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Update package math/linalg

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This commit is contained in:
gingerBill
2019-12-28 23:00:13 +00:00
parent 6a7ccd8c0a
commit 33a458c520
1 changed files with 719 additions and 100 deletions
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819
core/math/linalg/linalg.odin
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@@ -5,76 +5,292 @@ import "intrinsics"
// Generic
dot_vector :: proc(a, b: $T/[$N]$E) -> (c: E) {
@private IS_NUMERIC :: intrinsics.type_is_numeric;
@private IS_QUATERNION :: intrinsics.type_is_quaternion;
@private IS_ARRAY :: intrinsics.type_is_array;
vector_dot :: proc(a, b: $T/[$N]$E) -> (c: E) where IS_NUMERIC(E) {
for i in 0..<N {
c += a[i] * b[i];
}
return;
}
dot_quaternion128 :: proc(a, b: $T/quaternion128) -> (c: f32) {
quaternion128_dot :: proc(a, b: $T/quaternion128) -> (c: f32) {
return real(a)*real(a) + imag(a)*imag(b) + jmag(a)*jmag(b) + kmag(a)*kmag(b);
}
dot_quaternion256 :: proc(a, b: $T/quaternion256) -> (c: f64) {
quaternion256_dot :: proc(a, b: $T/quaternion256) -> (c: f64) {
return real(a)*real(a) + imag(a)*imag(b) + jmag(a)*jmag(b) + kmag(a)*kmag(b);
}
dot :: proc{dot_vector, dot_quaternion128, dot_quaternion256};
dot :: proc{vector_dot, quaternion128_dot, quaternion256_dot};
cross2 :: proc(a, b: $T/[2]$E) -> E {
quaternion_inverse :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
return conj(q) * quaternion(1.0/dot(q, q), 0, 0, 0);
}
vector_cross2 :: proc(a, b: $T/[2]$E) -> E where IS_NUMERIC(E) {
return a[0]*b[1] - b[0]*a[1];
}
cross3 :: proc(a, b: $T/[3]$E) -> (c: T) {
c[0] = +(a[1]*b[2] - b[1]*a[2]);
c[1] = -(a[2]*b[0] - b[2]*a[0]);
c[2] = +(a[0]*b[1] - b[0]*a[1]);
vector_cross3 :: proc(a, b: $T/[3]$E) -> (c: T) where IS_NUMERIC(E) {
c[0] = a[1]*b[2] - b[1]*a[2];
c[1] = a[2]*b[0] - b[2]*a[0];
c[2] = a[0]*b[1] - b[0]*a[1];
return;
}
cross :: proc{cross2, cross3};
vector_cross :: proc{vector_cross2, vector_cross3};
cross :: vector_cross;
normalize_vector :: proc(v: $T/[$N]$E) -> T {
vector_normalize :: proc(v: $T/[$N]$E) -> T where IS_NUMERIC(E) {
return v / length(v);
}
normalize_quaternion128 :: proc(q: $Q/quaternion128) -> Q {
quaternion_normalize :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
return q/abs(q);
}
normalize_quaternion256 :: proc(q: $Q/quaternion256) -> Q {
return q/abs(q);
}
normalize :: proc{normalize_vector, normalize_quaternion128, normalize_quaternion256};
normalize :: proc{vector_normalize, quaternion_normalize};
normalize0_vector :: proc(v: $T/[$N]$E) -> T {
vector_normalize0 :: proc(v: $T/[$N]$E) -> T where IS_NUMERIC(E) {
m := length(v);
return m == 0 ? 0 : v/m;
}
normalize0_quaternion128 :: proc(q: $Q/quaternion128) -> Q {
quaternion_normalize0 :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
m := abs(q);
return m == 0 ? 0 : q/m;
}
normalize0_quaternion256 :: proc(q: $Q/quaternion256) -> Q {
m := abs(q);
return m == 0 ? 0 : q/m;
}
normalize0 :: proc{normalize0_vector, normalize0_quaternion128, normalize0_quaternion256};
normalize0 :: proc{vector_normalize0, quaternion_normalize0};
length :: proc(v: $T/[$N]$E) -> E {
vector_length :: proc(v: $T/[$N]$E) -> E where IS_NUMERIC(E) {
return math.sqrt(dot(v, v));
}
length2 :: proc(v: $T/[$N]$E) -> E {
vector_length2 :: proc(v: $T/[$N]$E) -> E where IS_NUMERIC(E) {
return dot(v, v);
}
