transpose_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) { return c; } matrix2_inverse_transpose :: proc{ + matrix2_inverse_transpose_f16, matrix2_inverse_transpose_f32, matrix2_inverse_transpose_f64, }; +matrix2_determinant_f16 :: proc(m: Matrix2f16) -> f16 { + return m[0][0]*m[1][1] - m[1][0]*m[0][1]; +} matrix2_determinant_f32 :: proc(m: Matrix2f32) -> f32 { return m[0][0]*m[1][1] - m[1][0]*m[0][1]; } @@ -798,11 +1134,21 @@ matrix2_determinant_f64 :: proc(m: Matrix2f64) -> f64 { return m[0][0]*m[1][1] - m[1][0]*m[0][1]; } matrix2_determinant :: proc{ + matrix2_determinant_f16, matrix2_determinant_f32, matrix2_determinant_f64, }; +matrix2_inverse_f16 :: proc(m: Matrix2f16) -> (c: Matrix2f16) { + d := m[0][0]*m[1][1] - m[1][0]*m[0][1]; + id := 1.0/d; + c[0][0] = +m[1][1] * id; + c[1][0] = -m[0][1] * id; + c[0][1] = -m[1][0] * id; + c[1][1] = +m[0][0] * id; + return c; +} matrix2_inverse_f32 :: proc(m: Matrix2f32) -> (c: Matrix2f32) { d := m[0][0]*m[1][1] - m[1][0]*m[0][1]; id := 1.0/d; @@ -822,11 +1168,19 @@ matrix2_inverse_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) { return c; } matrix2_inverse :: proc{ + matrix2_inverse_f16, matrix2_inverse_f32, matrix2_inverse_f64, }; +matrix2_adjoint_f16 :: proc(m: Matrix2f16) -> (c: Matrix2f16) { + c[0][0] = +m[1][1]; + c[0][1] = -m[1][0]; + c[1][0] = -m[0][1]; + c[1][1] = +m[0][0]; + return c; +} matrix2_adjoint_f32 :: proc(m: Matrix2f32) -> (c: Matrix2f32) { c[0][0] = +m[1][1]; c[0][1] = -m[1][0]; @@ -842,11 +1196,36 @@ matrix2_adjoint_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) { return c; } matrix2_adjoint :: proc{ + matrix2_adjoint_f16, matrix2_adjoint_f32, matrix2_adjoint_f64, }; +matrix3_from_quaternion_f16 :: proc(q: Quaternionf16) -> (m: Matrix3f16) { + qxx := q.x * q.x; + qyy := q.y * q.y; + qzz := q.z * q.z; + qxz := q.x * q.z; + qxy := q.x * q.y; + qyz := q.y * q.z; + qwx := q.w * q.x; + qwy := q.w * q.y; + qwz := q.w * q.z; + + m[0][0] = 1 - 2 * (qyy + qzz); + m[0][1] = 2 * (qxy + qwz); + m[0][2] = 2 * (qxz - qwy); + + m[1][0] = 2 * (qxy - qwz); + m[1][1] = 1 - 2 * (qxx + qzz); + m[1][2] = 2 * (qyz + qwx); + + m[2][0] = 2 * (qxz + qwy); + m[2][1] = 2 * (qyz - qwx); + m[2][2] = 1 - 2 * (qxx + qyy); + return m; +} matrix3_from_quaternion_f32 :: proc(q: Quaternionf32) -> (m: Matrix3f32) { qxx := q.x * q.x; qyy := q.y * q.y; @@ -896,11 +1275,15 @@ matrix3_from_quaternion_f64 :: proc(q: Quaternionf64) -> (m: Matrix3f64) { return m; } matrix3_from_quaternion :: proc{ + matrix3_from_quaternion_f16, matrix3_from_quaternion_f32, matrix3_from_quaternion_f64, }; +matrix3_inverse_f16 :: proc(m: Matrix3f16) -> Matrix3f16 { + return transpose(matrix3_inverse_transpose(m)); +} matrix3_inverse_f32 :: proc(m: Matrix3f32) -> Matrix3f32 { return transpose(matrix3_inverse_transpose(m)); } @@ -908,11 +1291,18 @@ matrix3_inverse_f64 :: proc(m: Matrix3f64) -> Matrix3f64 { return transpose(matrix3_inverse_transpose(m)); } matrix3_inverse :: proc{ + matrix3_inverse_f16, matrix3_inverse_f32, matrix3_inverse_f64, }; +matrix3_determinant_f16 :: proc(m: Matrix3f16) -> f16 { + a := +m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2]); + b := -m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2]); + c := +m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]); + return a + b + c; +} matrix3_determinant_f32 :: proc(m: Matrix3f32) -> f32 { a := +m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2]); b := -m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2]); @@ -926,11 +1316,24 @@ matrix3_determinant_f64 :: proc(m: Matrix3f64) -> f64 { return a + b + c; } matrix3_determinant :: proc{ + matrix3_determinant_f16, matrix3_determinant_f32, matrix3_determinant_f64, }; +matrix3_adjoint_f16 :: proc(m: Matrix3f16) -> (adjoint: Matrix3f16) { + adjoint[0][0] = +(m[1][1] * m[2][2] - m[1][2] * m[2][1]); + adjoint[1][0] = -(m[0][1] * m[2][2] - m[0][2] * m[2][1]); + adjoint[2][0] = +(m[0][1] * m[1][2] - m[0][2] * m[1][1]); + adjoint[0][1] = -(m[1][0] * m[2][2] - m[1][2] * m[2][0]); + adjoint[1][1] = +(m[0][0] * m[2][2] - m[0][2] * m[2][0]); + adjoint[2][1] = -(m[0][0] * m[1][2] - m[0][2] * m[1][0]); + adjoint[0][2] = +(m[1][0] * m[2][1] - m[1][1] * m[2][0]); + adjoint[1][2] = -(m[0][0] * m[2][1] - m[0][1] * m[2][0]); + adjoint[2][2] = +(m[0][0] * m[1][1] - m[0][1] * m[1][0]); + return adjoint; +} matrix3_adjoint_f32 :: proc(m: Matrix3f32) -> (adjoint: Matrix3f32) { adjoint[0][0] = +(m[1][1] * m[2][2] - m[1][2] * m[2][1]); adjoint[1][0] = -(m[0][1] * m[2][2] - m[0][2] * m[2][1]); @@ -956,11 +1359,24 @@ matrix3_adjoint_f64 :: proc(m: Matrix3f64) -> (adjoint: Matrix3f64) { return adjoint; } matrix3_adjoint :: proc{ + matrix3_adjoint_f16, matrix3_adjoint_f32, matrix3_adjoint_f64, }; + +matrix3_inverse_transpose_f16 :: proc(m: Matrix3f16) -> (inverse_transpose: Matrix3f16) { + adjoint := matrix3_adjoint(m); + determinant := matrix3_determinant(m); + inv_determinant := 1.0 / determinant; + for i in 0..<3 { + for j in 0..<3 { + inverse_transpose[i][j] = adjoint[i][j] * inv_determinant; + } + } + return; +} matrix3_inverse_transpose_f32 :: proc(m: Matrix3f32) -> (inverse_transpose: Matrix3f32) { adjoint := matrix3_adjoint(m); determinant := matrix3_determinant(m); @@ -984,11 +1400,18 @@ matrix3_inverse_transpose_f64 :: proc(m: Matrix3f64) -> (inverse_transpose: Matr return; } matrix3_inverse_transpose :: proc{ + matrix3_inverse_transpose_f16, matrix3_inverse_transpose_f32, matrix3_inverse_transpose_f64, }; +matrix3_scale_f16 :: proc(s: Vector3f16) -> (m: Matrix3f16) { + m[0][0] = s[0]; + m[1][1] = s[1]; + m[2][2] = s[2]; + return m; +} matrix3_scale_f32 :: proc(s: Vector3f32) -> (m: Matrix3f32) { m[0][0] = s[0]; m[1][1] = s[1]; @@ -1002,11 +1425,33 @@ matrix3_scale_f64 :: proc(s: Vector3f64) -> (m: Matrix3f64) { return m; } matrix3_scale :: proc{ + matrix3_scale_f16, matrix3_scale_f32, matrix3_scale_f64, }; +matrix3_rotate_f16 :: proc(angle_radians: f16, v: Vector3f16) -> (rot: Matrix3f16) { + c := math.cos(angle_radians); + s := math.sin(angle_radians); + + a := normalize(v); + t := a * (1-c); + + rot[0][0] = c + t[0]*a[0]; + rot[0][1] = 0 + t[0]*a[1] + s*a[2]; + rot[0][2] = 0 + t[0]*a[2] - s*a[1]; + + rot[1][0] = 0 + t[1]*a[0] - s*a[2]; + rot[1][1] = c + t[1]*a[1]; + rot[1][2] = 0 + t[1]*a[2] + s*a[0]; + + rot[2][0] = 0 + t[2]*a[0] + s*a[1]; + rot[2][1] = 0 + t[2]*a[1] - s*a[0]; + rot[2][2] = c + t[2]*a[2]; + + return rot; +} matrix3_rotate_f32 :: proc(angle_radians: f32, v: Vector3f32) -> (rot: Matrix3f32) { c := math.cos(angle_radians); s := math.sin(angle_radians); @@ -1050,11 +1495,22 @@ matrix3_rotate_f64 :: proc(angle_radians: f64, v: Vector3f64) -> (rot: Matrix3f6 return rot; } matrix3_rotate :: proc{ + matrix3_rotate_f16, matrix3_rotate_f32, matrix3_rotate_f64, }; +matrix3_look_at_f16 :: proc(eye, centre, up: Vector3f16) -> Matrix3f16 { + f := normalize(centre - eye); + s := normalize(cross(f, up)); + u := cross(s, f); + return Matrix3f16{ + {+s.x, +u.x, -f.x}, + {+s.y, +u.y, -f.y}, + {+s.z, +u.z, -f.z}, + }; +} matrix3_look_at_f32 :: proc(eye, centre, up: Vector3f32) -> Matrix3f32 { f := normalize(centre - eye); s := normalize(cross(f, up)); @@ -1076,11 +1532,39 @@ matrix3_look_at_f64 :: proc(eye, centre, up: Vector3f64) -> Matrix3f64 { }; } matrix3_look_at :: proc{ + matrix3_look_at_f16, matrix3_look_at_f32, matrix3_look_at_f64, }; +matrix4_from_quaternion_f16 :: proc(q: Quaternionf16) -> (m: Matrix4f16) { + qxx := q.x * q.x; + qyy := q.y * q.y; + qzz := q.z * q.z; + qxz := q.x * q.z; + qxy := q.x * q.y; + qyz := q.y * q.z; + qwx := q.w * q.x; + qwy := q.w * q.y; + qwz := q.w * q.z; + + m[0][0] = 1 - 2 * (qyy + qzz); + m[0][1] = 2 * (qxy + qwz); + m[0][2] = 2 * (qxz - qwy); + + m[1][0] = 2 * (qxy - qwz); + m[1][1] = 1 - 2 * (qxx + qzz); + m[1][2] = 2 * (qyz + qwx); + + m[2][0] = 2 * (qxz + qwy); + m[2][1] = 2 * (qyz - qwx); + m[2][2] = 1 - 2 * (qxx + qyy); + + m[3][3] = 1; + + return m; +} matrix4_from_quaternion_f32 :: proc(q: Quaternionf32) -> (m: Matrix4f32) { qxx := q.x * q.x; qyy := q.y * q.y; @@ -1136,11 +1620,18 @@ matrix4_from_quaternion_f64 :: proc(q: Quaternionf64) -> (m: Matrix4f64) { return m; } matrix4_from_quaternion :: proc{ + matrix4_from_quaternion_f16, matrix4_from_quaternion_f32, matrix4_from_quaternion_f64, }; +matrix4_from_trs_f16 :: proc(t: Vector3f16, r: Quaternionf16, s: Vector3f16) -> Matrix4f16 { + translation := matrix4_translate(t); + rotation := matrix4_from_quaternion(r); + scale := matrix4_scale(s); + return mul(translation, mul(rotation, scale)); +} matrix4_from_trs_f32 :: proc(t: Vector3f32, r: Quaternionf32, s: Vector3f32) -> Matrix4f32 { translation := matrix4_translate(t); rotation := matrix4_from_quaternion(r); @@ -1154,12 +1645,16 @@ matrix4_from_trs_f64 :: proc(t: Vector3f64, r: Quaternionf64, s: Vector3f64) -> return mul(translation, mul(rotation, scale)); } matrix4_from_trs :: proc{ + matrix4_from_trs_f16, matrix4_from_trs_f32, matrix4_from_trs_f64, }; +matrix4_inverse_f16 :: proc(m: Matrix4f16) -> Matrix4f16 { + return transpose(matrix4_inverse_transpose(m)); +} matrix4_inverse_f32 :: proc(m: Matrix4f32) -> Matrix4f32 { return transpose(matrix4_inverse_transpose(m)); } @@ -1167,11 +1662,23 @@ matrix4_inverse_f64 :: proc(m: Matrix4f64) -> Matrix4f64 { return transpose(matrix4_inverse_transpose(m)); } matrix4_inverse :: proc{ + matrix4_inverse_f16, matrix4_inverse_f32, matrix4_inverse_f64, }; +matrix4_minor_f16 :: proc(m: Matrix4f16, c, r: int) -> f16 { + cut_down: Matrix3f16; + for i in 0..<3 { + col := i if i < c else i+1; + for j in 0..<3 { + row := j if j < r else j+1; + cut_down[i][j] = m[col][row]; + } + } + return matrix3_determinant(cut_down); +} matrix4_minor_f32 :: proc(m: Matrix4f32, c, r: int) -> f32 { cut_down: Matrix3f32; for i in 0..<3 { @@ -1195,11 +1702,18 @@ matrix4_minor_f64 :: proc(m: Matrix4f64, c, r: int) -> f64 { return matrix3_determinant(cut_down); } matrix4_minor :: proc{ + matrix4_minor_f16, matrix4_minor_f32, matrix4_minor_f64, }; +matrix4_cofactor_f16 :: proc(m: Matrix4f16, c, r: int) -> f16 { + sign, minor: f16; + sign = 1 if (c + r) % 2 == 0 else -1; + minor = matrix4_minor(m, c, r); + return sign * minor; +} matrix4_cofactor_f32 :: proc(m: Matrix4f32, c, r: int) -> f32 { sign, minor: f32; sign = 1 if (c + r) % 2 == 0 else -1; @@ -1213,11 +1727,20 @@ matrix4_cofactor_f64 :: proc(m: Matrix4f64, c, r: int) -> f64 { return sign * minor; } matrix4_cofactor :: proc{ + matrix4_cofactor_f16, matrix4_cofactor_f32, matrix4_cofactor_f64, }; +matrix4_adjoint_f16 :: proc(m: Matrix4f16) -> (adjoint: Matrix4f16) { + for i in 0..<4 { + for j in 0..<4 { + adjoint[i][j] = matrix4_cofactor(m, i, j); + } + } + return; +} matrix4_adjoint_f32 :: proc(m: Matrix4f32) -> (adjoint: Matrix4f32) { for i in 0..<4 { for j in 0..<4 { @@ -1235,11 +1758,19 @@ matrix4_adjoint_f64 :: proc(m: Matrix4f64) -> (adjoint: Matrix4f64) { return; } matrix4_adjoint :: proc{ + matrix4_adjoint_f16, matrix4_adjoint_f32, matrix4_adjoint_f64, }; +matrix4_determinant_f16 :: proc(m: Matrix4f16) -> (determinant: f16) { + adjoint := matrix4_adjoint(m); + for i in 0..<4 { + determinant += m[i][0] * adjoint[i][0]; + } + return; +} matrix4_determinant_f32 :: proc(m: Matrix4f32) -> (determinant: f32) { adjoint := matrix4_adjoint(m); for i in 0..