path: root/linmath.h

/*
 * Copyright (C) 2013 Wolfgang 'datenwolf' Draxinger <code@datenwolf.net>
 * Copyright (C) 2018 Tomasz Kramkowski <tk@the-tk.com>
 * SPDX-License-Identifier: WTFPL
 */
#ifndef LINMATH_H
#define LINMATH_H

#include <math.h>

typedef float lm_elem;
#define LINMATH_H_DEFINE_VEC(n) \
typedef lm_elem vec##n[n]; \
static inline void vec##n##_add(vec##n r, vec##n const a, vec##n const b) \
{ \
	for (int i = 0; i < n; ++i) \
		r[i] = a[i] + b[i]; \
} \
static inline void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) \
{ \
	for (int i = 0; i < n; ++i) \
		r[i] = a[i] - b[i]; \
} \
static inline void vec##n##_scale(vec##n r, vec##n const v, lm_elem const s) \
{ \
	for (int i = 0; i < n; ++i) \
		r[i] = v[i] * s; \
} \
static inline lm_elem vec##n##_mul_inner(vec##n const a, vec##n const b) \
{ \
	lm_elem p = 0.0; \
	for (int i = 0; i < n; ++i) \
		p += b[i] * a[i]; \
	return p; \
} \
static inline lm_elem vec##n##_len(vec##n const v) \
{ \
	return sqrtf(vec##n##_mul_inner(v, v)); \
} \
static inline void vec##n##_norm(vec##n r, vec##n const v) \
{ \
	lm_elem k = 1.0 / vec##n##_len(v); \
	vec##n##_scale(r, v, k); \
} \
static inline void vec##n##_min(vec##n r, vec##n a, vec##n b) \
{ \
	for (int i = 0; i < n; ++i) \
		r[i] = a[i] < b[i] ? a[i] : b[i]; \
} \
static inline void vec##n##_max(vec##n r, vec##n a, vec##n b) \
{ \
	for (int i = 0; i < n; ++i) \
		r[i] = a[i] > b[i] ? a[i] : b[i]; \
}

LINMATH_H_DEFINE_VEC(2)
LINMATH_H_DEFINE_VEC(3)
LINMATH_H_DEFINE_VEC(4)

static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b)
{
	r[0] = a[1] * b[2] - a[2] * b[1];
	r[1] = a[2] * b[0] - a[0] * b[2];
	r[2] = a[0] * b[1] - a[1] * b[0];
}

static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n)
{
	lm_elem p  = 2.0f * vec3_mul_inner(v, n);
	for (int i = 0; i < 3; ++i)
		r[i] = v[i] - p * n[i];
}

static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b)
{
	r[0] = a[1] * b[2] - a[2] * b[1];
	r[1] = a[2] * b[0] - a[0] * b[2];
	r[2] = a[0] * b[1] - a[1] * b[0];
	r[3] = 1.0f;
}

static inline void vec4_reflect(vec4 r, vec4 v, vec4 n)
{
	lm_elem p  = 2.0f * vec4_mul_inner(v, n);
	for (int i = 0; i < 4; ++i)
		r[i] = v[i] - p * n[i];
}

typedef vec4 mat4x4[4];
static inline void mat4x4_identity(mat4x4 M)
{
	for (int i = 0; i < 4; ++i)
		for (int j = 0; j < 4; ++j)
			M[i][j] = i == j ? 1.0f : 0.0f;
}
static inline void mat4x4_dup(mat4x4 M, mat4x4 N)
{
	for (int i = 0; i < 4; ++i)
		for (int j = 0; j < 4; ++j)
			M[i][j] = N[i][j];
}
static inline void mat4x4_row(vec4 r, mat4x4 M, int i)
{
	for (int k = 0; k < 4; ++k)
		r[k] = M[k][i];
}
static inline void mat4x4_col(vec4 r, mat4x4 M, int i)
{
	for (int k = 0; k < 4; ++k)
		r[k] = M[i][k];
}
static inline void mat4x4_transpose(mat4x4 M, mat4x4 N)
{
	for (int j = 0; j < 4; ++j)
		for (int i = 0; i < 4; ++i)
			M[i][j] = N[j][i];
}
static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b)
{
	for (int i = 0; i < 4; ++i)
		vec4_add(M[i], a[i], b[i]);
}
static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b)
{
	for (int i = 0; i < 4; ++i)
		vec4_sub(M[i], a[i], b[i]);
}
static inline void mat4x4_scale(mat4x4 M, mat4x4 a, lm_elem k)
{
	for (int i = 0; i < 4; ++i)
		vec4_scale(M[i], a[i], k);
}
static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, lm_elem x, lm_elem y, lm_elem z)
{
	vec4_scale(M[0], a[0], x);
	vec4_scale(M[1], a[1], y);
	vec4_scale(M[2], a[2], z);
	for (int i = 0; i < 4; ++i)
		M[3][i] = a[3][i];
}
static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b)
{
	mat4x4 temp;
	for (int c = 0; c < 4; ++c) {
		for (int r = 0; r < 4; ++r) {
			temp[c][r] = 0.0f;
			for (int k = 0; k < 4; ++k)
				temp[c][r] += a[k][r] * b[c][k];
		}
	}
	mat4x4_dup(M, temp);
}
static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v)
{
	for (int j = 0; j < 4; ++j) {
		r[j] = 0.0f;
		for (int i = 0; i < 4; ++i)
			r[j] += M[i][j] * v[i];
	}
}
static inline void mat4x4_translate(mat4x4 T, lm_elem x, lm_elem y, lm_elem z)
{
	mat4x4_identity(T);
	T[3][0] = x;
	T[3][1] = y;
	T[3][2] = z;
}
static inline void mat4x4_translate_in_place(mat4x4 M, lm_elem x, lm_elem y, lm_elem z)
{
	vec4 t = {x, y, z, 0};
	vec4 r;
	for (int i = 0; i < 4; ++i) {
		mat4x4_row(r, M, i);
		M[3][i] += vec4_mul_inner(r, t);
	}
}
static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b)
{
	for (int i = 0; i < 4; ++i)
		for (int j = 0; j < 4; ++j)
			M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.0f;
}
static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, lm_elem x, lm_elem y, lm_elem z, lm_elem angle)
{
	lm_elem s = sinf(angle);
	lm_elem c = cosf(angle);
	vec3 u = {x, y, z};