quaternion_length :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
return abs(q);
}
quaternion_length2 :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
return dot(q, q);
}
length :: proc{vector_length, quaternion_length};
length2 :: proc{vector_length2, quaternion_length2};
vector_sin :: proc(angle: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.sin(angle[i]);
}
return s;
}
vector_cos :: proc(angle: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.cos(angle[i]);
}
return s;
}
vector_tan :: proc(angle: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.tan(angle[i]);
}
return s;
}
vector_asin :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.asin(x[i]);
}
return s;
}
vector_acos :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.acos(x[i]);
}
return s;
}
vector_atan :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.atan(x[i]);
}
return s;
}
vector_atan2 :: proc(y, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.atan(y[i], x[i]);
}
return s;
}
vector_pow :: proc(x, y: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.pow(x[i], y[i]);
}
return s;
}
vector_expr :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.expr(x[i]);
}
return s;
}
vector_sqrt :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.sqrt(x[i]);
}
return s;
}
vector_abs :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = abs(x[i]);
}
return s;
}
vector_sign :: proc(v: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.sign(v[i]);
}
return s;
}
vector_floor :: proc(v: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.floor(v[i]);
}
return s;
}
vector_ceil :: proc(v: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.ceil(v[i]);
}
return s;
}
vector_mod :: proc(x, y: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = math.mod(x[i], y[i]);
}
return s;
}
vector_min :: proc(a, b: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = min(a[i], b[i]);
}
return s;
}
vector_max :: proc(a, b: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = max(a[i], b[i]);
}
return s;
}
vector_clamp :: proc(x, a, b: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = clamp(x[i], a[i], b[i]);
}
return s;
}
vector_mix :: proc(x, y, a: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = x[i]*(1-a[i]) + y[i]*a[i];
}
return s;
}
vector_step :: proc(edge, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
s[i] = x[i] < edge[i] ? 0 : 1;
}
return s;
}
vector_smoothstep :: proc(edge0, edge1, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
e0, e1 := edge0[i], edge1[i];
t := clamp((x[i] - e0) / (e1 - e0), 0, 1);
s[i] = t * t * (3 - 2*t);
}
return s;
}
vector_smootherstep :: proc(edge0, edge1, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
s: V;
for i in 0..<N {
e0, e1 := edge0[i], edge1[i];
t := clamp((x[i] - e0) / (e1 - e0), 0, 1);
s[i] = t * t * t * (t * (6*t - 15) + 10);
}
return s;
}
vector_distance :: proc(p0, p1: $V/[$N]$E) -> V where IS_NUMERIC(E) {
return length(p1 - p0);
}
vector_reflect :: proc(i, n: $V/[$N]$E) -> V where IS_NUMERIC(E) {
b := n * (2 * dot(n, i));
return i - b;
}
vector_refract :: proc(i, n: $V/[$N]$E, eta: E) -> V where IS_NUMERIC(E) {
dv := dot(n, i);
k := 1 - eta*eta - (1 - dv*dv);
a := i * eta;
b := n * eta*dv*math.sqrt(k);
return (a - b) * E(int(k >= 0));
}
identity :: proc($T: typeid/[$N][N]$E) -> (m: T) {
for i in 0..<N do m[i][i] = E(1);
return m;
}
transpose :: proc(a: $T/[$N][$M]$E) -> (m: [M][N]E) {
