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authorWolfgang Draxinger <Wolfgang.Draxinger@draxit.de>2016-04-24 23:52:45 +0200
committerWolfgang Draxinger <Wolfgang.Draxinger@draxit.de>2016-04-24 23:52:45 +0200
commit2ca04fbe7985ee944f3fa6302886a252a51add0c (patch)
treeb373879928a1060e564d29d44f6e20b620b272e9 /linmath.h
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Diffstat (limited to 'linmath.h')
-rw-r--r--linmath.h/LICENCE13
-rw-r--r--linmath.h/README12
-rw-r--r--linmath.h/linmath.h474
3 files changed, 499 insertions, 0 deletions
diff --git a/linmath.h/LICENCE b/linmath.h/LICENCE
new file mode 100644
index 0000000..bb3444d
--- /dev/null
+++ b/linmath.h/LICENCE
@@ -0,0 +1,13 @@
+ DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
+ Version 2, December 2004
+
+ Copyright (C) 2013 Wolfgang 'datenwolf' Draxinger <code@datenwolf.net>
+
+ Everyone is permitted to copy and distribute verbatim or modified
+ copies of this license document, and changing it is allowed as long
+ as the name is changed.
+
+ DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. You just DO WHAT THE FUCK YOU WANT TO.
diff --git a/linmath.h/README b/linmath.h/README
new file mode 100644
index 0000000..9c43c8e
--- /dev/null
+++ b/linmath.h/README
@@ -0,0 +1,12 @@
+# linmath.h -- A small library for linear math as required for computer graphics
+
+linmath.h provides the most used types required programming computer graphice:
+
+vec3 -- 3 element vector of floats
+vec4 -- 4 element vector of floats (4th component used for homogenous computations)
+mat4x4 -- 4 by 4 elements matrix, computations are done in column major order
+quat -- quaternion
+
+The types are deliberately named like the types in GLSL. In fact they are meant to
+be used for the client side computations and passing to same typed GLSL uniforms.
+
diff --git a/linmath.h/linmath.h b/linmath.h/linmath.h
new file mode 100644
index 0000000..d21fd7d
--- /dev/null
+++ b/linmath.h/linmath.h
@@ -0,0 +1,474 @@
+#ifndef LINMATH_H
+#define LINMATH_H
+
+#include <math.h>
+#include <string.h>
+
+#define LINMATH_H_DEFINE_VEC(n) \
+typedef float vec##n[n]; \
+static inline void vec##n##_add(vec##n r, vec##n a, vec##n b) \
+{ \
+ int i; \
+ for(i=0; i<n; ++i) \
+ r[i] = a[i] + b[i]; \
+} \
+static inline void vec##n##_sub(vec##n r, vec##n a, vec##n b) \
+{ \
+ int i; \
+ for(i=0; i<n; ++i) \
+ r[i] = a[i] - b[i]; \
+} \
+static inline void vec##n##_scale(vec##n r, vec##n v, float s) \
+{ \
+ int i; \
+ for(i=0; i<n; ++i) \
+ r[i] = v[i] * s; \
+} \
+static inline float vec##n##_mul_inner(vec##n a, vec##n b) \
+{ \
+ float p = 0.; \
+ int i; \
+ for(i=0; i<n; ++i) \
+ p += b[i]*a[i]; \
+ return p; \
+} \
+static inline float vec##n##_len(vec##n v) \
+{ \
+ return sqrtf(vec##n##_mul_inner(v,v)); \
+} \
+static inline void vec##n##_norm(vec##n r, vec##n v) \
+{ \
+ float k = 1.0 / vec##n##_len(v); \
+ vec##n##_scale(r, v, k); \
+}
+
+LINMATH_H_DEFINE_VEC(2);
+LINMATH_H_DEFINE_VEC(3);
+LINMATH_H_DEFINE_VEC(4);
+
+static inline void vec3_mul_cross(vec3 r, vec3 a, vec3 b)
+{
+ vec3 c;
+ c[0] = a[1]*b[2] - a[2]*b[1];