	if (vec3_len(u) > 1e-4) {
		vec3_norm(u, u);
		mat4x4 T;
		mat4x4_from_vec3_mul_outer(T, u, u);

		mat4x4 S = {
			{    0,  u[2], -u[1], 0},
			{-u[2],     0,  u[0], 0},
			{ u[1], -u[0],     0, 0},
			{    0,     0,     0, 0}
		};
		mat4x4_scale(S, S, s);

		mat4x4 C;
		mat4x4_identity(C);
		mat4x4_sub(C, C, T);

		mat4x4_scale(C, C, c);

		mat4x4_add(T, T, C);
		mat4x4_add(T, T, S);

		T[3][3] = 1.;
		mat4x4_mul(R, M, T);
	} else {
		mat4x4_dup(R, M);
	}
}
static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, lm_elem angle)
{
	lm_elem s = sinf(angle);
	lm_elem c = cosf(angle);
	mat4x4 R = {
		{1.0f, 0.0f, 0.0f, 0.0f},
		{0.0f,    c,    s, 0.0f},
		{0.0f,   -s,    c, 0.0f},
		{0.0f, 0.0f, 0.0f, 1.0f}
	};
	mat4x4_mul(Q, M, R);
}
static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, lm_elem angle)
{
	lm_elem s = sinf(angle);
	lm_elem c = cosf(angle);
	mat4x4 R = {
		{    c, 0.0f,    s, 0.0f},
		{ 0.0f, 1.0f, 0.0f, 0.0f},
		{   -s, 0.0f,    c, 0.0f},
		{ 0.0f, 0.0f, 0.0f, 1.0f}
	};
	mat4x4_mul(Q, M, R);
}
static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, lm_elem angle)
{
	lm_elem s = sinf(angle);
	lm_elem c = cosf(angle);
	mat4x4 R = {
		{    c,    s, 0.0f, 0.0f},
		{   -s,    c, 0.0f, 0.0f},
		{ 0.0f, 0.0f, 1.0f, 0.0f},
		{ 0.0f, 0.0f, 0.0f, 1.0f}
	};
	mat4x4_mul(Q, M, R);
}
static inline void mat4x4_invert(mat4x4 T, mat4x4 M)
{
	lm_elem s[6];
	lm_elem c[6];
	s[0] = M[0][0] * M[1][1] - M[1][0] * M[0][1];
	s[1] = M[0][0] * M[1][2] - M[1][0] * M[0][2];
	s[2] = M[0][0] * M[1][3] - M[1][0] * M[0][3];
	s[3] = M[0][1] * M[1][2] - M[1][1] * M[0][2];
	s[4] = M[0][1] * M[1][3] - M[1][1] * M[0][3];
	s[5] = M[0][2] * M[1][3] - M[1][2] * M[0][3];

	c[0] = M[2][0] * M[3][1] - M[3][0] * M[2][1];
	c[1] = M[2][0] * M[3][2] - M[3][0] * M[2][2];
	c[2] = M[2][0] * M[3][3] - M[3][0] * M[2][3];
	c[3] = M[2][1] * M[3][2] - M[3][1] * M[2][2];
	c[4] = M[2][1] * M[3][3] - M[3][1] * M[2][3];
	c[5] = M[2][2] * M[3][3] - M[3][2] * M[2][3];