transpose :: proc(a: $T/[$N][$M]$E) -> (m: T) {
for j in 0..<M {
for i in 0..<N {
m[j][i] = a[i][j];
@@ -83,9 +299,9 @@ transpose :: proc(a: $T/[$N][$M]$E) -> (m: [M][N]E) {
return;
}
mul_matrix :: proc(a, b: $M/[$N][N]$E) -> (c: M)
where !intrinsics.type_is_array(E),
intrinsics.type_is_numeric(E) {
matrix_mul :: proc(a, b: $M/[$N][N]$E) -> (c: M)
where !IS_ARRAY(E),
IS_NUMERIC(E) {
for i in 0..<N {
for k in 0..<N {
for j in 0..<N {
@@ -96,10 +312,10 @@ mul_matrix :: proc(a, b: $M/[$N][N]$E) -> (c: M)
return;
}
mul_matrix_differ :: proc(a: $A/[$J][$I]$E, b: $B/[$K][J]E) -> (c: [K][I]E)
where !intrinsics.type_is_array(E),
intrinsics.type_is_numeric(E),
I != K {
matrix_mul_differ :: proc(a: $A/[$J][$I]$E, b: $B/[$K][J]E) -> (c: [K][I]E)
where !IS_ARRAY(E),
IS_NUMERIC(E),
I != K {
for k in 0..<K {
for j in 0..<J {
for i in 0..<I {
@@ -111,9 +327,9 @@ mul_matrix_differ :: proc(a: $A/[$J][$I]$E, b: $B/[$K][J]E) -> (c: [K][I]E)
}
mul_matrix_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B)
where !intrinsics.type_is_array(E),
intrinsics.type_is_numeric(E) {
matrix_mul_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B)
where !IS_ARRAY(E),
IS_NUMERIC(E) {
for i in 0..<I {
for j in 0..<J {
c[i] += a[i][j] * b[i];
@@ -122,7 +338,7 @@ mul_matrix_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B)
return;
}
mul_quaternion128_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
quaternion128_mul_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
Raw_Quaternion :: struct {xyz: [3]f32, r: f32};
q := transmute(Raw_Quaternion)q;
@@ -132,7 +348,7 @@ mul_quaternion128_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
return V(v + q.r*t + cross(q.xyz, t));
}
mul_quaternion256_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V {
quaternion256_mul_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V {
Raw_Quaternion :: struct {xyz: [3]f64, r: f64};
q := transmute(Raw_Quaternion)q;
@@ -141,16 +357,23 @@ mul_quaternion256_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));
}
mul_quaternion_vector3 :: proc{mul_quaternion128_vector3, mul_quaternion256_vector3};
quaternion_mul_vector3 :: proc{quaternion128_mul_vector3, quaternion256_mul_vector3};
mul :: proc{
mul_matrix,
mul_matrix_differ,
mul_matrix_vector,
mul_quaternion128_vector3,
mul_quaternion256_vector3,
matrix_mul,
matrix_mul_differ,
matrix_mul_vector,
quaternion128_mul_vector3,
quaternion256_mul_vector3,
};
vector_to_ptr :: proc(v: ^$V/[$N]$E) -> ^E where IS_NUMERIC(E) {
return &v[0];
}
matrix_to_ptr :: proc(m: ^$A/[$I][$J]$E) -> ^E where IS_NUMERIC(E) {
return &m[0][0];
}
// Specific
@@ -199,6 +422,11 @@ VECTOR3_Y_AXIS :: Vector3{0, 1, 0};
VECTOR3_Z_AXIS :: Vector3{0, 0, 1};
vector2_orthogonal :: proc(v: Vector2) -> Vector2 {
return {-v.y, v.x};
}
vector3_orthogonal :: proc(v: Vector3) -> Vector3 {
x := abs(v.x);
y := abs(v.y);
@@ -206,20 +434,442 @@ vector3_orthogonal :: proc(v: Vector3) -> Vector3 {
other: Vector3 = x < y ? (x < z ? {1, 0, 0} : {0, 0, 1}) : (y < z ? {0, 1, 0} : {0, 0, 1});
return normalize(cross3(v, other));
return normalize(cross(v, other));
}
vector3_reflect :: proc(i, n: Vector3) -> Vector3 {
b := n * 2 * dot(n, i);
return i - b;
vector4_srgb_to_linear :: proc(col: Vector4) -> Vector4 {
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};
}
vector3_refract :: proc(i, n: Vector3, eta: Float) -> Vector3 {
dv := dot(n, i);