<4 { @@ -1255,11 +1786,26 @@ matrix4_determinant_f64 :: proc(m: Matrix4f64) -> (determinant: f64) { return; } matrix4_determinant :: proc{ + matrix4_determinant_f16, matrix4_determinant_f32, matrix4_determinant_f64, }; +matrix4_inverse_transpose_f16 :: proc(m: Matrix4f16) -> (inverse_transpose: Matrix4f16) { + adjoint := matrix4_adjoint(m); + determinant: f16 = 0; + for i in 0..<4 { + determinant += m[i][0] * adjoint[i][0]; + } + inv_determinant := 1.0 / determinant; + for i in 0..<4 { + for j in 0..<4 { + inverse_transpose[i][j] = adjoint[i][j] * inv_determinant; + } + } + return; +} matrix4_inverse_transpose_f32 :: proc(m: Matrix4f32) -> (inverse_transpose: Matrix4f32) { adjoint := matrix4_adjoint(m); determinant: f32 = 0; @@ -1289,11 +1835,19 @@ matrix4_inverse_transpose_f64 :: proc(m: Matrix4f64) -> (inverse_transpose: Matr return; } matrix4_inverse_transpose :: proc{ + matrix4_inverse_transpose_f16, matrix4_inverse_transpose_f32, matrix4_inverse_transpose_f64, }; +matrix4_translate_f16 :: proc(v: Vector3f16) -> Matrix4f16 { + m := MATRIX4F16_IDENTITY; + m[3][0] = v[0]; + m[3][1] = v[1]; + m[3][2] = v[2]; + return m; +} matrix4_translate_f32 :: proc(v: Vector3f32) -> Matrix4f32 { m := MATRIX4F32_IDENTITY; m[3][0] = v[0]; @@ -1309,11 +1863,38 @@ matrix4_translate_f64 :: proc(v: Vector3f64) -> Matrix4f64 { return m; } matrix4_translate :: proc{ + matrix4_translate_f16, matrix4_translate_f32, matrix4_translate_f64, }; +matrix4_rotate_f16 :: proc(angle_radians: f16, v: Vector3f16) -> Matrix4f16 { + c := math.cos(angle_radians); + s := math.sin(angle_radians); + + a := normalize(v); + t := a * (1-c); + + rot := MATRIX4F16_IDENTITY; + + rot[0][0] = c + t[0]*a[0]; + rot[0][1] = 0 + t[0]*a[1] + s*a[2]; + rot[0][2] = 0 + t[0]*a[2] - s*a[1]; + rot[0][3] = 0; + + rot[1][0] = 0 + t[1]*a[0] - s*a[2]; + rot[1][1] = c + t[1]*a[1]; + rot[1][2] = 0 + t[1]*a[2] + s*a[0]; + rot[1][3] = 0; + + rot[2][0] = 0 + t[2]*a[0] + s*a[1]; + rot[2][1] = 0 + t[2]*a[1] - s*a[0]; + rot[2][2] = c + t[2]*a[2]; + rot[2][3] = 0; + + return rot; +} matrix4_rotate_f32 :: proc(angle_radians: f32, v: Vector3f32) -> Matrix4f32 { c := math.cos(angle_radians); s := math.sin(angle_radians); @@ -1367,11 +1948,19 @@ matrix4_rotate_f64 :: proc(angle_radians: f64, v: Vector3f64) -> Matrix4f64 { return rot; } matrix4_rotate :: proc{ + matrix4_rotate_f16, matrix4_rotate_f32, matrix4_rotate_f64, }; +matrix4_scale_f16 :: proc(v: Vector3f16) -> (m: Matrix4f16) { + m[0][0] = v[0]; + m[1][1] = v[1]; + m[2][2] = v[2]; + m[3][3] = 1; + return; +} matrix4_scale_f32 :: proc(v: Vector3f32) -> (m: Matrix4f32) { m[0][0] = v[0]; m[1][1] = v[1]; @@ -1387,11 +1976,26 @@ matrix4_scale_f64 :: proc(v: Vector3f64) -> (m: Matrix4f64) { return; } matrix4_scale :: proc{ + matrix4_scale_f16, matrix4_scale_f32, matrix4_scale_f64, }; +matrix4_look_at_f16 :: proc(eye, centre, up: Vector3f16, flip_z_axis := true) -> (m: Matrix4f16) { + f := normalize(centre - eye); + s := normalize(cross(f, up)); + u := cross(s, f); + + fe := dot(f, eye); + + return { + {+s.x, +u.x, -f.x, 0}, + {+s.y, +u.y, -f.y, 0}, + {+s.z, +u.z, -f.z, 0}, + {-dot(s, eye), -dot(u, eye), +fe if flip_z_axis else -fe, 1}, + }; +} matrix4_look_at_f32 :: proc(eye, centre, up: Vector3f32, flip_z_axis := true) -> (m: Matrix4f32) { f := normalize(centre - eye); s := normalize(cross(f, up)); @@ -1421,12 +2025,26 @@ matrix4_look_at_f64 :: proc(eye, centre, up: Vector3f64, flip_z_axis := true) -> }; } matrix4_look_at :: proc{ + matrix4_look_at_f16, matrix4_look_at_f32, matrix4_look_at_f64, }; +matrix4_perspective_f16 :: proc(fovy, aspect, near, far: f16, flip_z_axis := true) -> (m: Matrix4f16) { + tan_half_fovy := math.tan(0.5 * fovy); + m[0][0] = 1 / (aspect*tan_half_fovy); + m[1][1] = 1 / (tan_half_fovy); + m[2][2] = +(far + near) / (far - near); + m[2][3] = +1; + m[3][2] = -2*far*near / (far - near); + + if flip_z_axis { + m[2] = -m[2]; + } + return; +} matrix4_perspective_f32 :: proc(fovy, aspect, near, far: f32, flip_z_axis := true) -> (m: Matrix4f32) { tan_half_fovy := math.tan(0.5 * fovy); m[0][0] = 1 / (aspect*tan_half_fovy); @@ -1456,11 +2074,28 @@ matrix4_perspective_f64 :: proc(fovy, aspect, near, far: f64, flip_z_axis := tru return; } matrix4_perspective :: proc{ + matrix4_perspective_f16, matrix4_perspective_f32, matrix4_perspective_f64, }; + +matrix_ortho3d_f16 :: proc(left, right, bottom, top, near, far: f16, flip_z_axis := true) -> (m: Matrix4f16) { + m[0][0] = +2 / (right - left); + m[1][1] = +2 / (top - bottom); + m[2][2] = +2 / (far - near); + m[3][0] = -(right + left) / (right - left); + m[3][1] = -(top + bottom) / (top - bottom); + m[3][2] = -(far + near) / (far- near); + m[3][3] = 1; + + if flip_z_axis { + m[2] = -m[2]; + } + + return; +} matrix_ortho3d_f32 :: proc(left, right, bottom, top, near, far: f32, flip_z_axis := true) -> (m: Matrix4f32) { m[0][0] = +2 / (right - left); m[1][1] = +2 / (top - bottom); @@ -1492,11 +2127,27 @@ matrix_ortho3d_f64 :: proc(left, right, bottom, top, near, far: f64, flip_z_axis return; } matrix_ortho3d :: proc{ + matrix_ortho3d_f16, matrix_ortho3d_f32, matrix_ortho3d_f64, }; + +matrix4_infinite_perspective_f16 :: proc(fovy, aspect, near: f16, flip_z_axis := true) -> (m: Matrix4f16) { + tan_half_fovy := math.tan(0.5 * fovy); + m[0][0] = 1 / (aspect*tan_half_fovy); + m[1][1] = 1 / (tan_half_fovy); + m[2][2] = +1; + m[2][3] = +1; + m[3][2] = -2*near; + + if flip_z_axis { + m[2] = -m[2]; + } + + return; +} matrix4_infinite_perspective_f32 :: proc(fovy, aspect, near: f32, flip_z_axis := true) -> (m: Matrix4f32) { tan_half_fovy := math.tan(0.5 * fovy); m[0][0] = 1 / (aspect*tan_half_fovy); @@ -1526,12 +2177,18 @@ matrix4_infinite_perspective_f64 :: proc(fovy, aspect, near: f64, flip_z_axis := return; } matrix4_infinite_perspective :: proc{ + matrix4_infinite_perspective_f16, matrix4_infinite_perspective_f32, matrix4_infinite_perspective_f64, }; +matrix2_from_scalar_f16 :: proc(f: f16) -> (m: Matrix2f16) { + m[0][0], m[0][1] = f, 0; + m[1][0], m[1][1] = 0, f; + return; +} matrix2_from_scalar_f32 :: proc(f: f32) -> (m: Matrix2f32) { m[0][0], m[0][1] = f, 0; m[1][0], m[1][1] = 0, f; @@ -1543,11 +2200,18 @@ matrix2_from_scalar_f64 :: proc(f: f64) -> (m: Matrix2f64) { return; } matrix2_from_scalar :: proc{ + matrix2_from_scalar_f16, matrix2_from_scalar_f32, matrix2_from_scalar_f64, }; +matrix3_from_scalar_f16 :: proc(f: f16) -> (m: Matrix3f16) { + m[0][0], m[0][1], m[0][2] = f, 0, 0; + m[1][0], m[1][1], m[1][2] = 0, f, 0; + m[2][0], m[2][1], m[2][2] = 0, 0, f; + return; +} matrix3_from_scalar_f32 :: proc(f: f32) -> (m: Matrix3f32) { m[0][0], m[0][1], m[0][2] = f, 0, 0; m[1][0], m[1][1], m[1][2] = 0, f, 0; @@ -1561,11 +2225,19 @@ matrix3_from_scalar_f64 :: proc(f: f64) -> (m: Matrix3f64) { return; } matrix3_from_scalar :: proc{ + matrix3_from_scalar_f16, matrix3_from_scalar_f32, matrix3_from_scalar_f64, }; +matrix4_from_scalar_f16 :: proc(f: f16) -> (m: Matrix4f16) { + m[0][0], m[0][1], m[0][2], m[0][3] = f, 0, 0, 0; + m[1][0], m[1][1], m[1][2], m[1][3] = 0, f, 0, 0; + m[2][0], m[2][1], m[2][2], m[2][3] = 0, 0, f, 0; + m[3][0], m[3][1], m[3][2], m[3][3] = 0, 0, 0, f; + return; +} matrix4_from_scalar_f32 :: proc(f: f32) -> (m: Matrix4f32) { m[0][0], m[0][1], m[0][2], m[0][3] = f, 0, 0, 0; m[1][0], m[1][1], m[1][2], m[1][3] = 0, f, 0, 0; @@ -1581,11 +2253,17 @@ matrix4_from_scalar_f64 :: proc(f: f64) -> (m: Matrix4f64) { return; } matrix4_from_scalar :: proc{ + matrix4_from_scalar_f16, matrix4_from_scalar_f32, matrix4_from_scalar_f64, }; +matrix2_from_matrix3_f16 :: proc(m: Matrix3f16) -> (r: Matrix2f16) { + r[0][0], r[0][1] = m[0][0], m[0][1]; + r[1][0], r[1][1] = m[1][0], m[1][1]; + return; +} matrix2_from_matrix3_f32 :: proc(m: Matrix3f32) -> (r: Matrix2f32) { r[0][0], r[0][1] = m[0][0], m[0][1]; r[1][0], r[1][1] = m[1][0], m[1][1]; @@ -1597,11 +2275,17 @@ matrix2_from_matrix3_f64 :: proc(m: Matrix3f64) -> (r: Matrix2f64) { return; } matrix2_from_matrix3 :: proc{ + matrix2_from_matrix3_f16, matrix2_from_matrix3_f32, matrix2_from_matrix3_f64, }; +matrix2_from_matrix4_f16 :: proc(m: Matrix4f16) -> (r: Matrix2f16) { + r[0][0], r[0][1] = m[0][0], m[0][1]; + r[1][0], r[1][1] = m[1][0], m[1][1]; + return; +} matrix2_from_matrix4_f32 :: proc(m: Matrix4f32) -> (r: Matrix2f32) { r[0][0], r[0][1] = m[0][0], m[0][1]; r[1][0], r[1][1] = m[1][0], m[1][1]; @@ -1613,11 +2297,18 @@ matrix2_from_matrix4_f64 :: proc(m: Matrix4f64) -> (r: Matrix2f64) { return; } matrix2_from_matrix4 :: proc{ + matrix2_from_matrix4_f16, matrix2_from_matrix4_f32, matrix2_from_matrix4_f64, }; +matrix3_from_matrix2_f16 :: proc(m: Matrix2f16) -> (r: Matrix3f16) { + r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], 0; + r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], 0; + r[2][0], r[2][1], r[2][2] = 0, 0, 1; + return; +} matrix3_from_matrix2_f32 :: proc(m: Matrix2f32) -> (r: Matrix3f32) { r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], 0; r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], 0; @@ -1631,11 +2322,18 @@ matrix3_from_matrix2_f64 :: proc(m: Matrix2f64) -> (r: Matrix3f64) { return; } matrix3_from_matrix2 :: proc{ + matrix3_from_matrix2_f16, matrix3_from_matrix2_f32, matrix3_from_matrix2_f64, }; +matrix3_from_matrix4_f16 :: proc(m: Matrix4f16) -> (r: Matrix3f16) { + r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], m[0][2]; + r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], m[1][2]; + r[2][0], r[2][1], r[2][2] = m[2][0], m[2][1], m[2][2]; + return; +} matrix3_from_matrix4_f32 :: proc(m: Matrix4f32) -> (r: Matrix3f32) { r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], m[0][2]; r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], m[1][2]; @@ -1649,11 +2347,19 @@ matrix3_from_matrix4_f64 :: proc(m: Matrix4f64) -> (r: Matrix3f64) { return; } matrix3_from_matrix4 :: proc{ + matrix3_from_matrix4_f16, matrix3_from_matrix4_f32, matrix3_from_matrix4_f64, }; +matrix4_from_matrix2_f16 :: proc(m: Matrix2f16) -> (r: Matrix4f16) { + r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], 0, 0; + r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], 0, 0; + r[2][0], r[2][1], r[2][2], r[2][3] = 0, 0, 1, 0; + r[3][0], r[3][1], r[3][2], r[3][3] = 0, 0, 0, 1; + return; +} matrix4_from_matrix2_f32 :: proc(m: Matrix2f32) -> (r: Matrix4f32) { r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], 0, 0; r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], 0, 0; @@ -1669,11 +2375,19 @@ matrix4_from_matrix2_f64 :: proc(m: Matrix2f64) -> (r: Matrix4f64) { return; } matrix4_from_matrix2 :: proc{ + matrix4_from_matrix2_f16, matrix4_from_matrix2_f32, matrix4_from_matrix2_f64, }; +matrix4_from_matrix3_f16 :: proc(m: Matrix3f16) -> (r: Matrix4f16) { + r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], m[0][2], 0; + r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], m[1][2], 0; + r[2][0], r[2][1], r[2][2], r[2][3] = m[2][0], m[2][1], m[2][2], 0; + r[3][0], r[3][1], r[3][2], r[3][3] = 0, 0, 0, 1; + return; +} matrix4_from_matrix3_f32 :: proc(m: Matrix3f32) -> (r: Matrix4f32) { r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], m[0][2], 0; r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], m[1][2], 0; @@ -1689,11 +2403,16 @@ matrix4_from_matrix3_f64 :: proc(m: Matrix3f64) -> (r: Matrix4f64) { return; } matrix4_from_matrix3 :: proc{ + matrix4_from_matrix3_f16, matrix4_from_matrix3_f32, matrix4_from_matrix3_f64, }; +quaternion_from_scalar_f16 :: proc(f: f16) -> (q: Quaternionf16) { + q.w = f; + return; +} quaternion_from_scalar_f32 :: proc(f: f32) -> (q: Quaternionf32) { q.w = f; return; @@ -1703,23 +2422,29 @@ quaternion_from_scalar_f64 :: proc(f: f64) -> (q: Quaternionf64) { return; } quaternion_from_scalar :: proc{ + quaternion_from_scalar_f16, quaternion_from_scalar_f32, quaternion_from_scalar_f64, }; -to_matrix2f32 :: proc{matrix2_from_scalar_f32, matrix2_from_matrix3_f32, matrix2_from_matrix4_f32}; -to_matrix3f32 :: proc{matrix3_from_scalar_f32, matrix3_from_matrix2_f32, matrix3_from_matrix4_f32, matrix3_from_quaternion_f32}; -to_matrix4f32 :: proc{matrix4_from_scalar_f32, matrix4_from_matrix2_f32, matrix4_from_matrix3_f32, matrix4_from_quaternion_f32}; -to_quaternionf32 :: proc{quaternion_from_scalar_f32, quaternion_from_matrix3_f32, quaternion_from_matrix4_f32}; +to_matrix2f16 :: proc{matrix2_from_scalar_f16, matrix2_from_matrix3_f16, matrix2_from_matrix4_f16}; +to_matrix3f16 :: proc{matrix3_from_scalar_f16, matrix3_from_matrix2_f16, matrix3_from_matrix4_f16, matrix3_from_quaternion_f16}; +to_matrix4f16 :: proc{matrix4_from_scalar_f16, matrix4_from_matrix2_f16, matrix4_from_matrix3_f16, matrix4_from_quaternion_f16}; +to_quaternionf16 :: proc{quaternion_from_scalar_f16, quaternion_from_matrix3_f16, quaternion_from_matrix4_f16}; -to_matrix2f64 :: proc{matrix2_from_scalar_f64, matrix2_from_matrix3_f64, matrix2_from_matrix4_f64}; +to_matrix2f32 :: proc{matrix2_from_scalar_f32, matrix2_from_matrix3_f32, matrix2_from_matrix4_f32}; +to_matrix3f32 :: proc{matrix3_from_scalar_f32, matrix3_from_matrix2_f32, matrix3_from_matrix4_f32, matrix3_from_quaternion_f32}; +to_matrix4f32 :: proc{matrix4_from_scalar_f32, matrix4_from_matrix2_f32, matrix4_from_matrix3_f32, matrix4_from_quaternion_f32}; +to_quaternionf32 :: proc{quaternion_from_scalar_f32, quaternion_from_matrix3_f32, quaternion_from_matrix4_f32}; + -to_matrix3f64 :: proc{matrix3_from_scalar_f64, matrix3_from_matrix2_f64, matrix3_from_matrix4_f64, matrix3_from_quaternion_f64}; -to_matrix4f64 :: proc{matrix4_from_scalar_f64, matrix4_from_matrix2_f64, matrix4_from_matrix3_f64, matrix4_from_quaternion_f64}; +to_matrix2f64 :: proc{matrix2_from_scalar_f64, matrix2_from_matrix3_f64, matrix2_from_matrix4_f64}; +to_matrix3f64 :: proc{matrix3_from_scalar_f64, matrix3_from_matrix2_f64, matrix3_from_matrix4_f64, matrix3_from_quaternion_f64}; +to_matrix4f64 :: proc{matrix4_from_scalar_f64, matrix4_from_matrix2_f64, matrix4_from_matrix3_f64, matrix4_from_quaternion_f64}; to_quaternionf64 :: proc{quaternion_from_scalar_f64, quaternion_from_matrix3_f64, quaternion_from_matrix4_f64}; @@ -1727,28 +2452,40 @@ to_quaternionf64 :: proc{quaternion_from_scalar_f64, quaternion_from_matrix3_f64 to_matrix2f :: proc{ - + matrix2_from_scalar_f16, matrix2_from_matrix3_f16, matrix2_from_matrix4_f16, matrix2_from_scalar_f32, matrix2_from_matrix3_f32, matrix2_from_matrix4_f32, matrix2_from_scalar_f64, matrix2_from_matrix3_f64, matrix2_from_matrix4_f64, }; to_matrix3 :: proc{ + matrix3_from_scalar_f16, matrix3_from_matrix2_f16, matrix3_from_matrix4_f16, matrix3_from_quaternion_f16, matrix3_from_scalar_f32, matrix3_from_matrix2_f32, matrix3_from_matrix4_f32, matrix3_from_quaternion_f32, matrix3_from_scalar_f64, matrix3_from_matrix2_f64, matrix3_from_matrix4_f64, matrix3_from_quaternion_f64, }; to_matrix4 :: proc{ + matrix4_from_scalar_f16, matrix4_from_matrix2_f16, matrix4_from_matrix3_f16, matrix4_from_quaternion_f16, matrix4_from_scalar_f32, matrix4_from_matrix2_f32, matrix4_from_matrix3_f32, matrix4_from_quaternion_f32, matrix4_from_scalar_f64, matrix4_from_matrix2_f64, matrix4_from_matrix3_f64, matrix4_from_quaternion_f64, }; to_quaternion :: proc{ + quaternion_from_scalar_f16, quaternion_from_matrix3_f16, quaternion_from_matrix4_f16, quaternion_from_scalar_f32, quaternion_from_matrix3_f32, quaternion_from_matrix4_f32, quaternion_from_scalar_f64, quaternion_from_matrix3_f64, quaternion_from_matrix4_f64, }; +matrix2_orthonormalize_f16 :: proc(m: Matrix2f16) -> (r: Matrix2f16) { + r[0] = normalize(m[0]); + + d0 := dot(r[0], r[1]); + r[1] -= r[0] * d0; + r[1] = normalize(r[1]); + + return; +} matrix2_orthonormalize_f32 :: proc(m: Matrix2f32) -> (r: Matrix2f32) { r[0] = normalize(m[0]); @@ -1768,11 +2505,26 @@ matrix2_orthonormalize_f64 :: proc(m: Matrix2f64) -> (r: Matrix2f64) { return; } matrix2_orthonormalize :: proc{ + matrix2_orthonormalize_f16, matrix2_orthonormalize_f32, matrix2_orthonormalize_f64, }; +matrix3_orthonormalize_f16 :: proc(m: Matrix3f16) -> (r: Matrix3f16) { + r[0] = normalize(m[0]); + + d0 := dot(r[0], r[1]); + r[1] -= r[0] * d0; + r[1] = normalize(r[1]); + + d1 := dot(r[1], r[2]); + d0 = dot(r[0], r[2]); + r[2] -= r[0]*d0 + r[1]*d1; + r[2] = normalize(r[2]); + + return; +} matrix3_orthonormalize_f32 :: proc(m: Matrix3f32) -> (r: Matrix3f32) { r[0] = normalize(m[0]); @@ -1802,11 +2554,15 @@ matrix3_orthonormalize_f64 :: proc(m: Matrix3f64) -> (r: Matrix3f64) { return; } matrix3_orthonormalize :: proc{ + matrix3_orthonormalize_f16, matrix3_orthonormalize_f32, matrix3_orthonormalize_f64, }; +vector3_orthonormalize_f16 :: proc(x, y: Vector3f16) -> (z: Vector3f16) { + return normalize(x - y * dot(y, x)); +} vector3_orthonormalize_f32 :: proc(x, y: Vector3f32) -> (z: Vector3f32) { return normalize(x - y * dot(y, x)); } @@ -1814,22 +2570,29 @@ vector3_orthonormalize_f64 :: proc(x, y: Vector3f64) -> (z: Vector3f64) { return normalize(x - y * dot(y, x)); } vector3_orthonormalize :: proc{ + vector3_orthonormalize_f16, vector3_orthonormalize_f32, vector3_orthonormalize_f64, }; orthonormalize :: proc{ - matrix2_orthonormalize_f32, - matrix2_orthonormalize_f64, - matrix3_orthonormalize_f32, - - matrix3_orthonormalize_f64, - vector3_orthonormalize_f32, - vector3_orthonormalize_f64, + matrix2_orthonormalize_f16, matrix3_orthonormalize_f16, vector3_orthonormalize_f16, + matrix2_orthonormalize_f32, matrix3_orthonormalize_f32, vector3_orthonormalize_f32, + matrix2_orthonormalize_f64, matrix3_orthonormalize_f64, vector3_orthonormalize_f64, }; +matrix4_orientation_f16 :: proc(normal, up: Vector3f16) -> Matrix4f16 { + if all(equal(normal, up)) { + return MATRIX4F16_IDENTITY; + } + + rotation_axis := cross(up, normal); + angle := math.acos(dot(normal, up)); + + return matrix4_rotate(angle, rotation_axis); +} matrix4_orientation_f32 :: proc(normal, up: Vector3f32) -> Matrix4f32 { if all(equal(normal, up)) { return MATRIX4F32_IDENTITY; @@ -1851,11 +2614,23 @@ matrix4_orientation_f64 :: proc(normal, up: Vector3f64) -> Matrix4f64 { return matrix4_rotate(angle, rotation_axis); } matrix4_orientation :: proc{ + matrix4_orientation_f16, matrix4_orientation_f32, matrix4_orientation_f64, }; +euclidean_from_polar_f16 :: proc(polar: Vector2f16) -> Vector3f16 { + latitude, longitude := polar.x, polar.y; + cx, sx := math.cos(latitude), math.sin(latitude); + cy, sy := math.cos(longitude), math.sin(longitude); + + return { + cx*sy, + sx, + cx*cy, + }; +} euclidean_from_polar_f32 :: proc(polar: Vector2f32) -> Vector3f32 { latitude, longitude := polar.x, polar.y; cx, sx := math.cos(latitude), math.sin(latitude); @@ -1879,11 +2654,24 @@ euclidean_from_polar_f64 :: proc(polar: Vector2f64) -> Vector3f64 { }; } euclidean_from_polar :: proc{ + euclidean_from_polar_f16, euclidean_from_polar_f32, euclidean_from_polar_f64, }; +polar_from_euclidean_f16 :: proc(euclidean: Vector3f16) -> Vector3f16 { + n := length(euclidean); + tmp := euclidean / n; + + xz_dist := math.sqrt(tmp.x*tmp.x + tmp.z*tmp.z); + + return { + math.asin(tmp.y), + math.atan2(tmp.x, tmp.z), + xz_dist, + }; +} polar_from_euclidean_f32 :: proc(euclidean: Vector3f32) -> Vector3f32 { n := length(euclidean); tmp := euclidean / n; @@ -1909,6 +2697,7 @@ polar_from_euclidean_f64 :: proc(euclidean: Vector3f64) -> Vector3f64 { }; } polar_from_euclidean :: proc{ + polar_from_euclidean_f16, polar_from_euclidean_f32, polar_from_euclidean_f64, }; diff --git a/core/math/linalg/specific_euler_angles.odin b/core/math/linalg/specific_euler_angles.odin index 53b33cfe0..000edda12 100644 --- a/core/math/linalg/specific_euler_angles.odin +++ b/core/math/linalg/specific_euler_angles.odin @@ -19,109 +19,109 @@ Euler_Angle_Order :: enum { } -quaternion_from_euler_angles :: proc{quaternion_from_euler_angles_f32, quaternion_from_euler_angles_f64}; -quaternion_from_euler_angle_x :: proc{quaternion_from_euler_angle_x_f32, quaternion_from_euler_angle_x_f64}; -quaternion_from_euler_angle_y :: proc{quaternion_from_euler_angle_y_f32, quaternion_from_euler_angle_y_f64}; -quaternion_from_euler_angle_z :: proc{quaternion_from_euler_angle_z_f32, quaternion_from_euler_angle_z_f64}; -quaternion_from_pitch_yaw_roll :: proc{quaternion_from_pitch_yaw_roll_f32, quaternion_from_pitch_yaw_roll_f64}; +quaternion_from_euler_angles :: proc{quaternion_from_euler_angles_f16, quaternion_from_euler_angles_f32, quaternion_from_euler_angles_f64}; +quaternion_from_euler_angle_x :: proc{quaternion_from_euler_angle_x_f16, quaternion_from_euler_angle_x_f32, quaternion_from_euler_angle_x_f64}; +quaternion_from_euler_angle_y :: proc{quaternion_from_euler_angle_y_f16, quaternion_from_euler_angle_y_f32, quaternion_from_euler_angle_y_f64}; +quaternion_from_euler_angle_z :: proc{quaternion_from_euler_angle_z_f16, quaternion_from_euler_angle_z_f32, quaternion_from_euler_angle_z_f64}; +quaternion_from_pitch_yaw_roll :: proc{quaternion_from_pitch_yaw_roll_f16, quaternion_from_pitch_yaw_roll_f32, quaternion_from_pitch_yaw_roll_f64}; -euler_angles_from_quaternion :: proc{euler_angles_from_quaternion_f32, euler_angles_from_quaternion_f64}; -euler_angles_xyz_from_quaternion :: proc{euler_angles_xyz_from_quaternion_f32, euler_angles_xyz_from_quaternion_f64}; -euler_angles_yxz_from_quaternion :: proc{euler_angles_yxz_from_quaternion_f32, euler_angles_yxz_from_quaternion_f64}; -euler_angles_xzx_from_quaternion :: proc{euler_angles_xzx_from_quaternion_f32, euler_angles_xzx_from_quaternion_f64}; -euler_angles_xyx_from_quaternion :: proc{euler_angles_xyx_from_quaternion_f32, euler_angles_xyx_from_quaternion_f64}; -euler_angles_yxy_from_quaternion :: proc{euler_angles_yxy_from_quaternion_f32, euler_angles_yxy_from_quaternion_f64}; -euler_angles_yzy_from_quaternion :: proc{euler_angles_yzy_from_quaternion_f32, euler_angles_yzy_from_quaternion_f64}; -euler_angles_zyz_from_quaternion :: proc{euler_angles_zyz_from_quaternion_f32, euler_angles_zyz_from_quaternion_f64}; -euler_angles_zxz_from_quaternion :: proc{euler_angles_zxz_from_quaternion_f32, euler_angles_zxz_from_quaternion_f64}; -euler_angles_xzy_from_quaternion :: proc{euler_angles_xzy_from_quaternion_f32, euler_angles_xzy_from_quaternion_f64}; -euler_angles_yzx_from_quaternion :: proc{euler_angles_yzx_from_quaternion_f32, euler_angles_yzx_from_quaternion_f64}; -euler_angles_zyx_from_quaternion :: proc{euler_angles_zyx_from_quaternion_f32, euler_angles_zyx_from_quaternion_f64}; -euler_angles_zxy_from_quaternion :: proc{euler_angles_zxy_from_quaternion_f32, euler_angles_zxy_from_quaternion_f64}; +euler_angles_from_quaternion :: proc{euler_angles_from_quaternion_f16, euler_angles_from_quaternion_f32, euler_angles_from_quaternion_f64}; +euler_angles_xyz_from_quaternion :: proc{euler_angles_xyz_from_quaternion_f16, euler_angles_xyz_from_quaternion_f32, euler_angles_xyz_from_quaternion_f64}; +euler_angles_yxz_from_quaternion :: proc{euler_angles_yxz_from_quaternion_f16, euler_angles_yxz_from_quaternion_f32, euler_angles_yxz_from_quaternion_f64}; +euler_angles_xzx_from_quaternion :: proc{euler_angles_xzx_from_quaternion_f16, euler_angles_xzx_from_quaternion_f32, euler_angles_xzx_from_quaternion_f64}; +euler_angles_xyx_from_quaternion :: proc{euler_angles_xyx_from_quaternion_f16, euler_angles_xyx_from_quaternion_f32, euler_angles_xyx_from_quaternion_f64}; +euler_angles_yxy_from_quaternion :: proc{euler_angles_yxy_from_quaternion_f16, euler_angles_yxy_from_quaternion_f32, euler_angles_yxy_from_quaternion_f64}; +euler_angles_yzy_from_quaternion :: proc{euler_angles_yzy_from_quaternion_f16, euler_angles_yzy_from_quaternion_f32, euler_angles_yzy_from_quaternion_f64}; +euler_angles_zyz_from_quaternion :: proc{euler_angles_zyz_from_quaternion_f16, euler_angles_zyz_from_quaternion_f32, euler_angles_zyz_from_quaternion_f64}; +euler_angles_zxz_from_quaternion :: proc{euler_angles_zxz_from_quaternion_f16, euler_angles_zxz_from_quaternion_f32, euler_angles_zxz_from_quaternion_f64}; +euler_angles_xzy_from_quaternion :: proc{euler_angles_xzy_from_quaternion_f16, euler_angles_xzy_from_quaternion_f32, euler_angles_xzy_from_quaternion_f64}; +euler_angles_yzx_from_quaternion :: proc{euler_angles_yzx_from_quaternion_f16, euler_angles_yzx_from_quaternion_f32, euler_angles_yzx_from_quaternion_f64}; +euler_angles_zyx_from_quaternion :: proc{euler_angles_zyx_from_quaternion_f16, euler_angles_zyx_from_quaternion_f32, euler_angles_zyx_from_quaternion_f64}; +euler_angles_zxy_from_quaternion :: proc{euler_angles_zxy_from_quaternion_f16, euler_angles_zxy_from_quaternion_f32, euler_angles_zxy_from_quaternion_f64}; -roll_from_quaternion :: proc{roll_from_quaternion_f32, roll_from_quaternion_f64}; -pitch_from_quaternion :: proc{pitch_from_quaternion_f32, pitch_from_quaternion_f64}; -yaw_from_quaternion :: proc{yaw_from_quaternion_f32, yaw_from_quaternion_f64}; -pitch_yaw_roll_from_quaternion :: proc{pitch_yaw_roll_from_quaternion_f32, pitch_yaw_roll_from_quaternion_f64}; +roll_from_quaternion :: proc{roll_from_quaternion_f16, roll_from_quaternion_f32, roll_from_quaternion_f64}; +pitch_from_quaternion :: proc{pitch_from_quaternion_f16, pitch_from_quaternion_f32, pitch_from_quaternion_f64}; +yaw_from_quaternion :: proc{yaw_from_quaternion_f16, yaw_from_quaternion_f32, yaw_from_quaternion_f64}; +pitch_yaw_roll_from_quaternion :: proc{pitch_yaw_roll_from_quaternion_f16, pitch_yaw_roll_from_quaternion_f32, pitch_yaw_roll_from_quaternion_f64}; -matrix3_from_euler_angles :: proc{matrix3_from_euler_angles_f32, matrix3_from_euler_angles_f64}; -matrix3_from_euler_angle_x :: proc{matrix3_from_euler_angle_x_f32, matrix3_from_euler_angle_x_f64}; -matrix3_from_euler_angle_y :: proc{matrix3_from_euler_angle_y_f32, matrix3_from_euler_angle_y_f64}; -matrix3_from_euler_angle_z :: proc{matrix3_from_euler_angle_z_f32, matrix3_from_euler_angle_z_f64}; -matrix3_from_derived_euler_angle_x :: proc{matrix3_from_derived_euler_angle_x_f32, matrix3_from_derived_euler_angle_x_f64}; -matrix3_from_derived_euler_angle_y :: proc{matrix3_from_derived_euler_angle_y_f32, matrix3_from_derived_euler_angle_y_f64}; -matrix3_from_derived_euler_angle_z :: proc{matrix3_from_derived_euler_angle_z_f32, matrix3_from_derived_euler_angle_z_f64}; -matrix3_from_euler_angles_xy :: proc{matrix3_from_euler_angles_xy_f32, matrix3_from_euler_angles_xy_f64}; -matrix3_from_euler_angles_yx :: proc{matrix3_from_euler_angles_yx_f32, matrix3_from_euler_angles_yx_f64}; -matrix3_from_euler_angles_xz :: proc{matrix3_from_euler_angles_xz_f32, matrix3_from_euler_angles_xz_f64}; -matrix3_from_euler_angles_zx :: proc{matrix3_from_euler_angles_zx_f32, matrix3_from_euler_angles_zx_f64}; -matrix3_from_euler_angles_yz :: proc{matrix3_from_euler_angles_yz_f32, matrix3_from_euler_angles_yz_f64}; -matrix3_from_euler_angles_zy :: proc{matrix3_from_euler_angles_zy_f32, matrix3_from_euler_angles_zy_f64}; -matrix3_from_euler_angles_xyz :: proc{matrix3_from_euler_angles_xyz_f32, matrix3_from_euler_angles_xyz_f64}; -matrix3_from_euler_angles_yxz :: proc{matrix3_from_euler_angles_yxz_f32, matrix3_from_euler_angles_yxz_f64}; -matrix3_from_euler_angles_xzx :: proc{matrix3_from_euler_angles_xzx_f32, matrix3_from_euler_angles_xzx_f64}; -matrix3_from_euler_angles_xyx :: proc{matrix3_from_euler_angles_xyx_f32, matrix3_from_euler_angles_xyx_f64}; -matrix3_from_euler_angles_yxy :: proc{matrix3_from_euler_angles_yxy_f32, matrix3_from_euler_angles_yxy_f64}; -matrix3_from_euler_angles_yzy :: proc{matrix3_from_euler_angles_yzy_f32, matrix3_from_euler_angles_yzy_f64}; -matrix3_from_euler_angles_zyz :: proc{matrix3_from_euler_angles_zyz_f32, matrix3_from_euler_angles_zyz_f64}; -matrix3_from_euler_angles_zxz :: proc{matrix3_from_euler_angles_zxz_f32, matrix3_from_euler_angles_zxz_f64}; -matrix3_from_euler_angles_xzy :: proc{matrix3_from_euler_angles_xzy_f32, matrix3_from_euler_angles_xzy_f64}; -matrix3_from_euler_angles_yzx :: proc{matrix3_from_euler_angles_yzx_f32, matrix3_from_euler_angles_yzx_f64}; -matrix3_from_euler_angles_zyx :: proc{matrix3_from_euler_angles_zyx_f32, matrix3_from_euler_angles_zyx_f64}; -matrix3_from_euler_angles_zxy :: proc{matrix3_from_euler_angles_zxy_f32, matrix3_from_euler_angles_zxy_f64}; -matrix3_from_yaw_pitch_roll :: proc{matrix3_from_yaw_pitch_roll_f32, matrix3_from_yaw_pitch_roll_f64}; +matrix3_from_euler_angles :: proc{matrix3_from_euler_angles_f16, matrix3_from_euler_angles_f32, matrix3_from_euler_angles_f64}; +matrix3_from_euler_angle_x :: proc{matrix3_from_euler_angle_x_f16, matrix3_from_euler_angle_x_f32, matrix3_from_euler_angle_x_f64}; +matrix3_from_euler_angle_y :: proc{matrix3_from_euler_angle_y_f16, matrix3_from_euler_angle_y_f32, matrix3_from_euler_angle_y_f64}; +matrix3_from_euler_angle_z :: proc{matrix3_from_euler_angle_z_f16, matrix3_from_euler_angle_z_f32, matrix3_from_euler_angle_z_f64}; +matrix3_from_derived_euler_angle_x :: proc{matrix3_from_derived_euler_angle_x_f16, matrix3_from_derived_euler_angle_x_f32, matrix3_from_derived_euler_angle_x_f64}; +matrix3_from_derived_euler_angle_y :: proc{matrix3_from_derived_euler_angle_y_f16, matrix3_from_derived_euler_angle_y_f32, matrix3_from_derived_euler_angle_y_f64}; +matrix3_from_derived_euler_angle_z :: proc{matrix3_from_derived_euler_angle_z_f16, matrix3_from_derived_euler_angle_z_f32, matrix3_from_derived_euler_angle_z_f64}; +matrix3_from_euler_angles_xy :: proc{matrix3_from_euler_angles_xy_f16, matrix3_from_euler_angles_xy_f32, matrix3_from_euler_angles_xy_f64}; +matrix3_from_euler_angles_yx :: proc{matrix3_from_euler_angles_yx_f16, matrix3_from_euler_angles_yx_f32, matrix3_from_euler_angles_yx_f64}; +matrix3_from_euler_angles_xz :: proc{matrix3_from_euler_angles_xz_f16, matrix3_from_euler_angles_xz_f32, matrix3_from_euler_angles_xz_f64}; +matrix3_from_euler_angles_zx :: proc{matrix3_from_euler_angles_zx_f16, matrix3_from_euler_angles_zx_f32, matrix3_from_euler_angles_zx_f64}; +matrix3_from_euler_angles_yz :: proc{matrix3_from_euler_angles_yz_f16, matrix3_from_euler_angles_yz_f32, matrix3_from_euler_angles_yz_f64}; +matrix3_from_euler_angles_zy :: proc{matrix3_from_euler_angles_zy_f16, matrix3_from_euler_angles_zy_f32, matrix3_from_euler_angles_zy_f64}; +matrix3_from_euler_angles_xyz :: proc{matrix3_from_euler_angles_xyz_f16, matrix3_from_euler_angles_xyz_f32, matrix3_from_euler_angles_xyz_f64}; +matrix3_from_euler_angles_yxz :: proc{matrix3_from_euler_angles_yxz_f16, matrix3_from_euler_angles_yxz_f32, matrix3_from_euler_angles_yxz_f64}; +matrix3_from_euler_angles_xzx :: proc{matrix3_from_euler_angles_xzx_f16, matrix3_from_euler_angles_xzx_f32, matrix3_from_euler_angles_xzx_f64}; +matrix3_from_euler_angles_xyx :: proc{matrix3_from_euler_angles_xyx_f16, matrix3_from_euler_angles_xyx_f32, matrix3_from_euler_angles_xyx_f64}; +matrix3_from_euler_angles_yxy :: proc{matrix3_from_euler_angles_yxy_f16, matrix3_from_euler_angles_yxy_f32, matrix3_from_euler_angles_yxy_f64}; +matrix3_from_euler_angles_yzy :: proc{matrix3_from_euler_angles_yzy_f16, matrix3_from_euler_angles_yzy_f32, matrix3_from_euler_angles_yzy_f64}; +matrix3_from_euler_angles_zyz :: proc{matrix3_from_euler_angles_zyz_f16, matrix3_from_euler_angles_zyz_f32, matrix3_from_euler_angles_zyz_f64}; +matrix3_from_euler_angles_zxz :: proc{matrix3_from_euler_angles_zxz_f16, matrix3_from_euler_angles_zxz_f32, matrix3_from_euler_angles_zxz_f64}; +matrix3_from_euler_angles_xzy :: proc{matrix3_from_euler_angles_xzy_f16, matrix3_from_euler_angles_xzy_f32, matrix3_from_euler_angles_xzy_f64}; +matrix3_from_euler_angles_yzx :: proc{matrix3_from_euler_angles_yzx_f16, matrix3_from_euler_angles_yzx_f32, matrix3_from_euler_angles_yzx_f64}; +matrix3_from_euler_angles_zyx :: proc{matrix3_from_euler_angles_zyx_f16, matrix3_from_euler_angles_zyx_f32, matrix3_from_euler_angles_zyx_f64}; +matrix3_from_euler_angles_zxy :: proc{matrix3_from_euler_angles_zxy_f16, matrix3_from_euler_angles_zxy_f32, matrix3_from_euler_angles_zxy_f64}; +matrix3_from_yaw_pitch_roll :: proc{matrix3_from_yaw_pitch_roll_f16, matrix3_from_yaw_pitch_roll_f32, matrix3_from_yaw_pitch_roll_f64}; -euler_angles_from_matrix3 :: proc{euler_angles_from_matrix3_f32, euler_angles_from_matrix3_f64}; -euler_angles_xyz_from_matrix3 :: proc{euler_angles_xyz_from_matrix3_f32, euler_angles_xyz_from_matrix3_f64}; -euler_angles_yxz_from_matrix3 :: proc{euler_angles_yxz_from_matrix3_f32, euler_angles_yxz_from_matrix3_f64}; -euler_angles_xzx_from_matrix3 :: proc{euler_angles_xzx_from_matrix3_f32, euler_angles_xzx_from_matrix3_f64}; -euler_angles_xyx_from_matrix3 :: proc{euler_angles_xyx_from_matrix3_f32, euler_angles_xyx_from_matrix3_f64}; -euler_angles_yxy_from_matrix3 :: proc{euler_angles_yxy_from_matrix3_f32, euler_angles_yxy_from_matrix3_f64}; -euler_angles_yzy_from_matrix3 :: proc{euler_angles_yzy_from_matrix3_f32, euler_angles_yzy_from_matrix3_f64}; -euler_angles_zyz_from_matrix3 :: proc{euler_angles_zyz_from_matrix3_f32, euler_angles_zyz_from_matrix3_f64}; -euler_angles_zxz_from_matrix3 :: proc{euler_angles_zxz_from_matrix3_f32, euler_angles_zxz_from_matrix3_f64}; -euler_angles_xzy_from_matrix3 :: proc{euler_angles_xzy_from_matrix3_f32, euler_angles_xzy_from_matrix3_f64}; -euler_angles_yzx_from_matrix3 :: proc{euler_angles_yzx_from_matrix3_f32, euler_angles_yzx_from_matrix3_f64}; -euler_angles_zyx_from_matrix3 :: proc{euler_angles_zyx_from_matrix3_f32, euler_angles_zyx_from_matrix3_f64}; -euler_angles_zxy_from_matrix3 :: proc{euler_angles_zxy_from_matrix3_f32, euler_angles_zxy_from_matrix3_f64}; +euler_angles_from_matrix3 :: proc{euler_angles_from_matrix3_f16, euler_angles_from_matrix3_f32, euler_angles_from_matrix3_f64}; +euler_angles_xyz_from_matrix3 :: proc{euler_angles_xyz_from_matrix3_f16, euler_angles_xyz_from_matrix3_f32, euler_angles_xyz_from_matrix3_f64}; +euler_angles_yxz_from_matrix3 :: proc{euler_angles_yxz_from_matrix3_f16, euler_angles_yxz_from_matrix3_f32, euler_angles_yxz_from_matrix3_f64}; +euler_angles_xzx_from_matrix3 :: proc{euler_angles_xzx_from_matrix3_f16, euler_angles_xzx_from_matrix3_f32, euler_angles_xzx_from_matrix3_f64}; +euler_angles_xyx_from_matrix3 :: proc{euler_angles_xyx_from_matrix3_f16, euler_angles_xyx_from_matrix3_f32, euler_angles_xyx_from_matrix3_f64}; +euler_angles_yxy_from_matrix3 :: proc{euler_angles_yxy_from_matrix3_f16, euler_angles_yxy_from_matrix3_f32, euler_angles_yxy_from_matrix3_f64}; +euler_angles_yzy_from_matrix3 :: proc{euler_angles_yzy_from_matrix3_f16, euler_angles_yzy_from_matrix3_f32, euler_angles_yzy_from_matrix3_f64}; +euler_angles_zyz_from_matrix3 :: proc{euler_angles_zyz_from_matrix3_f16, euler_angles_zyz_from_matrix3_f32, euler_angles_zyz_from_matrix3_f64}; +euler_angles_zxz_from_matrix3 :: proc{euler_angles_zxz_from_matrix3_f16, euler_angles_zxz_from_matrix3_f32, euler_angles_zxz_from_matrix3_f64}; +euler_angles_xzy_from_matrix3 :: proc{euler_angles_xzy_from_matrix3_f16, euler_angles_xzy_from_matrix3_f32, euler_angles_xzy_from_matrix3_f64}; +euler_angles_yzx_from_matrix3 :: proc{euler_angles_yzx_from_matrix3_f16, euler_angles_yzx_from_matrix3_f32, euler_angles_yzx_from_matrix3_f64}; +euler_angles_zyx_from_matrix3 :: proc{euler_angles_zyx_from_matrix3_f16, euler_angles_zyx_from_matrix3_f32, euler_angles_zyx_from_matrix3_f64}; +euler_angles_zxy_from_matrix3 :: proc{euler_angles_zxy_from_matrix3_f16, euler_angles_zxy_from_matrix3_f32, euler_angles_zxy_from_matrix3_f64}; -matrix4_from_euler_angles :: proc{matrix4_from_euler_angles_f32, matrix4_from_euler_angles_f64}; -matrix4_from_euler_angle_x :: proc{matrix4_from_euler_angle_x_f32, matrix4_from_euler_angle_x_f64}; -matrix4_from_euler_angle_y :: proc{matrix4_from_euler_angle_y_f32, matrix4_from_euler_angle_y_f64}; -matrix4_from_euler_angle_z :: proc{matrix4_from_euler_angle_z_f32, matrix4_from_euler_angle_z_f64}; -matrix4_from_derived_euler_angle_x :: proc{matrix4_from_derived_euler_angle_x_f32, matrix4_from_derived_euler_angle_x_f64}; -matrix4_from_derived_euler_angle_y :: proc{matrix4_from_derived_euler_angle_y_f32, matrix4_from_derived_euler_angle_y_f64}; -matrix4_from_derived_euler_angle_z :: proc{matrix4_from_derived_euler_angle_z_f32, matrix4_from_derived_euler_angle_z_f64}; -matrix4_from_euler_angles_xy :: proc{matrix4_from_euler_angles_xy_f32, matrix4_from_euler_angles_xy_f64}; -matrix4_from_euler_angles_yx :: proc{matrix4_from_euler_angles_yx_f32, matrix4_from_euler_angles_yx_f64}; -matrix4_from_euler_angles_xz :: proc{matrix4_from_euler_angles_xz_f32, matrix4_from_euler_angles_xz_f64}; -matrix4_from_euler_angles_zx :: proc{matrix4_from_euler_angles_zx_f32, matrix4_from_euler_angles_zx_f64}; -matrix4_from_euler_angles_yz :: proc{matrix4_from_euler_angles_yz_f32, matrix4_from_euler_angles_yz_f64}; -matrix4_from_euler_angles_zy :: proc{matrix4_from_euler_angles_zy_f32, matrix4_from_euler_angles_zy_f64}; -matrix4_from_euler_angles_xyz :: proc{matrix4_from_euler_angles_xyz_f32, matrix4_from_euler_angles_xyz_f64}; -matrix4_from_euler_angles_yxz :: proc{matrix4_from_euler_angles_yxz_f32, matrix4_from_euler_angles_yxz_f64}; -matrix4_from_euler_angles_xzx :: proc{matrix4_from_euler_angles_xzx_f32, matrix4_from_euler_angles_xzx_f64}; -matrix4_from_euler_angles_xyx :: proc{matrix4_from_euler_angles_xyx_f32, matrix4_from_euler_angles_xyx_f64}; -matrix4_from_euler_angles_yxy :: proc{matrix4_from_euler_angles_yxy_f32, matrix4_from_euler_angles_yxy_f64}; -matrix4_from_euler_angles_yzy :: proc{matrix4_from_euler_angles_yzy_f32, matrix4_from_euler_angles_yzy_f64}; -matrix4_from_euler_angles_zyz :: proc{matrix4_from_euler_angles_zyz_f32, matrix4_from_euler_angles_zyz_f64}; -matrix4_from_euler_angles_zxz :: proc{matrix4_from_euler_angles_zxz_f32, matrix4_from_euler_angles_zxz_f64}; -matrix4_from_euler_angles_xzy :: proc{matrix4_from_euler_angles_xzy_f32, matrix4_from_euler_angles_xzy_f64}; -matrix4_from_euler_angles_yzx :: proc{matrix4_from_euler_angles_yzx_f32, matrix4_from_euler_angles_yzx_f64}; -matrix4_from_euler_angles_zyx :: proc{matrix4_from_euler_angles_zyx_f32, matrix4_from_euler_angles_zyx_f64}; -matrix4_from_euler_angles_zxy :: proc{matrix4_from_euler_angles_zxy_f32, matrix4_from_euler_angles_zxy_f64}; -matrix4_from_yaw_pitch_roll :: proc{matrix4_from_yaw_pitch_roll_f32, matrix4_from_yaw_pitch_roll_f64}; +matrix4_from_euler_angles :: proc{matrix4_from_euler_angles_f16, matrix4_from_euler_angles_f32, matrix4_from_euler_angles_f64}; +matrix4_from_euler_angle_x :: proc{matrix4_from_euler_angle_x_f16, matrix4_from_euler_angle_x_f32, matrix4_from_euler_angle_x_f64}; +matrix4_from_euler_angle_y :: proc{matrix4_from_euler_angle_y_f16, matrix4_from_euler_angle_y_f32, matrix4_from_euler_angle_y_f64}; +matrix4_from_euler_angle_z :: proc{matrix4_from_euler_angle_z_f16, matrix4_from_euler_angle_z_f32, matrix4_from_euler_angle_z_f64}; +matrix4_from_derived_euler_angle_x :: proc{matrix4_from_derived_euler_angle_x_f16, matrix4_from_derived_euler_angle_x_f32, matrix4_from_derived_euler_angle_x_f64}; +matrix4_from_derived_euler_angle_y :: proc{matrix4_from_derived_euler_angle_y_f16, matrix4_from_derived_euler_angle_y_f32, matrix4_from_derived_euler_angle_y_f64}; +matrix4_from_derived_euler_angle_z :: proc{matrix4_from_derived_euler_angle_z_f16, matrix4_from_derived_euler_angle_z_f32, matrix4_from_derived_euler_angle_z_f64}; +matrix4_from_euler_angles_xy :: proc{matrix4_from_euler_angles_xy_f16, matrix4_from_euler_angles_xy_f32, matrix4_from_euler_angles_xy_f64}; +matrix4_from_euler_angles_yx :: proc{matrix4_from_euler_angles_yx_f16, matrix4_from_euler_angles_yx_f32, matrix4_from_euler_angles_yx_f64}; +matrix4_from_euler_angles_xz :: proc{matrix4_from_euler_angles_xz_f16, matrix4_from_euler_angles_xz_f32, matrix4_from_euler_angles_xz_f64}; +matrix4_from_euler_angles_zx :: proc{matrix4_from_euler_angles_zx_f16, matrix4_from_euler_angles_zx_f32, matrix4_from_euler_angles_zx_f64}; +matrix4_from_euler_angles_yz :: proc{matrix4_from_euler_angles_yz_f16, matrix4_from_euler_angles_yz_f32, matrix4_from_euler_angles_yz_f64}; +matrix4_from_euler_angles_zy :: proc{matrix4_from_euler_angles_zy_f16, matrix4_from_euler_angles_zy_f32, matrix4_from_euler_angles_zy_f64}; +matrix4_from_euler_angles_xyz :: proc{matrix4_from_euler_angles_xyz_f16, matrix4_from_euler_angles_xyz_f32, matrix4_from_euler_angles_xyz_f64}; +matrix4_from_euler_angles_yxz :: proc{matrix4_from_euler_angles_yxz_f16, matrix4_from_euler_angles_yxz_f32, matrix4_from_euler_angles_yxz_f64}; +matrix4_from_euler_angles_xzx :: proc{matrix4_from_euler_angles_xzx_f16, matrix4_from_euler_angles_xzx_f32, matrix4_from_euler_angles_xzx_f64}; +matrix4_from_euler_angles_xyx :: proc{matrix4_from_euler_angles_xyx_f16, matrix4_from_euler_angles_xyx_f32, matrix4_from_euler_angles_xyx_f64}; +matrix4_from_euler_angles_yxy :: proc{matrix4_from_euler_angles_yxy_f16, matrix4_from_euler_angles_yxy_f32, matrix4_from_euler_angles_yxy_f64}; +matrix4_from_euler_angles_yzy :: proc{matrix4_from_euler_angles_yzy_f16, matrix4_from_euler_angles_yzy_f32, matrix4_from_euler_angles_yzy_f64}; +matrix4_from_euler_angles_zyz :: proc{matrix4_from_euler_angles_zyz_f16, matrix4_from_euler_angles_zyz_f32, matrix4_from_euler_angles_zyz_f64}; +matrix4_from_euler_angles_zxz :: proc{matrix4_from_euler_angles_zxz_f16, matrix4_from_euler_angles_zxz_f32, matrix4_from_euler_angles_zxz_f64}; +matrix4_from_euler_angles_xzy :: proc{matrix4_from_euler_angles_xzy_f16, matrix4_from_euler_angles_xzy_f32, matrix4_from_euler_angles_xzy_f64}; +matrix4_from_euler_angles_yzx :: proc{matrix4_from_euler_angles_yzx_f16, matrix4_from_euler_angles_yzx_f32, matrix4_from_euler_angles_yzx_f64}; +matrix4_from_euler_angles_zyx :: proc{matrix4_from_euler_angles_zyx_f16, matrix4_from_euler_angles_zyx_f32, matrix4_from_euler_angles_zyx_f64}; +matrix4_from_euler_angles_zxy :: proc{matrix4_from_euler_angles_zxy_f16, matrix4_from_euler_angles_zxy_f32, matrix4_from_euler_angles_zxy_f64}; +matrix4_from_yaw_pitch_roll :: proc{matrix4_from_yaw_pitch_roll_f16, matrix4_from_yaw_pitch_roll_f32, matrix4_from_yaw_pitch_roll_f64}; -euler_angles_from_matrix4 :: proc{euler_angles_from_matrix4_f32, euler_angles_from_matrix4_f64}; -euler_angles_xyz_from_matrix4 :: proc{euler_angles_xyz_from_matrix4_f32, euler_angles_xyz_from_matrix4_f64}; -euler_angles_yxz_from_matrix4 :: proc{euler_angles_yxz_from_matrix4_f32, euler_angles_yxz_from_matrix4_f64}; -euler_angles_xzx_from_matrix4 :: proc{euler_angles_xzx_from_matrix4_f32, euler_angles_xzx_from_matrix4_f64}; -euler_angles_xyx_from_matrix4 :: proc{euler_angles_xyx_from_matrix4_f32, euler_angles_xyx_from_matrix4_f64}; -euler_angles_yxy_from_matrix4 :: proc{euler_angles_yxy_from_matrix4_f32, euler_angles_yxy_from_matrix4_f64}; -euler_angles_yzy_from_matrix4 :: proc{euler_angles_yzy_from_matrix4_f32, euler_angles_yzy_from_matrix4_f64}; -euler_angles_zyz_from_matrix4 :: proc{euler_angles_zyz_from_matrix4_f32, euler_angles_zyz_from_matrix4_f64}; -euler_angles_zxz_from_matrix4 :: proc{euler_angles_zxz_from_matrix4_f32, euler_angles_zxz_from_matrix4_f64}; -euler_angles_xzy_from_matrix4 :: proc{euler_angles_xzy_from_matrix4_f32, euler_angles_xzy_from_matrix4_f64}; -euler_angles_yzx_from_matrix4 :: proc{euler_angles_yzx_from_matrix4_f32, euler_angles_yzx_from_matrix4_f64}; -euler_angles_zyx_from_matrix4 :: proc{euler_angles_zyx_from_matrix4_f32, euler_angles_zyx_from_matrix4_f64}; -euler_angles_zxy_from_matrix4 :: proc{euler_angles_zxy_from_matrix4_f32, euler_angles_zxy_from_matrix4_f64}; +euler_angles_from_matrix4 :: proc{euler_angles_from_matrix4_f16, euler_angles_from_matrix4_f32, euler_angles_from_matrix4_f64}; +euler_angles_xyz_from_matrix4 :: proc{euler_angles_xyz_from_matrix4_f16, euler_angles_xyz_from_matrix4_f32, euler_angles_xyz_from_matrix4_f64}; +euler_angles_yxz_from_matrix4 :: proc{euler_angles_yxz_from_matrix4_f16, euler_angles_yxz_from_matrix4_f32, euler_angles_yxz_from_matrix4_f64}; +euler_angles_xzx_from_matrix4 :: proc{euler_angles_xzx_from_matrix4_f16, euler_angles_xzx_from_matrix4_f32, euler_angles_xzx_from_matrix4_f64}; +euler_angles_xyx_from_matrix4 :: proc{euler_angles_xyx_from_matrix4_f16, euler_angles_xyx_from_matrix4_f32, euler_angles_xyx_from_matrix4_f64}; +euler_angles_yxy_from_matrix4 :: proc{euler_angles_yxy_from_matrix4_f16, euler_angles_yxy_from_matrix4_f32, euler_angles_yxy_from_matrix4_f64}; +euler_angles_yzy_from_matrix4 :: proc{euler_angles_yzy_from_matrix4_f16, euler_angles_yzy_from_matrix4_f32, euler_angles_yzy_from_matrix4_f64}; +euler_angles_zyz_from_matrix4 :: proc{euler_angles_zyz_from_matrix4_f16, euler_angles_zyz_from_matrix4_f32, euler_angles_zyz_from_matrix4_f64}; +euler_angles_zxz_from_matrix4 :: proc{euler_angles_zxz_from_matrix4_f16, euler_angles_zxz_from_matrix4_f32, euler_angles_zxz_from_matrix4_f64}; +euler_angles_xzy_from_matrix4 :: proc{euler_angles_xzy_from_matrix4_f16, euler_angles_xzy_from_matrix4_f32, euler_angles_xzy_from_matrix4_f64}; +euler_angles_yzx_from_matrix4 :: proc{euler_angles_yzx_from_matrix4_f16, euler_angles_yzx_from_matrix4_f32, euler_angles_yzx_from_matrix4_f64}; +euler_angles_zyx_from_matrix4 :: proc{euler_angles_zyx_from_matrix4_f16, euler_angles_zyx_from_matrix4_f32, euler_angles_zyx_from_matrix4_f64}; +euler_angles_zxy_from_matrix4 :: proc{euler_angles_zxy_from_matrix4_f16, euler_angles_zxy_from_matrix4_f32, euler_angles_zxy_from_matrix4_f64}; diff --git a/core/math/linalg/specific_euler_angles_f16.odin b/core/math/linalg/specific_euler_angles_f16.odin new file mode 100644 index 000000000..bcfac6039 --- /dev/null +++ b/core/math/linalg/specific_euler_angles_f16.odin @@ -0,0 +1,1356 @@ +package linalg + +import "core:math" + +euler_angles_from_matrix3_f16 :: proc(m: Matrix3f16, order: Euler_Angle_Order) -> (t1, t2, t3: f16) { + switch order { + case .XYZ: t1, t2, t3 = euler_angles_xyz_from_matrix3(m); + case .XZY: t1, t2, t3 = euler_angles_xzy_from_matrix3(m); + case .YXZ: t1, t2, t3 = euler_angles_yxz_from_matrix3(m); + case .YZX: t1, t2, t3 = euler_angles_yzx_from_matrix3(m); + case .ZXY: t1, t2, t3 = euler_angles_zxy_from_matrix3(m); + case .ZYX: t1, t2, t3 = euler_angles_zyx_from_matrix3(m); + case .XYX: t1, t2, t3 = euler_angles_xyx_from_matrix3(m); + case .XZX: t1, t2, t3 = euler_angles_xzx_from_matrix3(m); + case .YXY: t1, t2, t3 = euler_angles_yxy_from_matrix3(m); + case .YZY: t1, t2, t3 = euler_angles_yzy_from_matrix3(m); + case .ZXZ: t1, t2, t3 = euler_angles_zxz_from_matrix3(m); + case .ZYZ: t1, t2, t3 = euler_angles_zyz_from_matrix3(m); + } + return; +} +euler_angles_from_matrix4_f16 :: proc(m: Matrix4f16, order: Euler_Angle_Order) -> (t1, t2, t3: f16) { + switch order { + case .XYZ: t1, t2, t3 = euler_angles_xyz_from_matrix4(m); + case .XZY: t1, t2, t3 = euler_angles_xzy_from_matrix4(m); + case .YXZ: t1, t2, t3 = euler_angles_yxz_from_matrix4(m); + case .YZX: t1, t2, t3 = euler_angles_yzx_from_matrix4(m); + case .ZXY: t1, t2, t3 = euler_angles_zxy_from_matrix4(m); + case .ZYX: t1, t2, t3 = euler_angles_zyx_from_matrix4(m); + case .XYX: t1, t2, t3 = euler_angles_xyx_from_matrix4(m); + case .XZX: t1, t2, t3 = euler_angles_xzx_from_matrix4(m); + case .YXY: t1, t2, t3 = euler_angles_yxy_from_matrix4(m); + case .YZY: t1, t2, t3 = euler_angles_yzy_from_matrix4(m); + case .ZXZ: t1, t2, t3 = euler_angles_zxz_from_matrix4(m); + case .ZYZ: t1, t2, t3 = euler_angles_zyz_from_matrix4(m); + } + return; +} +euler_angles_from_quaternion_f16 :: proc(m: Quaternionf16, order: Euler_Angle_Order) -> (t1, t2, t3: f16) { + switch order { + case .XYZ: t1, t2, t3 = euler_angles_xyz_from_quaternion(m); + case .XZY: t1, t2, t3 = euler_angles_xzy_from_quaternion(m); + case .YXZ: t1, t2, t3 = euler_angles_yxz_from_quaternion(m); + case .YZX: t1, t2, t3 = euler_angles_yzx_from_quaternion(m); + case .ZXY: t1, t2, t3 = euler_angles_zxy_from_quaternion(m); + case .ZYX: t1, t2, t3 = euler_angles_zyx_from_quaternion(m); + case .XYX: t1, t2, t3 = euler_angles_xyx_from_quaternion(m); + case .XZX: t1, t2, t3 = euler_angles_xzx_from_quaternion(m); + case .YXY: t1, t2, t3 = euler_angles_yxy_from_quaternion(m); + case .YZY: t1, t2, t3 = euler_angles_yzy_from_quaternion(m); + case .ZXZ: t1, t2, t3 = euler_angles_zxz_from_quaternion(m); + case .ZYZ: t1, t2, t3 = euler_angles_zyz_from_quaternion(m); + } + return; +} + +matrix3_from_euler_angles_f16 :: proc(t1, t2, t3: f16, order: Euler_Angle_Order) -> (m: Matrix3f16) { + switch order { + case .XYZ: return matrix3_from_euler_angles_xyz(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), Z(t3); + case .XZY: return matrix3_from_euler_angles_xzy(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), Y(t3); + case .YXZ: return matrix3_from_euler_angles_yxz(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Z(t3); + case .YZX: return matrix3_from_euler_angles_yzx(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), X(t3); + case .ZXY: return matrix3_from_euler_angles_zxy(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Y(t3); + case .ZYX: return matrix3_from_euler_angles_zyx(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), X(t3); + case .XYX: return matrix3_from_euler_angles_xyx(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), X(t3); + case .XZX: return matrix3_from_euler_angles_xzx(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), X(t3); + case .YXY: return matrix3_from_euler_angles_yxy(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Y(t3); + case .YZY: return matrix3_from_euler_angles_yzy(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), Y(t3); + case .ZXZ: return matrix3_from_euler_angles_zxz(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Z(t3); + case .ZYZ: return matrix3_from_euler_angles_zyz(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), Z(t3); + } + return; +} +matrix4_from_euler_angles_f16 :: proc(t1, t2, t3: f16, order: Euler_Angle_Order) -> (m: Matrix4f16) { + switch order { + case .XYZ: return matrix4_from_euler_angles_xyz(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), Z(t3); + case .XZY: return matrix4_from_euler_angles_xzy(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), Y(t3); + case .YXZ: return matrix4_from_euler_angles_yxz(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Z(t3); + case .YZX: return matrix4_from_euler_angles_yzx(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), X(t3); + case .ZXY: return matrix4_from_euler_angles_zxy(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Y(t3); + case .ZYX: return matrix4_from_euler_angles_zyx(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), X(t3); + case .XYX: return matrix4_from_euler_angles_xyx(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), X(t3); + case .XZX: return matrix4_from_euler_angles_xzx(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), X(t3); + case .YXY: return matrix4_from_euler_angles_yxy(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Y(t3); + case .YZY: return matrix4_from_euler_angles_yzy(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), Y(t3); + case .ZXZ: return matrix4_from_euler_angles_zxz(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Z(t3); + case .ZYZ: return matrix4_from_euler_angles_zyz(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), Z(t3); + } + return; +} + +quaternion_from_euler_angles_f16 :: proc(t1, t2, t3: f16, order: Euler_Angle_Order) -> Quaternionf16 { + X :: quaternion_from_euler_angle_x; + Y :: quaternion_from_euler_angle_y; + Z :: quaternion_from_euler_angle_z; + + q1, q2, q3: Quaternionf16; + + switch order { + case .XYZ: q1, q2, q3 = X(t1), Y(t2), Z(t3); + case .XZY: q1, q2, q3 = X(t1), Z(t2), Y(t3); + case .YXZ: q1, q2, q3 = Y(t1), X(t2), Z(t3); + case .YZX: q1, q2, q3 = Y(t1), Z(t2), X(t3); + case .ZXY: q1, q2, q3 = Z(t1), X(t2), Y(t3); + case .ZYX: q1, q2, q3 = Z(t1), Y(t2), X(t3); + case .XYX: q1, q2, q3 = X(t1), Y(t2), X(t3); + case .XZX: q1, q2, q3 = X(t1), Z(t2), X(t3); + case .YXY: q1, q2, q3 = Y(t1), X(t2), Y(t3); + case .YZY: q1, q2, q3 = Y(t1), Z(t2), Y(t3); + case .ZXZ: q1, q2, q3 = Z(t1), X(t2), Z(t3); + case .ZYZ: q1, q2, q3 = Z(t1), Y(t2), Z(t3); + } + + return q1 * (q2 * q3); +} + + +// Quaternionf16s + +quaternion_from_euler_angle_x_f16 :: proc(angle_x: f16) -> (q: Quaternionf16) { + return quaternion_angle_axis_f16(angle_x, {1, 0, 0}); +} +quaternion_from_euler_angle_y_f16 :: proc(angle_y: f16) -> (q: Quaternionf16) { + return quaternion_angle_axis_f16(angle_y, {0, 1, 0}); +} +quaternion_from_euler_angle_z_f16 :: proc(angle_z: f16) -> (q: Quaternionf16) { + return quaternion_angle_axis_f16(angle_z, {0, 0, 1}); +} + +quaternion_from_pitch_yaw_roll_f16 :: proc(pitch, yaw, roll: f16) -> Quaternionf16 { + a, b, c := pitch, yaw, roll; + + ca, sa := math.cos(a*0.5), math.sin(a*0.5); + cb, sb := math.cos(b*0.5), math.sin(b*0.5); + cc, sc := math.cos(c*0.5), math.sin(c*0.5); + + q: Quaternionf16; + q.x = sa*cb*cc - ca*sb*sc; + q.y = ca*sb*cc + sa*cb*sc; + q.z = ca*cb*sc - sa*sb*cc; + q.w = ca*cb*cc + sa*sb*sc; + return q; +} + +roll_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 { + return math.atan2(2 * q.x*q.y + q.w*q.z, q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z); +} + +pitch_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 { + y := 2 * (q.y*q.z + q.w*q.w); + x := q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z; + + if abs(x) <= F16_EPSILON && abs(y) <= F16_EPSILON { + return 2 * math.atan2(q.x, q.w); + } + + return math.atan2(y, x); +} + +yaw_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 { + return math.asin(clamp(-2 * (q.x*q.z - q.w*q.y), -1, 1)); +} + + +pitch_yaw_roll_from_quaternion_f16 :: proc(q: Quaternionf16) -> (pitch, yaw, roll: f16) { + pitch = pitch_from_quaternion(q); + yaw = yaw_from_quaternion(q); + roll = roll_from_quaternion(q); + return; +} + +euler_angles_xyz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_xyz_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_yxz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_yxz_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_xzx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_xzx_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_xyx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_xyx_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_yxy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_yxy_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_yzy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_yzy_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_zyz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_zyz_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_zxz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_zxz_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_xzy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_xzy_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_yzx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_yzx_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_zyx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_zyx_from_matrix4(matrix4_from_quaternion(q)); +} +euler_angles_zxy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) { + return euler_angles_zxy_from_matrix4(matrix4_from_quaternion(q)); +} + + +// Matrix3 + + +matrix3_from_euler_angle_x_f16 :: proc(angle_x: f16) -> (m: Matrix3f16) { + cos_x, sin_x := math.cos(angle_x), math.sin(angle_x); + m[0][0] = 1; + m[1][1] = +cos_x; + m[2][1] = +sin_x; + m[1][2] = -sin_x; + m[2][2] = +cos_x; + return; +} +matrix3_from_euler_angle_y_f16 :: proc(angle_y: f16) -> (m: Matrix3f16) { + cos_y, sin_y := math.cos(angle_y), math.sin(angle_y); + m[0][0] = +cos_y; + m[2][0] = -sin_y; + m[1][1] = 1; + m[0][2] = +sin_y; + m[2][2] = +cos_y; + return; +} +matrix3_from_euler_angle_z_f16 :: proc(angle_z: f16) -> (m: Matrix3f16) { + cos_z, sin_z := math.cos(angle_z), math.sin(angle_z); + m[0][0] = +cos_z; + m[1][0] = +sin_z; + m[1][1] = +cos_z; + m[0][1] = -sin_z; + m[2][2] = 1; + return; +} + + +matrix3_from_derived_euler_angle_x_f16 :: proc(angle_x: f16, angular_velocity_x: f16) -> (m: Matrix3f16) { + cos_x := math.cos(angle_x) * angular_velocity_x; + sin_x := math.sin(angle_x) * angular_velocity_x; + m[0][0] = 1; + m[1][1] = +cos_x; + m[2][1] = +sin_x; + m[1][2] = -sin_x; + m[2][2] = +cos_x; + return; +} +matrix3_from_derived_euler_angle_y_f16 :: proc(angle_y: f16, angular_velocity_y: f16) -> (m: Matrix3f16) { + cos_y := math.cos(angle_y) * angular_velocity_y; + sin_y := math.sin(angle_y) * angular_velocity_y; + m[0][0] = +cos_y; + m[2][0] = -sin_y; + m[1][1] = 1; + m[0][2] = +sin_y; + m[2][2] = +cos_y; + return; +} +matrix3_from_derived_euler_angle_z_f16 :: proc(angle_z: f16, angular_velocity_z: f16) -> (m: Matrix3f16) { + cos_z := math.cos(angle_z) * angular_velocity_z; + sin_z := math.sin(angle_z) * angular_velocity_z; + m[0][0] = +cos_z; + m[1][0] = +sin_z; + m[1][1] = +cos_z; + m[0][1] = -sin_z; + m[2][2] = 1; + return; +} + + +matrix3_from_euler_angles_xy_f16 :: proc(angle_x, angle_y: f16) -> (m: Matrix3f16) { + cos_x, sin_x := math.cos(angle_x), math.sin(angle_x); + cos_y, sin_y := math.cos(angle_y), math.sin(angle_y); + m[0][0] = cos_y; + m[1][0] = -sin_x * - sin_y; + m[2][0] = -cos_x * - sin_y; + m[1][1] = cos_x; + m[2][1] = sin_x; + m[0][2] = sin_y; + m[1][2] = -sin_x * cos_y; + m[2][2] = cos_x * cos_y; + return; +} + + +matrix3_from_euler_angles_yx_f16 :: proc(angle_y, angle_x: f16) -> (m: Matrix3f16) { + cos_x, sin_x := math.cos(angle_x), math.sin(angle_x); + cos_y, sin_y := math.cos(angle_y), math.sin(angle_y); + m[0][0] = cos_y; + m[2][0] = -sin_y; + m[0][1] = sin_y*sin_x; + m[1][1] = cos_x; + m[2][1] = cos_y*sin_x; + m[0][2] = sin_y*cos_x; + m[1][2] = -sin_x; + m[2][2] = cos_y*cos_x; + return; +} + +matrix3_from_euler_angles_xz_f16 :: proc(angle_x, angle_z: f16) -> (m: Matrix3f16) { + return mul(matrix3_from_euler_angle_x(angle_x), matrix3_from_euler_angle_z(angle_z)); +} +matrix3_from_euler_angles_zx_f16 :: proc(angle_z, angle_x: f16) -> (m: Matrix3f16) { + return mul(matrix3_from_euler_angle_z(angle_z), matrix3_from_euler_angle_x(angle_x)); +} +matrix3_from_euler_angles_yz_f16 :: proc(angle_y, angle_z: f16) -> (m: Matrix3f16) { + return mul(matrix3_from_euler_angle_y(angle_y), matrix3_from_euler_angle_z(angle_z)); +} +matrix3_from_euler_angles_zy_f16 :: proc(angle_z, angle_y: f16) -> (m: Matrix3f16) { + return mul(matrix3_from_euler_angle_z(angle_z), matrix3_from_euler_angle_y(angle_y)); +} + + +matrix3_from_euler_angles_xyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(-t1); + c2 := math.cos(-t2); + c3 := math.cos(-t3); + s1 := math.sin(-t1); + s2 := math.sin(-t2); + s3 := math.sin(-t3); + + m[0][0] = c2 * c3; + m[0][1] =-c1 * s3 + s1 * s2 * c3; + m[0][2] = s1 * s3 + c1 * s2 * c3; + m[1][0] = c2 * s3; + m[1][1] = c1 * c3 + s1 * s2 * s3; + m[1][2] =-s1 * c3 + c1 * s2 * s3; + m[2][0] =-s2; + m[2][1] = s1 * c2; + m[2][2] = c1 * c2; + return; +} + +matrix3_from_euler_angles_yxz_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix3f16) { + ch := math.cos(yaw); + sh := math.sin(yaw); + cp := math.cos(pitch); + sp := math.sin(pitch); + cb := math.cos(roll); + sb := math.sin(roll); + + m[0][0] = ch * cb + sh * sp * sb; + m[0][1] = sb * cp; + m[0][2] = -sh * cb + ch * sp * sb; + m[1][0] = -ch * sb + sh * sp * cb; + m[1][1] = cb * cp; + m[1][2] = sb * sh + ch * sp * cb; + m[2][0] = sh * cp; + m[2][1] = -sp; + m[2][2] = ch * cp; + return; +} + +matrix3_from_euler_angles_xzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c2; + m[0][1] = c1 * s2; + m[0][2] = s1 * s2; + m[1][0] =-c3 * s2; + m[1][1] = c1 * c2 * c3 - s1 * s3; + m[1][2] = c1 * s3 + c2 * c3 * s1; + m[2][0] = s2 * s3; + m[2][1] =-c3 * s1 - c1 * c2 * s3; + m[2][2] = c1 * c3 - c2 * s1 * s3; + return; +} + +matrix3_from_euler_angles_xyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c2; + m[0][1] = s1 * s2; + m[0][2] =-c1 * s2; + m[1][0] = s2 * s3; + m[1][1] = c1 * c3 - c2 * s1 * s3; + m[1][2] = c3 * s1 + c1 * c2 * s3; + m[2][0] = c3 * s2; + m[2][1] =-c1 * s3 - c2 * c3 * s1; + m[2][2] = c1 * c2 * c3 - s1 * s3; + return; +} + +matrix3_from_euler_angles_yxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c3 - c2 * s1 * s3; + m[0][1] = s2* s3; + m[0][2] =-c3 * s1 - c1 * c2 * s3; + m[1][0] = s1 * s2; + m[1][1] = c2; + m[1][2] = c1 * s2; + m[2][0] = c1 * s3 + c2 * c3 * s1; + m[2][1] =-c3 * s2; + m[2][2] = c1 * c2 * c3 - s1 * s3; + return; +} + +matrix3_from_euler_angles_yzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2 * c3 - s1 * s3; + m[0][1] = c3 * s2; + m[0][2] =-c1 * s3 - c2 * c3 * s1; + m[1][0] =-c1 * s2; + m[1][1] = c2; + m[1][2] = s1 * s2; + m[2][0] = c3 * s1 + c1 * c2 * s3; + m[2][1] = s2 * s3; + m[2][2] = c1 * c3 - c2 * s1 * s3; + return; +} + +matrix3_from_euler_angles_zyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2 * c3 - s1 * s3; + m[0][1] = c1 * s3 + c2 * c3 * s1; + m[0][2] =-c3 * s2; + m[1][0] =-c3 * s1 - c1 * c2 * s3; + m[1][1] = c1 * c3 - c2 * s1 * s3; + m[1][2] = s2 * s3; + m[2][0] = c1 * s2; + m[2][1] = s1 * s2; + m[2][2] = c2; + return; +} + +matrix3_from_euler_angles_zxz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c3 - c2 * s1 * s3; + m[0][1] = c3 * s1 + c1 * c2 * s3; + m[0][2] = s2 *s3; + m[1][0] =-c1 * s3 - c2 * c3 * s1; + m[1][1] = c1 * c2 * c3 - s1 * s3; + m[1][2] = c3 * s2; + m[2][0] = s1 * s2; + m[2][1] =-c1 * s2; + m[2][2] = c2; + return; +} + + +matrix3_from_euler_angles_xzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c2 * c3; + m[0][1] = s1 * s3 + c1 * c3 * s2; + m[0][2] = c3 * s1 * s2 - c1 * s3; + m[1][0] =-s2; + m[1][1] = c1 * c2; + m[1][2] = c2 * s1; + m[2][0] = c2 * s3; + m[2][1] = c1 * s2 * s3 - c3 * s1; + m[2][2] = c1 * c3 + s1 * s2 *s3; + return; +} + +matrix3_from_euler_angles_yzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2; + m[0][1] = s2; + m[0][2] =-c2 * s1; + m[1][0] = s1 * s3 - c1 * c3 * s2; + m[1][1] = c2 * c3; + m[1][2] = c1 * s3 + c3 * s1 * s2; + m[2][0] = c3 * s1 + c1 * s2 * s3; + m[2][1] =-c2 * s3; + m[2][2] = c1 * c3 - s1 * s2 * s3; + return; +} + +matrix3_from_euler_angles_zyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2; + m[0][1] = c2 * s1; + m[0][2] =-s2; + m[1][0] = c1 * s2 * s3 - c3 * s1; + m[1][1] = c1 * c3 + s1 * s2 * s3; + m[1][2] = c2 * s3; + m[2][0] = s1 * s3 + c1 * c3 * s2; + m[2][1] = c3 * s1 * s2 - c1 * s3; + m[2][2] = c2 * c3; + return; +} + +matrix3_from_euler_angles_zxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c3 - s1 * s2 * s3; + m[0][1] = c3 * s1 + c1 * s2 * s3; + m[0][2] =-c2 * s3; + m[1][0] =-c2 * s1; + m[1][1] = c1 * c2; + m[1][2] = s2; + m[2][0] = c1 * s3 + c3 * s1 * s2; + m[2][1] = s1 * s3 - c1 * c3 * s2; + m[2][2] = c2 * c3; + return; +} + + +matrix3_from_yaw_pitch_roll_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix3f16) { + ch := math.cos(yaw); + sh := math.sin(yaw); + cp := math.cos(pitch); + sp := math.sin(pitch); + cb := math.cos(roll); + sb := math.sin(roll); + + m[0][0] = ch * cb + sh * sp * sb; + m[0][1] = sb * cp; + m[0][2] = -sh * cb + ch * sp * sb; + m[1][0] = -ch * sb + sh * sp * cb; + m[1][1] = cb * cp; + m[1][2] = sb * sh + ch * sp * cb; + m[2][0] = sh * cp; + m[2][1] = -sp; + m[2][2] = ch * cp; + return m; +} + +euler_angles_xyz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][1], m[2][2]); + C2 := math.sqrt(m[0][0]*m[0][0] + m[1][0]*m[1][0]); + T2 := math.atan2(-m[2][0], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[0][2] - C1*m[0][1], C1*m[1][1] - S1*m[1][2]); + t1 = -T1; + t2 = -T2; + t3 = -T3; + return; +} + +euler_angles_yxz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][0], m[2][2]); + C2 := math.sqrt(m[0][1]*m[0][1] + m[1][1]*m[1][1]); + T2 := math.atan2(-m[2][1], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[1][2] - C1*m[1][0], C1*m[0][0] - S1*m[0][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_xzx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[0][2], m[0][1]); + S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]); + T2 := math.atan2(S2, m[0][0]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[1][2] - S1*m[1][1], C1*m[2][2] - S1*m[2][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_xyx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[0][1], -m[0][2]); + S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]); + T2 := math.atan2(S2, m[0][0]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(-C1*m[2][1] - S1*m[2][2], C1*m[1][1] + S1*m[1][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_yxy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[1][0], m[1][2]); + S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]); + T2 := math.atan2(S2, m[1][1]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[2][0] - S1*m[2][2], C1*m[0][0] - S1*m[0][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_yzy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[1][2], -m[1][0]); + S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]); + T2 := math.atan2(S2, m[1][1]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(-S1*m[0][0] - C1*m[0][2], S1*m[2][0] + C1*m[2][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} +euler_angles_zyz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][1], m[2][0]); + S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]); + T2 := math.atan2(S2, m[2][2]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[0][1] - S1*m[0][0], C1*m[1][1] - S1*m[1][0]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_zxz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][0], -m[2][1]); + S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]); + T2 := math.atan2(S2, m[2][2]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(-C1*m[1][0] - S1*m[1][1], C1*m[0][0] + S1*m[0][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_xzy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[1][2], m[1][1]); + C2 := math.sqrt(m[0][0]*m[0][0] + m[2][0]*m[2][0]); + T2 := math.atan2(-m[1][0], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[0][1] - C1*m[0][2], C1*m[2][2] - S1*m[2][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_yzx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(-m[0][2], m[0][0]); + C2 := math.sqrt(m[1][1]*m[1][1] + m[2][1]*m[2][1]); + T2 := math.atan2(m[0][1], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[1][0] + C1*m[1][2], S1*m[2][0] + C1*m[2][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_zyx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[0][1], m[0][0]); + C2 := math.sqrt(m[1][2]*m[1][2] + m[2][2]*m[2][2]); + T2 := math.atan2(-m[0][2], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[2][0] - C1*m[2][1], C1*m[1][1] - S1*m[1][0]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_zxy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(-m[1][0], m[1][1]); + C2 := math.sqrt(m[0][2]*m[0][2] + m[2][2]*m[2][2]); + T2 := math.atan2(m[1][2], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[2][0] + S1*m[2][1], C1*m[0][0] + S1*m[0][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + + +// Matrix4 + + +matrix4_from_euler_angle_x_f16 :: proc(angle_x: f16) -> (m: Matrix4f16) { + cos_x, sin_x := math.cos(angle_x), math.sin(angle_x); + m[0][0] = 1; + m[1][1] = +cos_x; + m[2][1] = +sin_x; + m[1][2] = -sin_x; + m[2][2] = +cos_x; + m[3][3] = 1; + return; +} +matrix4_from_euler_angle_y_f16 :: proc(angle_y: f16) -> (m: Matrix4f16) { + cos_y, sin_y := math.cos(angle_y), math.sin(angle_y); + m[0][0] = +cos_y; + m[2][0] = -sin_y; + m[1][1] = 1; + m[0][2] = +sin_y; + m[2][2] = +cos_y; + m[3][3] = 1; + return; +} +matrix4_from_euler_angle_z_f16 :: proc(angle_z: f16) -> (m: Matrix4f16) { + cos_z, sin_z := math.cos(angle_z), math.sin(angle_z); + m[0][0] = +cos_z; + m[1][0] = +sin_z; + m[1][1] = +cos_z; + m[0][1] = -sin_z; + m[2][2] = 1; + m[3][3] = 1; + return; +} + + +matrix4_from_derived_euler_angle_x_f16 :: proc(angle_x: f16, angular_velocity_x: f16) -> (m: Matrix4f16) { + cos_x := math.cos(angle_x) * angular_velocity_x; + sin_x := math.sin(angle_x) * angular_velocity_x; + m[0][0] = 1; + m[1][1] = +cos_x; + m[2][1] = +sin_x; + m[1][2] = -sin_x; + m[2][2] = +cos_x; + m[3][3] = 1; + return; +} +matrix4_from_derived_euler_angle_y_f16 :: proc(angle_y: f16, angular_velocity_y: f16) -> (m: Matrix4f16) { + cos_y := math.cos(angle_y) * angular_velocity_y; + sin_y := math.sin(angle_y) * angular_velocity_y; + m[0][0] = +cos_y; + m[2][0] = -sin_y; + m[1][1] = 1; + m[0][2] = +sin_y; + m[2][2] = +cos_y; + m[3][3] = 