	/* Assumes it is invertible */
	lm_elem idet = 1.0f / (s[0] * c[5] - s[1] * c[4]
			       + s[2] * c[3] + s[3] * c[2]
			       - s[4] * c[1] + s[5] * c[0]);

	T[0][0] = ( M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet;
	T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet;
	T[0][2] = ( M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet;
	T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet;

	T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet;
	T[1][1] = ( M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet;
	T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet;
	T[1][3] = ( M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet;

	T[2][0] = ( M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet;
	T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet;
	T[2][2] = ( M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet;
	T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet;

	T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet;
	T[3][1] = ( M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet;
	T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet;
	T[3][3] = ( M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet;
}
static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M)
{
	mat4x4_dup(R, M);
	lm_elem s = 1.;
	vec3 h;

	vec3_norm(R[2], R[2]);

	s = vec3_mul_inner(R[1], R[2]);
	vec3_scale(h, R[2], s);
	vec3_sub(R[1], R[1], h);
	vec3_norm(R[2], R[2]);

	s = vec3_mul_inner(R[1], R[2]);
	vec3_scale(h, R[2], s);
	vec3_sub(R[1], R[1], h);
	vec3_norm(R[1], R[1]);

	s = vec3_mul_inner(R[0], R[1]);
	vec3_scale(h, R[1], s);
	vec3_sub(R[0], R[0], h);
	vec3_norm(R[0], R[0]);
}

static inline void mat4x4_frustum(mat4x4 M, lm_elem l, lm_elem r, lm_elem b, lm_elem t, lm_elem n, lm_elem f)
{
	M[0][0] = 2.0f * n/(r-l);
	M[0][1] = M[0][2] = M[0][3] = 0.0f;

	M[1][1] = 2.0 * n/(t-b);
	M[1][0] = M[1][2] = M[1][3] = 0.0f;

	M[2][0] = (r+l)/(r-l);
	M[2][1] = (t+b)/(t-b);
	M[2][2] = -(f+n)/(f-n);
	M[2][3] = -1.0f;

	M[3][2] = -2.0f * (f * n)/(f-n);
	M[3][0] = M[3][1] = M[3][3] = 0.0f;
}
static inline void mat4x4_ortho(mat4x4 M, lm_elem l, lm_elem r, lm_elem b, lm_elem t, lm_elem n, lm_elem f)
{
	M[0][0] = 2.0f/(r-l);
	M[0][1] = M[0][2] = M[0][3] = 0.0f;

	M[1][1] = 2.0f/(t-b);
	M[1][0] = M[1][2] = M[1][3] = 0.0f;

	M[2][2] = -2.0f/(f-n);
	M[2][0] = M[2][1] = M[2][3] = 0.0f;

	M[3][0] = -(r+l)/(r-l);
	M[3][1] = -(t+b)/(t-b);
	M[3][2] = -(f+n)/(f-n);
	M[3][3] = 1.0f;
}
static inline void mat4x4_perspective(mat4x4 m, lm_elem y_fov, lm_elem aspect, lm_elem n, lm_elem f)
{
	lm_elem const a = 1.0f / tan(y_fov / 2.0f);

	m[0][0] = a / aspect;
	m[0][1] = 0.0f;
	m[0][2] = 0.0f;
	m[0][3] = 0.0f;

	m[1][0] = 0.0f;
	m[1][1] = a;
	m[1][2] = 0.0f;
	m[1][3] = 0.0f;

	m[2][0] = 0.0f;
	m[2][1] = 0.0f;
	m[2][2] = -((f + n) / (f - n));
	m[2][3] = -1.0f;

	m[3][0] = 0.0f;
	m[3][1] = 0.0f;
	m[3][2] = -((2.0f * f * n) / (f - n));
	m[3][3] = 0.0f;
}
static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up)
{
	/* Adapted from Android's OpenGL Matrix.java.                        */
	/* See the OpenGL GLUT documentation for gluLookAt for a description */
	/* of the algorithm. We implement it in a straightforward way:       */

	/* TODO: The negation of of can be spared by swapping the order of
	 *       operands in the following cross products in the right way. */
	vec3 f;
	vec3_sub(f, center, eye);
	vec3_norm(f, f);

	vec3 s;
	vec3_mul_cross(s, f, up);
	vec3_norm(s, s);

	vec3 t;
	vec3_mul_cross(t, s, f);

	m[0][0] =  s[0];
	m[0][1] =  t[0];
	m[0][2] = -f[0];
	m[0][3] =   0.0f;

	m[1][0] =  s[1];
	m[1][1] =  t[1];
	m[1][2] = -f[1];
	m[1][3] =   0.0f;

	m[2][0] =  s[2];
	m[2][1] =  t[2];
	m[2][2] = -f[2];
	m[2][3] =   0.0f;