k := 1 - eta*eta - (1 - dv*dv);
a := i * eta;
b := n * eta*dv*math.sqrt(k);
return (a - b) * Float(int(k >= 0));
vector4_linear_to_srgb :: proc(col: Vector4) -> Vector4 {
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_hsl_to_rgb :: proc(h, s, l: Float, a: Float = 1) -> Vector4 {
hue_to_rgb :: proc(p, q, t0: Float) -> Float {
t := math.mod(t0, 1.0);
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: Float;
if s == 0 {
r = l;
g = l;
b = l;
} else {
q := l < 0.5 ? l * (1+s) : 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_rgb_to_hsl :: proc(col: Vector4) -> Vector4 {
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: Float;
h = 0.0;
s = 0.0;
l = (v_min + v_max) * 0.5;
if v_max != v_min {
d: = v_max - v_min;
s = l > 0.5 ? d / (2.0 - v_max - v_min) : d / (v_max + v_min);
switch {
case v_max == r:
h = (g - b) / d + (g < b ? 6.0 : 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};
}
quaternion_angle_axis :: proc(angle_radians: Float, axis: Vector3) -> Quaternion {
t := angle_radians*0.5;
w := math.cos(t);
v := normalize(axis) * math.sin(t);
return quaternion(w, v.x, v.y, v.z);
}
quaternion_from_euler_angles :: proc(pitch, yaw, roll: Float) -> Quaternion {
p := quaternion_angle_axis(pitch, {1, 0, 0});
y := quaternion_angle_axis(yaw, {0, 1, 0});
r := quaternion_angle_axis(roll, {0, 0, 1});
return (y * p) * r;
}
euler_angles_from_quaternion :: proc(q: Quaternion) -> (roll, pitch, yaw: Float) {
// roll (x-axis rotation)
sinr_cosp: Float = 2 * (real(q)*imag(q) + jmag(q)*kmag(q));
cosr_cosp: Float = 1 - 2 * (imag(q)*imag(q) + jmag(q)*jmag(q));
roll = Float(math.atan2(sinr_cosp, cosr_cosp));
// pitch (y-axis rotation)
sinp: Float = 2 * (real(q)*kmag(q) - kmag(q)*imag(q));
if abs(sinp) >= 1 {
pitch = Float(math.copy_sign(math.TAU * 0.25, sinp));
} else {
pitch = Float(math.asin(sinp));
}
// yaw (z-axis rotation)
siny_cosp: Float = 2 * (real(q)*kmag(q) + imag(q)*jmag(q));
cosy_cosp: Float = 1 - 2 * (jmag(q)*jmag(q) + kmag(q)*kmag(q));
yaw = Float(math.atan2(siny_cosp, cosy_cosp));
return;
}
quaternion_nlerp :: proc(a, b: Quaternion, t: Float) -> Quaternion {
c := a + (b-a)*quaternion(t, 0, 0, 0);
return normalize(c);
}
quaternion_slerp :: proc(x, y: Quaternion, t: Float) -> Quaternion {
EPSILON :: size_of(Float) == 4 ? 1e-7 : 1e-15;
a, b := x, y;
cos_angle := dot(a, b);
if cos_angle < 0 {
b = -b;
cos_angle = -cos_angle;
}
if cos_angle > 1 - EPSILON {
return a + (b-a)*quaternion(t, 0, 0, 0);
}
angle := math.acos(cos_angle);
sin_angle := math.sin(angle);
factor_a, factor_b: Quaternion;
factor_a = quaternion(math.sin((1-t) * angle) / sin_angle, 0, 0, 0);
factor_b = quaternion(math.sin(t * angle) / sin_angle, 0, 0, 0);
return factor_a * a + factor_b * b;
}
quaternion_from_matrix4 :: proc(m: Matrix4) -> Quaternion {
four_x_squared_minus_1, four_y_squared_minus_1,
four_z_squared_minus_1, four_w_squared_minus_1,
four_biggest_squared_minus_1: Float;
/* xyzw */
/* 0123 */
biggest_index := 3;
biggest_value, mult: Float;
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];
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 = 0;
}
if four_y_squared_minus_1 > four_biggest_squared_minus_1 {
four_biggest_squared_minus_1 = four_y_squared_minus_1;
biggest_index = 1;
}
if four_z_squared_minus_1 > four_biggest_squared_minus_1 {
four_biggest_squared_minus_1 = four_z_squared_minus_1;
biggest_index = 2;
}
biggest_value = math.sqrt(four_biggest_squared_minus_1 + 1) * 0.5;
