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Add new procedures for package math: atan2, asin, acos, atan, sin_bit, ldexp

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This commit is contained in:
gingerBill
2019-12-28 18:12:27 +00:00
parent 9ba2926e7e
commit 6a7ccd8c0a
2 changed files with 240 additions and 23 deletions
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core/math/linalg/linalg.odin
+80 -21
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@@ -64,6 +64,10 @@ length :: proc(v: $T/[$N]$E) -> E {
return math.sqrt(dot(v, v));
}
length2 :: proc(v: $T/[$N]$E) -> E {
return dot(v, v);
}
identity :: proc($T: typeid/[$N][N]$E) -> (m: T) {
for i in 0..<N do m[i][i] = E(1);
@@ -176,17 +180,51 @@ Matrix4x2 :: distinct [4][2]Float;
Matrix4x3 :: distinct [4][3]Float;
Matrix4x4 :: distinct [4][4]Float;
Matrix1 :: Matrix1x1;
Matrix2 :: Matrix2x2;
Matrix3 :: Matrix3x3;
Matrix4 :: Matrix4x4;
Quaternion :: distinct (size_of(Float) == size_of(f32) ? quaternion128 : quaternion256);
MATRIX1_IDENTITY :: Matrix1{{1}};
MATRIX2_IDENTITY :: Matrix2{{1, 0}, {0, 1}};
MATRIX3_IDENTITY :: Matrix3{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
MATRIX4_IDENTITY :: Matrix4{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};
translate_matrix4 :: proc(v: Vector3) -> Matrix4 {
QUATERNION_IDENTITY :: Quaternion(1);
VECTOR3_X_AXIS :: Vector3{1, 0, 0};
VECTOR3_Y_AXIS :: Vector3{0, 1, 0};
VECTOR3_Z_AXIS :: Vector3{0, 0, 1};
vector3_orthogonal :: proc(v: Vector3) -> Vector3 {
x := abs(v.x);
y := abs(v.y);
z := abs(v.z);
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));
}
vector3_reflect :: proc(i, n: Vector3) -> Vector3 {
b := n * 2 * dot(n, i);
return i - b;
}
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));
}
translate_matrix4 :: matrix4_translate;
matrix4_translate :: proc(v: Vector3) -> Matrix4 {
m := identity(Matrix4);
m[3][0] = v[0];
m[3][1] = v[1];
@@ -195,7 +233,8 @@ translate_matrix4 :: proc(v: Vector3) -> Matrix4 {
}
rotate_matrix4 :: proc(v: Vector3, angle_radians: Float) -> Matrix4 {
rotate_matrix4 :: matrix4_rotate;
matrix4_rotate :: proc(v: Vector3, angle_radians: Float) -> Matrix4 {
c := math.cos(angle_radians);
s := math.sin(angle_radians);
@@ -222,7 +261,8 @@ rotate_matrix4 :: proc(v: Vector3, angle_radians: Float) -> Matrix4 {
return rot;
}
scale_matrix4 :: proc(m: Matrix4, v: Vector3) -> Matrix4 {
scale_matrix4 :: matrix4_scale;
matrix4_scale :: proc(m: Matrix4, v: Vector3) -> Matrix4 {
mm := m;
mm[0][0] *= v[0];
mm[1][1] *= v[1];
@@ -230,8 +270,8 @@ scale_matrix4 :: proc(m: Matrix4, v: Vector3) -> Matrix4 {
return mm;
}
look_at :: proc(eye, centre, up: Vector3) -> Matrix4 {
look_at :: matrix4_look_at;
matrix4_look_at :: proc(eye, centre, up: Vector3) -> Matrix4 {
f := normalize(centre - eye);
s := normalize(cross(f, up));
u := cross(s, f);
@@ -244,7 +284,8 @@ look_at :: proc(eye, centre, up: Vector3) -> Matrix4 {
}
perspective :: proc(fovy, aspect, near, far: Float) -> (m: 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);
m[1][1] = 1 / (tan_half_fovy);
@@ -255,7 +296,7 @@ perspective :: proc(fovy, aspect, near, far: Float) -> (m: Matrix4) {
}
ortho3d :: proc(left, right, bottom, top, near, far: Float) -> (m: Matrix4) {
matrix_ortho3d :: proc(left, right, bottom, top, near, far: Float) -> (m: Matrix4) {
m[0][0] = +2 / (right - left);
m[1][1] = +2 / (top - bottom);
m[2][2] = -2 / (far - near);
@@ -267,23 +308,41 @@ ortho3d :: proc(left, right, bottom, top, near, far: Float) -> (m: Matrix4) {
}
axis_angle :: proc(axis: Vector3, angle_radians: Float) -> Quaternion {
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);
}
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 :: proc(pitch, yaw, roll: Float) -> Quaternion {
p := axis_angle({1, 0, 0}, pitch);
y := axis_angle({0, 1, 0}, yaw);
r := axis_angle({0, 0, 1}, roll);
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));
return;
}