+ c[1] = a[2]*b[0] - a[0]*b[2];
+ c[2] = a[0]*b[1] - a[1]*b[0];
+ memcpy(r, c, sizeof(c));
+}
+
+static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b)
+{
+ vec4 c;
+ c[0] = a[1]*b[2] - a[2]*b[1];
+ c[1] = a[2]*b[0] - a[0]*b[2];
+ c[2] = a[0]*b[1] - a[1]*b[0];
+ c[3] = 1.;
+ memcpy(r, c, sizeof(c));
+}
+
+typedef vec4 mat4x4[4];
+static inline void mat4x4_identity(mat4x4 M)
+{
+ int i, j;
+ for(j=0; j<4; ++j) for(i=0; i<4; ++i) {
+ M[i][j] = i==j ? 1 : 0;
+ }
+}
+static inline void mat4x4_dup(mat4x4 M, mat4x4 N)
+{
+ int i, j;
+ for(j=0; j<4; ++j) {
+ for(i=0; i<4; ++i) {
+ M[i][j] = N[i][j];
+ }
+ }
+}
+static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b)
+{
+ int i;
+ for(i=0; i<4; ++i)
+ vec4_add(M[i], a[i], b[i]);
+}
+static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b)
+{
+ int i;
+ for(i=0; i<4; ++i)
+ vec4_sub(M[i], a[i], b[i]);
+}
+static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k)
+{
+ int i;
+ for(i=0; i<4; ++i)
+ vec4_scale(M[i], a[i], k);
+}
+static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z)
+{
+ vec4_scale(M[0], a[0], x);
+ vec4_scale(M[1], a[1], y);
+ vec4_scale(M[2], a[2], z);
+}
+static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b)
+{
+ int k, r, c;
+ mat4x4 R;
+ for(r=0; r<4; ++r) for(c=0; c<4; ++c) {
+ R[c][r] = 0;
+ for(k=0; k<4; ++k) {
+ R[c][r] += a[k][r] * b[c][k];
+ }
+ }
+ memcpy(M, R, sizeof(R));
+}
+static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v)
+{
+ vec4 r_;
+ int i, j;
+ for(j=0; j<4; ++j) {
+ r_[j] = 0.;
+ for(i=0; i<4; ++i) {
+ r_[j] += M[i][j] * v[i];
+ }
+ }
+ memcpy(r, r_, sizeof(r_));
+}
+static inline void mat4x4_translate(mat4x4 T, float x, float y, float z)
+{
+ mat4x4_identity(T);
+ T[3][0] = x;
+ T[3][1] = y;
+ T[3][2] = z;
+}
+static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b)
+{
+ int i, j;
+ for(i=0; i<4; ++i) for(j=0; j<4; ++j) {
+ M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.;
+ }
+}
+static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle)
+{
+ float s = sinf(angle);
+ float 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, float angle)
+{
+ float s = sinf(angle);
+ float c = cosf(angle);
+ mat4x4 R = {
+ {1, 0, 0, 0},
+ {0, c, s, 0},
+ {0,-s, c, 0},
+ {0, 0, 0, 1}
+ };
+ mat4x4_mul(Q, M, R);
+}
+static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle)
+{
+ float s = sinf(angle);
+ float c = cosf(angle);
+ mat4x4 R = {
+ { c, 0, s, 0},
+ { 0, 1, 0, 0},
+ {-s, 0, c, 0},
+ { 0, 0, 0, 1}
+ };
+ mat4x4_mul(Q, M, R);
+}
+static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle)
+{
+ float s = sinf(angle);
+ float c = cosf(angle);
+ mat4x4 R = {
+ { c, s, 0, 0},
+ {-s, c, 0, 0},
+ { 0, 0, 1, 0},
+ { 0, 0, 0, 1}
+ };
+ mat4x4_mul(Q, M, R);
+}
+static inline void mat4x4_row(vec4 r, mat4x4 M, int i)
+{
+ int k;
+ for(k=0; k<4; ++k)
+ r[k] = M[k][i];
+}
+static inline void mat4x4_col(vec4 r, mat4x4 M, int i)
+{
+ int k;
+ for(k=0; k<4; ++k)
+ r[k] = M[i][k];
+}
+static inline void mat4x4_transpose(mat4x4 M, mat4x4 N)
+{
+ int i, j;
+ mat4x4 R;
+ for(j=0; j<4; ++j) {
+ for(i=0; i<4; ++i) {
+ R[i][j] = N[j][i];