mult = 0.25 / biggest_value;
switch biggest_index {
case 0:
return quaternion(
biggest_value,
(m[0][1] + m[1][0]) * mult,
(m[2][0] + m[0][2]) * mult,
(m[1][2] - m[2][1]) * mult,
);
case 1:
return quaternion(
(m[0][1] + m[1][0]) * mult,
biggest_value,
(m[1][2] + m[2][1]) * mult,
(m[2][0] - m[0][2]) * mult,
);
case 2:
return quaternion(
(m[2][0] + m[0][2]) * mult,
(m[1][2] + m[2][1]) * mult,
biggest_value,
(m[0][1] - m[1][0]) * mult,
);
case 3:
return quaternion(
(m[1][2] - m[2][1]) * mult,
(m[2][0] - m[0][2]) * mult,
(m[0][1] - m[1][0]) * mult,
biggest_value,
);
}
return 0;
}
quaternion_between_two_vector3 :: proc(from, to: Vector3) -> Quaternion {
EPSILON :: size_of(Float) == 4 ? 1e-7 : 1e-15;
x := normalize(from);
y := normalize(to);
cos_theta := dot(x, y);
if abs(cos_theta + 1) < 2*EPSILON {
v := vector3_orthogonal(x);
return quaternion(0, v.x, v.y, v.z);
}
v := cross(x, y);
w := cos_theta + 1;
return Quaternion(normalize(quaternion(w, v.x, v.y, v.z)));
}
matrix2_inverse_transpose :: proc(m: Matrix2) -> Matrix2 {
c: Matrix2;
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_determinant :: proc(m: Matrix2) -> Float {
return m[0][0]*m[1][1] - m[1][0]*m[0][1];
}
matrix2_adjoint :: proc(m: Matrix2) -> Matrix2 {
c: Matrix2;
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;
}
matrix3_from_quaternion :: proc(q: Quaternion) -> Matrix3 {
xx := imag(q) * imag(q);
xy := imag(q) * jmag(q);
xz := imag(q) * kmag(q);
xw := imag(q) * real(q);
yy := jmag(q) * jmag(q);
yz := jmag(q) * kmag(q);
yw := jmag(q) * real(q);
zz := kmag(q) * kmag(q);
zw := kmag(q) * real(q);
m: Matrix3;
m[0][0] = 1 - 2 * (yy + zz);
m[1][0] = 2 * (xy - zw);
m[2][0] = 2 * (xz + yw);
m[0][1] = 2 * (xy + zw);
m[1][1] = 1 - 2 * (xx + zz);
m[2][1] = 2 * (yz - xw);
m[0][2] = 2 * (xz - yw);
m[1][2] = 2 * (yz + xw);
m[2][2] = 1 - 2 * (xx + yy);
return m;
}
matrix3_inverse :: proc(m: Matrix3) -> Matrix3 {
return transpose(matrix3_inverse_transpose(m));
}
matrix3_determinant :: proc(m: Matrix3) -> Float {
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_adjoint :: proc(m: Matrix3) -> Matrix3 {
adjoint: Matrix3;
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_inverse_transpose :: proc(m: Matrix3) -> Matrix3 {
inverse_transpose: Matrix3;
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 inverse_transpose;
}
matrix3_scale :: proc(s: Vector3) -> Matrix3 {
m: Matrix3;
m[0][0] = s[0];
m[1][1] = s[1];
m[2][2] = s[2];
return m;
}
matrix4_from_quaternion :: proc(q: Quaternion) -> Matrix4 {
m := identity(Matrix4);
xx := imag(q) * imag(q);
xy := imag(q) * jmag(q);
xz := imag(q) * kmag(q);
xw := imag(q) * real(q);
yy := jmag(q) * jmag(q);
yz := jmag(q) * kmag(q);
yw := jmag(q) * real(q);
zz := kmag(q) * kmag(q);
zw := kmag(q) * real(q);
m[0][0] = 1 - 2 * (yy + zz);
m[1][0] = 2 * (xy - zw);
m[2][0] = 2 * (xz + yw);
m[0][1] = 2 * (xy + zw);
m[1][1] = 1 - 2 * (xx + zz);
m[2][1] = 2 * (yz - xw);
m[0][2] = 2 * (xz - yw);
m[1][2] = 2 * (yz + xw);
m[2][2] = 1 - 2 * (xx + yy);
return m;
}
matrix4_from_trs :: proc(t: Vector3, r: Quaternion, s: Vector3) -> Matrix4 {
translation := matrix4_translate(t);
rotation := matrix4_from_quaternion(r);
scale := matrix4_scale(s);
return mul(translation, mul(rotation, scale));
}
matrix4_inverse :: proc(m: Matrix4) -> Matrix4 {
return transpose(matrix4_inverse_transpose(m));
}
matrix4_minor :: proc(m: Matrix4, c, r: int) -> Float {