1; + return; +} +matrix4_from_derived_euler_angle_z_f16 :: proc(angle_z: f16, angular_velocity_z: f16) -> (m: Matrix4f16) { + cos_z := math.cos(angle_z) * angular_velocity_z; + sin_z := math.sin(angle_z) * angular_velocity_z; + m[0][0] = +cos_z; + m[1][0] = +sin_z; + m[1][1] = +cos_z; + m[0][1] = -sin_z; + m[2][2] = 1; + m[3][3] = 1; + return; +} + + +matrix4_from_euler_angles_xy_f16 :: proc(angle_x, angle_y: f16) -> (m: Matrix4f16) { + cos_x, sin_x := math.cos(angle_x), math.sin(angle_x); + cos_y, sin_y := math.cos(angle_y), math.sin(angle_y); + m[0][0] = cos_y; + m[1][0] = -sin_x * - sin_y; + m[2][0] = -cos_x * - sin_y; + m[1][1] = cos_x; + m[2][1] = sin_x; + m[0][2] = sin_y; + m[1][2] = -sin_x * cos_y; + m[2][2] = cos_x * cos_y; + m[3][3] = 1; + return; +} + + +matrix4_from_euler_angles_yx_f16 :: proc(angle_y, angle_x: f16) -> (m: Matrix4f16) { + cos_x, sin_x := math.cos(angle_x), math.sin(angle_x); + cos_y, sin_y := math.cos(angle_y), math.sin(angle_y); + m[0][0] = cos_y; + m[2][0] = -sin_y; + m[0][1] = sin_y*sin_x; + m[1][1] = cos_x; + m[2][1] = cos_y*sin_x; + m[0][2] = sin_y*cos_x; + m[1][2] = -sin_x; + m[2][2] = cos_y*cos_x; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_xz_f16 :: proc(angle_x, angle_z: f16) -> (m: Matrix4f16) { + return mul(matrix4_from_euler_angle_x(angle_x), matrix4_from_euler_angle_z(angle_z)); +} +matrix4_from_euler_angles_zx_f16 :: proc(angle_z, angle_x: f16) -> (m: Matrix4f16) { + return mul(matrix4_from_euler_angle_z(angle_z), matrix4_from_euler_angle_x(angle_x)); +} +matrix4_from_euler_angles_yz_f16 :: proc(angle_y, angle_z: f16) -> (m: Matrix4f16) { + return mul(matrix4_from_euler_angle_y(angle_y), matrix4_from_euler_angle_z(angle_z)); +} +matrix4_from_euler_angles_zy_f16 :: proc(angle_z, angle_y: f16) -> (m: Matrix4f16) { + return mul(matrix4_from_euler_angle_z(angle_z), matrix4_from_euler_angle_y(angle_y)); +} + + +matrix4_from_euler_angles_xyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(-t1); + c2 := math.cos(-t2); + c3 := math.cos(-t3); + s1 := math.sin(-t1); + s2 := math.sin(-t2); + s3 := math.sin(-t3); + + m[0][0] = c2 * c3; + m[0][1] =-c1 * s3 + s1 * s2 * c3; + m[0][2] = s1 * s3 + c1 * s2 * c3; + m[0][3] = 0; + m[1][0] = c2 * s3; + m[1][1] = c1 * c3 + s1 * s2 * s3; + m[1][2] =-s1 * c3 + c1 * s2 * s3; + m[1][3] = 0; + m[2][0] =-s2; + m[2][1] = s1 * c2; + m[2][2] = c1 * c2; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_yxz_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix4f16) { + ch := math.cos(yaw); + sh := math.sin(yaw); + cp := math.cos(pitch); + sp := math.sin(pitch); + cb := math.cos(roll); + sb := math.sin(roll); + + m[0][0] = ch * cb + sh * sp * sb; + m[0][1] = sb * cp; + m[0][2] = -sh * cb + ch * sp * sb; + m[0][3] = 0; + m[1][0] = -ch * sb + sh * sp * cb; + m[1][1] = cb * cp; + m[1][2] = sb * sh + ch * sp * cb; + m[1][3] = 0; + m[2][0] = sh * cp; + m[2][1] = -sp; + m[2][2] = ch * cp; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_xzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c2; + m[0][1] = c1 * s2; + m[0][2] = s1 * s2; + m[0][3] = 0; + m[1][0] =-c3 * s2; + m[1][1] = c1 * c2 * c3 - s1 * s3; + m[1][2] = c1 * s3 + c2 * c3 * s1; + m[1][3] = 0; + m[2][0] = s2 * s3; + m[2][1] =-c3 * s1 - c1 * c2 * s3; + m[2][2] = c1 * c3 - c2 * s1 * s3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_xyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c2; + m[0][1] = s1 * s2; + m[0][2] =-c1 * s2; + m[0][3] = 0; + m[1][0] = s2 * s3; + m[1][1] = c1 * c3 - c2 * s1 * s3; + m[1][2] = c3 * s1 + c1 * c2 * s3; + m[1][3] = 0; + m[2][0] = c3 * s2; + m[2][1] =-c1 * s3 - c2 * c3 * s1; + m[2][2] = c1 * c2 * c3 - s1 * s3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_yxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c3 - c2 * s1 * s3; + m[0][1] = s2* s3; + m[0][2] =-c3 * s1 - c1 * c2 * s3; + m[0][3] = 0; + m[1][0] = s1 * s2; + m[1][1] = c2; + m[1][2] = c1 * s2; + m[1][3] = 0; + m[2][0] = c1 * s3 + c2 * c3 * s1; + m[2][1] =-c3 * s2; + m[2][2] = c1 * c2 * c3 - s1 * s3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_yzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2 * c3 - s1 * s3; + m[0][1] = c3 * s2; + m[0][2] =-c1 * s3 - c2 * c3 * s1; + m[0][3] = 0; + m[1][0] =-c1 * s2; + m[1][1] = c2; + m[1][2] = s1 * s2; + m[1][3] = 0; + m[2][0] = c3 * s1 + c1 * c2 * s3; + m[2][1] = s2 * s3; + m[2][2] = c1 * c3 - c2 * s1 * s3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_zyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2 * c3 - s1 * s3; + m[0][1] = c1 * s3 + c2 * c3 * s1; + m[0][2] =-c3 * s2; + m[0][3] = 0; + m[1][0] =-c3 * s1 - c1 * c2 * s3; + m[1][1] = c1 * c3 - c2 * s1 * s3; + m[1][2] = s2 * s3; + m[1][3] = 0; + m[2][0] = c1 * s2; + m[2][1] = s1 * s2; + m[2][2] = c2; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_zxz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c3 - c2 * s1 * s3; + m[0][1] = c3 * s1 + c1 * c2 * s3; + m[0][2] = s2 *s3; + m[0][3] = 0; + m[1][0] =-c1 * s3 - c2 * c3 * s1; + m[1][1] = c1 * c2 * c3 - s1 * s3; + m[1][2] = c3 * s2; + m[1][3] = 0; + m[2][0] = s1 * s2; + m[2][1] =-c1 * s2; + m[2][2] = c2; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + + +matrix4_from_euler_angles_xzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c2 * c3; + m[0][1] = s1 * s3 + c1 * c3 * s2; + m[0][2] = c3 * s1 * s2 - c1 * s3; + m[0][3] = 0; + m[1][0] =-s2; + m[1][1] = c1 * c2; + m[1][2] = c2 * s1; + m[1][3] = 0; + m[2][0] = c2 * s3; + m[2][1] = c1 * s2 * s3 - c3 * s1; + m[2][2] = c1 * c3 + s1 * s2 *s3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_yzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2; + m[0][1] = s2; + m[0][2] =-c2 * s1; + m[0][3] = 0; + m[1][0] = s1 * s3 - c1 * c3 * s2; + m[1][1] = c2 * c3; + m[1][2] = c1 * s3 + c3 * s1 * s2; + m[1][3] = 0; + m[2][0] = c3 * s1 + c1 * s2 * s3; + m[2][1] =-c2 * s3; + m[2][2] = c1 * c3 - s1 * s2 * s3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_zyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c2; + m[0][1] = c2 * s1; + m[0][2] =-s2; + m[0][3] = 0; + m[1][0] = c1 * s2 * s3 - c3 * s1; + m[1][1] = c1 * c3 + s1 * s2 * s3; + m[1][2] = c2 * s3; + m[1][3] = 0; + m[2][0] = s1 * s3 + c1 * c3 * s2; + m[2][1] = c3 * s1 * s2 - c1 * s3; + m[2][2] = c2 * c3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + +matrix4_from_euler_angles_zxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) { + c1 := math.cos(t1); + s1 := math.sin(t1); + c2 := math.cos(t2); + s2 := math.sin(t2); + c3 := math.cos(t3); + s3 := math.sin(t3); + + m[0][0] = c1 * c3 - s1 * s2 * s3; + m[0][1] = c3 * s1 + c1 * s2 * s3; + m[0][2] =-c2 * s3; + m[0][3] = 0; + m[1][0] =-c2 * s1; + m[1][1] = c1 * c2; + m[1][2] = s2; + m[1][3] = 0; + m[2][0] = c1 * s3 + c3 * s1 * s2; + m[2][1] = s1 * s3 - c1 * c3 * s2; + m[2][2] = c2 * c3; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return; +} + + +matrix4_from_yaw_pitch_roll_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix4f16) { + ch := math.cos(yaw); + sh := math.sin(yaw); + cp := math.cos(pitch); + sp := math.sin(pitch); + cb := math.cos(roll); + sb := math.sin(roll); + + m[0][0] = ch * cb + sh * sp * sb; + m[0][1] = sb * cp; + m[0][2] = -sh * cb + ch * sp * sb; + m[0][3] = 0; + m[1][0] = -ch * sb + sh * sp * cb; + m[1][1] = cb * cp; + m[1][2] = sb * sh + ch * sp * cb; + m[1][3] = 0; + m[2][0] = sh * cp; + m[2][1] = -sp; + m[2][2] = ch * cp; + m[2][3] = 0; + m[3][0] = 0; + m[3][1] = 0; + m[3][2] = 0; + m[3][3] = 1; + return m; +} + +euler_angles_xyz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][1], m[2][2]); + C2 := math.sqrt(m[0][0]*m[0][0] + m[1][0]*m[1][0]); + T2 := math.atan2(-m[2][0], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[0][2] - C1*m[0][1], C1*m[1][1] - S1*m[1][2]); + t1 = -T1; + t2 = -T2; + t3 = -T3; + return; +} + +euler_angles_yxz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][0], m[2][2]); + C2 := math.sqrt(m[0][1]*m[0][1] + m[1][1]*m[1][1]); + T2 := math.atan2(-m[2][1], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[1][2] - C1*m[1][0], C1*m[0][0] - S1*m[0][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_xzx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[0][2], m[0][1]); + S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]); + T2 := math.atan2(S2, m[0][0]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[1][2] - S1*m[1][1], C1*m[2][2] - S1*m[2][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_xyx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[0][1], -m[0][2]); + S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]); + T2 := math.atan2(S2, m[0][0]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(-C1*m[2][1] - S1*m[2][2], C1*m[1][1] + S1*m[1][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_yxy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[1][0], m[1][2]); + S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]); + T2 := math.atan2(S2, m[1][1]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[2][0] - S1*m[2][2], C1*m[0][0] - S1*m[0][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_yzy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[1][2], -m[1][0]); + S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]); + T2 := math.atan2(S2, m[1][1]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(-S1*m[0][0] - C1*m[0][2], S1*m[2][0] + C1*m[2][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} +euler_angles_zyz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][1], m[2][0]); + S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]); + T2 := math.atan2(S2, m[2][2]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[0][1] - S1*m[0][0], C1*m[1][1] - S1*m[1][0]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_zxz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[2][0], -m[2][1]); + S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]); + T2 := math.atan2(S2, m[2][2]); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(-C1*m[1][0] - S1*m[1][1], C1*m[0][0] + S1*m[0][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_xzy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[1][2], m[1][1]); + C2 := math.sqrt(m[0][0]*m[0][0] + m[2][0]*m[2][0]); + T2 := math.atan2(-m[1][0], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[0][1] - C1*m[0][2], C1*m[2][2] - S1*m[2][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_yzx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(-m[0][2], m[0][0]); + C2 := math.sqrt(m[1][1]*m[1][1] + m[2][1]*m[2][1]); + T2 := math.atan2(m[0][1], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[1][0] + C1*m[1][2], S1*m[2][0] + C1*m[2][2]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_zyx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(m[0][1], m[0][0]); + C2 := math.sqrt(m[1][2]*m[1][2] + m[2][2]*m[2][2]); + T2 := math.atan2(-m[0][2], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(S1*m[2][0] - C1*m[2][1], C1*m[1][1] - S1*m[1][0]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} + +euler_angles_zxy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) { + T1 := math.atan2(-m[1][0], m[1][1]); + C2 := math.sqrt(m[0][2]*m[0][2] + m[2][2]*m[2][2]); + T2 := math.atan2(m[1][2], C2); + S1 := math.sin(T1); + C1 := math.cos(T1); + T3 := math.atan2(C1*m[2][0] + S1*m[2][1], C1*m[0][0] + S1*m[0][1]); + t1 = T1; + t2 = T2; + t3 = T3; + return; +} |