+ }
+ }
+ memcpy(M, R, sizeof(R));
+}
+static inline void mat4x4_invert(mat4x4 T, mat4x4 M)
+{
+ mat4x4 R;
+ R[0][0] = M[1][1]*(M[2][2]*M[3][3] - M[2][3]*M[3][2]) - M[2][1]*(M[1][2]*M[3][3] - M[1][3]*M[3][2]) - M[3][1]*(M[1][3]*M[2][2] - M[1][2]*M[2][3]);
+ R[0][1] = M[0][1]*(M[2][3]*M[3][2] - M[2][2]*M[3][3]) - M[2][1]*(M[0][3]*M[3][2] - M[0][2]*M[3][3]) - M[3][1]*(M[0][2]*M[2][3] - M[0][3]*M[2][2]);
+ R[0][2] = M[0][1]*(M[1][2]*M[3][3] - M[1][3]*M[3][2]) - M[1][1]*(M[0][2]*M[3][3] - M[0][3]*M[3][2]) - M[3][1]*(M[0][3]*M[1][2] - M[0][2]*M[1][3]);
+ R[0][3] = M[0][1]*(M[1][3]*M[2][2] - M[1][2]*M[2][3]) - M[1][1]*(M[0][3]*M[2][2] - M[0][2]*M[2][3]) - M[2][1]*(M[0][2]*M[1][3] - M[0][3]*M[1][2]);
+
+ R[1][0] = M[1][0]*(M[2][3]*M[3][2] - M[2][2]*M[3][3]) - M[2][0]*(M[1][3]*M[3][2] - M[1][2]*M[3][3]) - M[3][0]*(M[1][2]*M[2][3] - M[1][3]*M[2][2]);
+ R[1][1] = M[0][0]*(M[2][2]*M[3][3] - M[2][3]*M[3][2]) - M[2][0]*(M[0][2]*M[3][3] - M[0][3]*M[3][2]) - M[3][0]*(M[0][3]*M[2][2] - M[0][2]*M[2][3]);
+ R[1][2] = M[0][0]*(M[1][3]*M[3][2] - M[1][2]*M[3][3]) - M[1][0]*(M[0][3]*M[3][2] - M[0][2]*M[3][3]) - M[3][0]*(M[0][2]*M[1][3] - M[0][3]*M[1][2]);
+ R[1][3] = M[0][0]*(M[1][2]*M[2][3] - M[1][3]*M[2][2]) - M[1][0]*(M[0][2]*M[2][3] - M[0][3]*M[2][2]) - M[2][0]*(M[0][3]*M[1][2] - M[0][2]*M[1][3]);
+
+ R[2][0] = M[1][0]*(M[2][1]*M[3][3] - M[2][3]*M[3][1]) - M[2][0]*(M[1][1]*M[3][3] - M[1][3]*M[3][1]) - M[3][0]*(M[1][3]*M[2][1] - M[1][1]*M[2][3]);
+ R[2][1] = M[0][0]*(M[2][3]*M[3][1] - M[2][1]*M[3][3]) - M[2][0]*(M[0][3]*M[3][1] - M[0][1]*M[3][3]) - M[3][0]*(M[0][1]*M[2][3] - M[0][3]*M[2][1]);
+ R[2][2] = M[0][0]*(M[1][1]*M[3][3] - M[1][3]*M[3][1]) - M[1][0]*(M[0][1]*M[3][3] - M[0][3]*M[3][1]) - M[3][0]*(M[0][3]*M[1][1] - M[0][1]*M[1][3]);
+ R[2][3] = M[0][0]*(M[1][3]*M[2][1] - M[1][1]*M[2][3]) - M[1][0]*(M[0][3]*M[2][1] - M[0][1]*M[2][3]) - M[2][0]*(M[0][1]*M[1][3] - M[0][3]*M[1][1]);
+
+ R[3][0] = M[1][0]*(M[2][2]*M[3][1] - M[2][1]*M[3][2]) - M[2][0]*(M[1][2]*M[3][1] - M[1][1]*M[3][2]) - M[3][0]*(M[1][1]*M[2][2] - M[1][2]*M[2][1]);
+ R[3][1] = M[0][0]*(M[2][1]*M[3][2] - M[2][2]*M[3][1]) - M[2][0]*(M[0][1]*M[3][2] - M[0][2]*M[3][1]) - M[3][0]*(M[0][2]*M[2][1] - M[0][1]*M[2][2]);
+ R[3][2] = M[0][0]*(M[1][2]*M[3][1] - M[1][1]*M[3][2]) - M[1][0]*(M[0][2]*M[3][1] - M[0][1]*M[3][2]) - M[3][0]*(M[0][1]*M[1][2] - M[0][2]*M[1][1]);
+ R[3][3] = M[0][0]*(M[1][1]*M[2][2] - M[1][2]*M[2][1]) - M[1][0]*(M[0][1]*M[2][2] - M[0][2]*M[2][1]) - M[2][0]*(M[0][2]*M[1][1] - M[0][1]*M[1][2]);
+ memcpy(T, R, 16*sizeof(float));
+}
+static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M)
+{
+ mat4x4_dup(R, M);
+ float 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, float l, float r, float b, float t, float n, float f)
+{
+ M[0][0] = 2.*n/(r-l);
+ M[0][1] = M[0][2] = M[0][3] = 0.;
+
+ M[1][1] = 2.*n/(t-b);
+ M[1][0] = M[1][2] = M[1][3] = 0.;
+
+ 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;
+
+ M[3][2] = -2.*(f*n)/(f-n);
+ M[3][0] = M[3][1] = M[3][3] = 0.;
+}
+static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f)
+{
+ M[0][0] = 2./(r-l);
+ M[0][1] = M[0][2] = M[0][3] = 0.;
