--- /dev/null
+/* gph-cmath - C graphics math library
+ * Copyright (C) 2018 John Tsiombikas <nuclear@member.fsf.org>
+ *
+ * This program is free software. Feel free to use, modify, and/or redistribute
+ * it under the terms of the MIT/X11 license. See LICENSE for details.
+ * If you intend to redistribute parts of the code without the LICENSE file
+ * replace this paragraph with the full contents of the LICENSE file.
+ */
+static inline void cgm_mcopy(float *dest, const float *src)
+{
+ memcpy(dest, src, 16 * sizeof(float));
+}
+
+static inline void cgm_mzero(float *m)
+{
+ static float z[16];
+ cgm_mcopy(m, z);
+}
+
+static inline void cgm_midentity(float *m)
+{
+ static float id[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};
+ cgm_mcopy(m, id);
+}
+
+static inline void cgm_mmul(float *a, const float *b)
+{
+ int i, j;
+ float res[16];
+ float *resptr = res;
+ float *arow = a;
+
+ for(i=0; i<4; i++) {
+ for(j=0; j<4; j++) {
+ *resptr++ = arow[0] * b[j] + arow[1] * b[4 + j] +
+ arow[2] * b[8 + j] + arow[3] * b[12 + j];
+ }
+ arow += 4;
+ }
+ cgm_mcopy(a, res);
+}
+
+static inline void cgm_mpremul(float *a, const float *b)
+{
+ int i, j;
+ float res[16];
+ float *resptr = res;
+ const float *brow = b;
+
+ for(i=0; i<4; i++) {
+ for(j=0; j<4; j++) {
+ *resptr++ = brow[0] * a[j] + brow[1] * a[4 + j] +
+ brow[2] * a[8 + j] + brow[3] * a[12 + j];
+ }
+ brow += 4;
+ }
+ cgm_mcopy(a, res);
+}
+
+static inline void cgm_msubmatrix(float *m, int row, int col)
+{
+ float orig[16];
+ int i, j, subi, subj;
+
+ cgm_mcopy(orig, m);
+
+ subi = 0;
+ for(i=0; i<4; i++) {
+ if(i == row) continue;
+
+ subj = 0;
+ for(j=0; j<4; j++) {
+ if(j == col) continue;
+
+ m[subi * 4 + subj++] = orig[i * 4 + j];
+ }
+ subi++;
+ }
+
+ cgm_mupper3(m);
+}
+
+static inline void cgm_mupper3(float *m)
+{
+ m[3] = m[7] = m[11] = m[12] = m[13] = m[14] = 0.0f;
+ m[15] = 1.0f;
+}
+
+static inline float cgm_msubdet(const float *m, int row, int col)
+{
+ float tmp[16];
+ float subdet00, subdet01, subdet02;
+
+ cgm_mcopy(tmp, m);
+ cgm_msubmatrix(tmp, row, col);
+
+ subdet00 = tmp[5] * tmp[10] - tmp[6] * tmp[9];
+ subdet01 = tmp[4] * tmp[10] - tmp[6] * tmp[8];
+ subdet02 = tmp[4] * tmp[9] - tmp[5] * tmp[8];
+
+ return tmp[0] * subdet00 - tmp[1] * subdet01 + tmp[2] * subdet02;
+}
+
+static inline float cgm_mcofactor(const float *m, int row, int col)
+{
+ float min = cgm_msubdet(m, row, col);
+ return (row + col) & 1 ? -min : min;
+}
+
+static inline float cgm_mdet(const float *m)
+{
+ return m[0] * cgm_msubdet(m, 0, 0) - m[1] * cgm_msubdet(m, 0, 1) +
+ m[2] * cgm_msubdet(m, 0, 2) - m[3] * cgm_msubdet(m, 0, 3);
+}
+
+static inline void cgm_mtranspose(float *m)
+{
+ int i, j;
+ for(i=0; i<4; i++) {
+ for(j=0; j<i; j++) {
+ int a = i * 4 + j;
+ int b = j * 4 + i;
+ float tmp = m[a];
+ m[a] = m[b];
+ m[b] = tmp;
+ }
+ }
+}
+
+static inline void cgm_mcofmatrix(float *m)
+{
+ float tmp[16];
+ int i, j;
+
+ cgm_mcopy(tmp, m);
+
+ for(i=0; i<4; i++) {
+ for(j=0; j<4; j++) {
+ m[i * 4 + j] = cgm_mcofactor(tmp, i, j);
+ }
+ }
+}
+
+static inline int cgm_minverse(float *m)
+{
+ int i, j;
+ float tmp[16];
+ float inv_det;
+ float det = cgm_mdet(m);
+ if(det == 0.0f) return -1;