	m[3][0] =  0.0f;
	m[3][1] =  0.0f;
	m[3][2] =  0.0f;
	m[3][3] =  1.0f;

	mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]);
}

typedef lm_elem quat[4];
static inline void quat_identity(quat q)
{
	q[0] = q[1] = q[2] = 0.0f;
	q[3] = 1.0f;
}
static inline void quat_add(quat r, quat a, quat b)
{
	for (int i = 0; i < 4; ++i)
		r[i] = a[i] + b[i];
}
static inline void quat_sub(quat r, quat a, quat b)
{
	for (int i = 0; i < 4; ++i)
		r[i] = a[i] - b[i];
}
static inline void quat_mul(quat r, quat p, quat q)
{
	vec3 w;
	vec3_mul_cross(r, p, q);
	vec3_scale(w, p, q[3]);
	vec3_add(r, r, w);
	vec3_scale(w, q, p[3]);
	vec3_add(r, r, w);
	r[3] = p[3]*q[3] - vec3_mul_inner(p, q);
}
static inline void quat_scale(quat r, quat v, lm_elem s)
{
	for (int i = 0; i < 4; ++i)
		r[i] = v[i] * s;
}
static inline lm_elem quat_inner_product(quat a, quat b)
{
	lm_elem p = 0.0f;
	for (int i = 0; i < 4; ++i)
		p += b[i]*a[i];
	return p;
}
static inline void quat_conj(quat r, quat q)
{
	for (int i = 0; i < 3; ++i)
		r[i] = -q[i];
	r[3] = q[3];
}
static inline void quat_rotate(quat r, lm_elem angle, vec3 axis) {
	vec3 v;
	vec3_scale(v, axis, sinf(angle / 2));
	for (int i = 0; i < 3; ++i)
		r[i] = v[i];
	r[3] = cosf(angle / 2);
}
#define quat_norm vec4_norm
static inline void quat_mul_vec3(vec3 r, quat q, vec3 v)
{
/*
 * Method by Fabian 'ryg' Giessen (of Farbrausch)
t = 2 * cross(q.xyz, v)
v' = v + q.w * t + cross(q.xyz, t)
 */
	vec3 t;
	vec3 q_xyz = { q[0], q[1], q[2] };
	vec3 u = { q[0], q[1], q[2] };

	vec3_mul_cross(t, q_xyz, v);
	vec3_scale(t, t, 2);

	vec3_mul_cross(u, q_xyz, t);
	vec3_scale(t, t, q[3]);

	vec3_add(r, v, t);
	vec3_add(r, r, u);
}
static inline void mat4x4_from_quat(mat4x4 M, quat q)
{
	lm_elem a = q[3];
	lm_elem b = q[0];
	lm_elem c = q[1];
	lm_elem d = q[2];
	lm_elem a2 = a * a;
	lm_elem b2 = b * b;
	lm_elem c2 = c * c;
	lm_elem d2 = d * d;

	M[0][0] = a2 + b2 - c2 - d2;
	M[0][1] = 2.0f * (b * c + a * d);
	M[0][2] = 2.0f * (b * d - a * c);
	M[0][3] = 0.0f;

	M[1][0] = 2 * (b * c - a * d);
	M[1][1] = a2 - b2 + c2 - d2;
	M[1][2] = 2.0f * (c * d + a * b);
	M[1][3] = 0.0f;

	M[2][0] = 2.0f * (b * d + a * c);
	M[2][1] = 2.0f * (c * d - a * b);
	M[2][2] = a2 - b2 - c2 + d2;
	M[2][3] = 0.0f;

	M[3][0] = M[3][1] = M[3][2] = 0.0f;
	M[3][3] = 1.0f;
}

static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q)
{
/*  XXX: The way this is written only works for othogonal matrices. */
/* TODO: Take care of non-orthogonal case. */
	quat_mul_vec3(R[0], q, M[0]);
	quat_mul_vec3(R[1], q, M[1]);
	quat_mul_vec3(R[2], q, M[2]);

	R[3][0] = R[3][1] = R[3][2] = 0.0f;
	R[3][3] = 1.0f;
}

static inline void quat_from_mat4x4(quat q, mat4x4 M)
{
	lm_elem r = 0.0f;
	int i;

	int perm[] = { 0, 1, 2, 0, 1 };
	int *p = perm;

	for (int i = 0; i < 3; i++) {
		lm_elem m = M[i][i];
		if (m < r)
			continue;
		m = r;
		p = &perm[i];
	}

	r = sqrtf(1.0f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]);

	if (r < 1e-6) {
		q[0] = 1.0f;
		q[1] = q[2] = q[3] = 0.0f;
		return;
	}

	q[0] = r/2.0f;
	q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.0f * r);
	q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.0f * r);
	q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.0f * r);
}

#endif // LINMATH_H