+
+ M[1][1] = 2./(t-b);
+ M[1][0] = M[1][2] = M[1][3] = 0.;
+
+ M[2][2] = -2./(f-n);
+ M[2][0] = M[2][1] = M[2][3] = 0.;
+
+ 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.;
+}
+
+typedef float quat[4];
+static inline void quat_identity(quat q)
+{
+ q[0] = q[1] = q[2] = 0.;
+ q[3] = 1.;
+}
+static inline void quat_add(quat r, quat a, quat b)
+{
+ int i;
+ for(i=0; i<4; ++i)
+ r[i] = a[i] + b[i];
+}
+static inline void quat_sub(quat r, quat a, quat b)
+{
+ int i;
+ for(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, float s)
+{
+ int i;
+ for(i=0; i<4; ++i)
+ r[i] = v[i] * s;
+}
+static inline float quat_inner_product(quat a, quat b)
+{
+ float p = 0.;
+ int i;
+ for(i=0; i<4; ++i)
+ p += b[i]*a[i];
+ return p;
+}
+static inline void quat_conj(quat r, quat q)
+{
+ int i;
+ for(i=0; i<3; ++i)
+ r[i] = -q[i];
+ r[3] = q[3];
+}
+static inline void quat_norm(quat r, quat v) { vec4_norm(r, v); }
+static inline void quat_mul_vec3(vec3 r, quat q, vec3 v)
+{
+ quat q_;
+ quat v_ = {v[0], v[1], v[2], 0.};
+
+ quat_conj(q_, q);
+ quat_norm(q_, q_);
+ quat_mul(q_, v_, q_);
+ quat_mul(q_, q, q_);
+ memcpy(r, q_, 3*sizeof(float));
+}
+static inline void mat4x4_from_quat(mat4x4 M, quat q)
+{
+ float a = q[3];
+ float b = q[0];
+ float c = q[1];
+ float d = q[2];
+ float a2 = a*a;
+ float b2 = b*b;
+ float c2 = c*c;
+ float d2 = d*d;
+
+ M[0][0] = a2 + b2 - c2 - d2;
+ M[0][1] = 2*(b*c + a*d);
+ M[0][2] = 2*(b*d - a*c);
+ M[0][3] = 0.;
+
+ M[1][0] = 2*(b*c - a*d);
+ M[1][1] = a2 - b2 + c2 - d2;
+ M[1][2] = 2*(c*d + a*b);
+ M[1][3] = 0.;
+
+ M[2][0] = 2*(b*d + a*c);
+ M[2][1] = 2*(c*d - a*b);
+ M[2][2] = a2 - b2 - c2 + d2;
+ M[2][3] = 0.;
+
+ M[3][0] = M[3][1] = M[3][2] = 0.;
+ M[3][3] = 1.;
+}
+static inline void mat4x4_mul_quat(mat4x4 R, mat4x4 M, quat q)
+{
+ quat_mul_vec3(R[0], M[0], q);
+ quat_mul_vec3(R[1], M[1], q);
+ quat_mul_vec3(R[2], M[2], q);
+
+ R[3][0] = R[3][1] = R[3][2] = 0.;
+ R[3][3] = 1.;
+}
+static inline void quat_from_mat4x4(quat q, mat4x4 M)
+{
+ float r=0.;
+ int i;
+
+ int perm[] = { 0, 1, 2, 0, 1 };
+ int *p = perm;
+
+ for(i = 0; i<3; i++) {
+ float m = M[i][i];
+ if( m < r )
+ continue;
+ m = r;
+ p = &perm[i];
+ }
+
+ r = sqrtf(1. + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]] );
+
+ q[0] = r/2.;
+ q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.*r);
+ q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.*r);
+ q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.*r);
+}
+
+static inline void mat4x4_arcball(mat4x4 R, mat4x4 M, vec2 _a, vec2 _b, float s)
+{
+ vec2 a; memcpy(a, _a, sizeof(a));
+ vec2 b; memcpy(b, _b, sizeof(b));
+
+ float z_a = 0.;
+ float z_b = 0.;
+
+ if(vec2_len(a) < 1.) {
+ z_a = sqrtf(1. - vec2_mul_inner(a, a));
+ } else {
+ vec2_norm(a, a);
+ }
+
+ if(vec2_len(b) < 1.) {
+ z_b = sqrtf(1. - vec2_mul_inner(b, b));
+ } else {
+ vec2_norm(b, b);
+ }
+
+ vec3 a_ = {a[0], a[1], z_a};
+ vec3 b_ = {b[0], b[1], z_b};
+
+ vec3 c_;
+ vec3_mul_cross(c_, a_, b_);
+
+ float const angle = acos(vec3_mul_inner(a_, b_)) * s;
+ mat4x4_rotate(R, M, c_[0], c_[1], c_[2], angle);
+}
+
+#endif