cut_down: Matrix3;
for i in 0..<3 {
col := i < c ? i : i+1;
for j in 0..<3 {
row := j < r ? j : j+1;
cut_down[i][j] = m[col][row];
}
}
return matrix3_determinant(cut_down);
}
matrix4_cofactor :: proc(m: Matrix4, c, r: int) -> Float {
sign := (c + r) % 2 == 0 ? Float(1) : Float(-1);
minor := matrix4_minor(m, c, r);
return sign * minor;
}
matrix4_adjoint :: proc(m: Matrix4) -> Matrix4 {
adjoint: Matrix4;
for i in 0..<4 {
for j in 0..<4 {
adjoint[i][j] = matrix4_cofactor(m, i, j);
}
}
return adjoint;
}
matrix4_determinant :: proc(m: Matrix4) -> Float {
adjoint := matrix4_adjoint(m);
determinant: Float = 0;
for i in 0..<4 {
determinant += m[i][0] * adjoint[i][0];
}
return determinant;
}
matrix4_inverse_transpose :: proc(m: Matrix4) -> Matrix4 {
adjoint := matrix4_adjoint(m);
determinant: Float = 0;
for i in 0..<4 {
determinant += m[i][0] * adjoint[i][0];
}
inv_determinant := 1.0 / determinant;
inverse_transpose: Matrix4;
for i in 0..<4 {
for j in 0..<4 {
inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
}
}
return inverse_transpose;
}
@@ -261,16 +911,15 @@ matrix4_rotate :: proc(v: Vector3, angle_radians: Float) -> Matrix4 {
return rot;
}
scale_matrix4 :: matrix4_scale;
matrix4_scale :: proc(m: Matrix4, v: Vector3) -> Matrix4 {
mm := m;
mm[0][0] *= v[0];
mm[1][1] *= v[1];
mm[2][2] *= v[2];
return mm;
matrix4_scale :: proc(v: Vector3) -> Matrix4 {
m: Matrix4;
m[0][0] = v[0];
m[1][1] = v[1];
m[2][2] = v[2];
m[3][3] = 1;
return m;
}
look_at :: matrix4_look_at;
matrix4_look_at :: proc(eye, centre, up: Vector3) -> Matrix4 {
f := normalize(centre - eye);
s := normalize(cross(f, up));
@@ -284,7 +933,6 @@ matrix4_look_at :: proc(eye, centre, up: Vector3) -> Matrix4 {
}
perspective :: matrix4_perspective;
matrix4_perspective :: proc(fovy, aspect, near, far: Float) -> (m: Matrix4) {
tan_half_fovy := math.tan(0.5 * fovy);
m[0][0] = 1 / (aspect*tan_half_fovy);
@@ -308,41 +956,12 @@ matrix_ortho3d :: proc(left, right, bottom, top, near, far: Float) -> (m: Matrix
}
axis_angle :: quaternion_angle_axis;
angle_axis :: quaternion_angle_axis;
quaternion_angle_axis :: proc(angle_radians: Float, axis: Vector3) -> Quaternion {
t := angle_radians*0.5;
w := math.cos(t);
v := normalize(axis) * math.sin(t);
return quaternion(w, v.x, v.y, v.z);
}
euler_angles :: quaternion_from_euler_angles;
quaternion_from_euler_angles :: proc(pitch, yaw, roll: Float) -> Quaternion {
p := quaternion_angle_axis(pitch, {1, 0, 0});
y := quaternion_angle_axis(yaw, {0, 1, 0});
r := quaternion_angle_axis(roll, {0, 0, 1});
return (y * p) * r;
}
euler_angles_from_quaternion :: proc(q: Quaternion) -> (roll, pitch, yaw: Float) {
// roll (x-axis rotation)
sinr_cosp: Float = 2 * (real(q)*imag(q) + jmag(q)*kmag(q));
cosr_cosp: Float = 1 - 2 * (imag(q)*imag(q) + jmag(q)*jmag(q));
roll = Float(math.atan2(sinr_cosp, cosr_cosp));
// pitch (y-axis rotation)
sinp: Float = 2 * (real(q)*kmag(q) - kmag(q)*imag(q));
if abs(sinp) >= 1 {
pitch = Float(math.copy_sign(math.TAU * 0.25, sinp));
} else {
pitch = Float(math.asin(sinp));
}
// yaw (z-axis rotation)
siny_cosp: Float = 2 * (real(q)*kmag(q) + imag(q)*jmag(q));
cosy_cosp: Float = 1 - 2 * (jmag(q)*jmag(q) + kmag(q)*kmag(q));
yaw = Float(math.atan2(siny_cosp, cosy_cosp));
matrix4_infinite_perspective :: proc(fovy, aspect, near: Float) -> (m: Matrix4) {
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;
return;
}