+ inv_det = 1.0f / det;
+
+ cgm_mcopy(tmp, m);
+
+ for(i=0; i<4; i++) {
+ for(j=0; j<4; j++) {
+ m[i * 4 + j] = cgm_mcofactor(tmp, j, i) * inv_det; /* transposed */
+ }
+ }
+ return 0;
+}
+
+static inline void cgm_mtranslation(float *m, float x, float y, float z)
+{
+ cgm_midentity(m);
+ m[12] = x;
+ m[13] = y;
+ m[14] = z;
+}
+
+static inline void cgm_mscaling(float *m, float sx, float sy, float sz)
+{
+ cgm_mzero(m);
+ m[0] = sx;
+ m[5] = sy;
+ m[10] = sz;
+ m[15] = 1.0f;
+}
+
+static inline void cgm_mrotation_x(float *m, float angle)
+{
+ float sa = sin(angle);
+ float ca = cos(angle);
+
+ cgm_midentity(m);
+ m[5] = ca;
+ m[6] = sa;
+ m[9] = -sa;
+ m[10] = ca;
+}
+
+static inline void cgm_mrotation_y(float *m, float angle)
+{
+ float sa = sin(angle);
+ float ca = cos(angle);
+
+ cgm_midentity(m);
+ m[0] = ca;
+ m[2] = -sa;
+ m[8] = sa;
+ m[10] = ca;
+}
+
+static inline void cgm_mrotation_z(float *m, float angle)
+{
+ float sa = sin(angle);
+ float ca = cos(angle);
+
+ cgm_midentity(m);
+ m[0] = ca;
+ m[1] = sa;
+ m[4] = -sa;
+ m[5] = ca;
+}
+
+static inline void cgm_mrotation_axis(float *m, int idx, float angle)
+{
+ switch(idx) {
+ case 0:
+ cgm_mrotation_x(m, angle);
+ break;
+ case 1:
+ cgm_mrotation_y(m, angle);
+ break;
+ case 2:
+ cgm_mrotation_z(m, angle);
+ break;
+ }
+}
+
+static inline void cgm_mrotation(float *m, float angle, float x, float y, float z)
+{
+ float sa = sin(angle);
+ float ca = cos(angle);
+ float invca = 1.0f - ca;
+ float xsq = x * x;
+ float ysq = y * y;
+ float zsq = z * z;
+
+ cgm_mzero(m);
+ m[15] = 1.0f;
+
+ m[0] = xsq + (1.0f - xsq) * ca;
+ m[4] = x * y * invca - z * sa;
+ m[8] = x * z * invca + y * sa;
+
+ m[1] = x * y * invca + z * sa;
+ m[5] = ysq + (1.0f - ysq) * ca;
+ m[9] = y * z * invca - x * sa;
+
+ m[2] = x * z * invca - y * sa;
+ m[6] = y * z * invca + x * sa;
+ m[10] = zsq + (1.0f - zsq) * ca;
+}
+
+static inline void cgm_mrotation_euler(float *m, float a, float b, float c, int mode)
+{
+ /* this array must match the EulerMode enum */
+ static const int axis[][3] = {
+ {0, 1, 2}, {0, 2, 1},
+ {1, 0, 2}, {1, 2, 0},
+ {2, 0, 1}, {2, 1, 0},
+ {2, 0, 2}, {2, 1, 2},
+ {1, 0, 1}, {1, 2, 1},
+ {0, 1, 0}, {0, 2, 0}
+ };
+
+ float ma[16], mb[16];
+ cgm_mrotation_axis(ma, axis[mode][0], a);
+ cgm_mrotation_axis(mb, axis[mode][1], b);
+ cgm_mrotation_axis(m, axis[mode][2], c);
+ cgm_mmul(m, mb);
+ cgm_mmul(m, ma);
+}
+
+static inline void cgm_mrotation_quat(float *m, const cgm_quat *q)
+{
+ float xsq2 = 2.0f * q->x * q->x;
+ float ysq2 = 2.0f * q->y * q->y;
+ float zsq2 = 2.0f * q->z * q->z;
+ float sx = 1.0f - ysq2 - zsq2;
+ float sy = 1.0f - xsq2 - zsq2;
+ float sz = 1.0f - xsq2 - ysq2;
+
+ m[3] = m[7] = m[11] = m[12] = m[13] = m[14] = 0.0f;
+ m[15] = 1.0f;
+
+ m[0] = sx;
+ m[1] = 2.0f * q->x * q->y + 2.0f * q->w * q->z;
+ m[2] = 2.0f * q->z * q->x - 2.0f * q->w * q->y;
+ m[4] = 2.0f * q->x * q->y - 2.0f * q->w * q->z;
+ m[5] = sy;
+ m[6] = 2.0f * q->y * q->z + 2.0f * q->w * q->x;
+ m[8] = 2.0f * q->z * q->x + 2.0f * q->w * q->y;
+ m[9] = 2.0f * q->y * q->z - 2.0f * q->w * q->x;
+ m[10] = sz;
+}
+
+static inline void cgm_mtranslate(float *m, float x, float y, float z)
+{
+ float tm[16];
+ cgm_mtranslation(tm, x, y, z);
+ cgm_mmul(m, tm);
+}
+
+static inline void cgm_mscale(float *m, float sx, float sy, float sz)
+{
+ float sm[16];
+ cgm_mscaling(sm, sx, sy, sz);
+ cgm_mmul(m, sm);
+}
+
+static inline void cgm_mrotate_x(float *m, float angle)
+{
+ float rm[16];
+ cgm_mrotation_x(rm, angle);
+ cgm_mmul(m, rm);
+}
+
+static inline void cgm_mrotate_y(float *m, float angle)
+{
+ float rm[16];
+ cgm_mrotation_y(rm, angle);
+ cgm_mmul(m, rm);
+}
+
+static inline void cgm_mrotate_z(float *m, float angle)
+{
+ float rm[16];
+ cgm_mrotation_z(rm, angle);
+ cgm_mmul(m, rm);
+}
+
+static inline void cgm_mrotate_axis(float *m, int idx, float angle)
+{
+ float rm[16];
+ cgm_mrotation_axis(rm, idx, angle);
+ cgm_mmul(m, rm);
+}
+
+static inline void cgm_mrotate(float *m, float angle, float x, float y, float z)
+{
+ float rm[16];
+ cgm_mrotation(rm, angle, x, y, z);
+ cgm_mmul(m, rm);
+}
+
+static inline void cgm_mrotate_euler(float *m, float a, float b, float c, int mode)
+{
+ float rm[16];
+ cgm_mrotation_euler(rm, a, b, c, mode);
+ cgm_mmul(m, rm);
+}
+
+static inline void cgm_mrotate_quat(float *m, const cgm_quat *q)
+{
+ float rm[16];
+ cgm_mrotation_quat(rm, q);
+ cgm_mmul(m, rm);
+}
+
+
+static inline void cgm_mpretranslate(float *m, float x, float y, float z)
+{
+ float tm[16];
+ cgm_mtranslation(tm, x, y, z);
+ cgm_mpremul(m, tm);
+}
+
+static inline void cgm_mprescale(float *m, float sx, float sy, float sz)
+{
+ float sm[16];
+ cgm_mscaling(sm, sx, sy, sz);
+ cgm_mpremul(m, sm);
+}
+
+static inline void cgm_mprerotate_x(float *m, float angle)
+{
+ float rm[16];
+ cgm_mrotation_x(rm, angle);
+ cgm_mpremul(m, rm);
+}
+
+static inline void cgm_mprerotate_y(float *m, float angle)
+{
+ float rm[16];
+ cgm_mrotation_y(rm, angle);
+ cgm_mpremul(m, rm);
+}
+
+static inline void cgm_mprerotate_z(float *m, float angle)
+{
+ float rm[16];
+ cgm_mrotation_z(rm, angle);
+ cgm_mpremul(m, rm);
+}
+
+static inline void cgm_mprerotate_axis(float *m, int idx, float angle)
+{
+ float rm[16];
+ cgm_mrotation_axis(rm, idx, angle);
+ cgm_mpremul(m, rm);
+}
+
+static inline void cgm_mprerotate(float *m, float angle, float x, float y, float z)
+{
+ float rm[16];
+ cgm_mrotation(rm, angle, x, y, z);
+ cgm_mpremul(m, rm);
+}
+
+static inline void cgm_mprerotate_euler(float *m, float a, float b, float c, int mode)
+{
+ float rm[16];
+ cgm_mrotation_euler(rm, a, b, c, mode);
+ cgm_mpremul(m, rm);
+}
+
+static inline void cgm_mprerotate_quat(float *m, const cgm_quat *q)
+{
+ float rm[16];
+ cgm_mrotation_quat(rm, q);
+ cgm_mpremul(m, rm);
+}
+
+
+static inline void cgm_mget_translation(const float *m, cgm_vec3 *res)
+{
+ res->x = m[12];
+ res->y = m[13];
+ res->z = m[14];
+}
+
+/* Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
+ * article "Quaternion Calculus and Fast Animation".
+ * adapted from: http://www.geometrictools.com/LibMathematics/Algebra/Wm5Quaternion.inl
+ */
+static inline void cgm_mget_rotation(const float *m, cgm_quat *res)
+{
+ static const int next[3] = {1, 2, 0};
+ float quat[4];
+ int i, j, k;
+
+ float trace = m[0] + m[5] + m[10];
+ float root;
+
+ if(trace > 0.0f) {
+ // |w| > 1/2
+ root = sqrt(trace + 1.0f); // 2w
+ res->w = 0.5f * root;
+ root = 0.5f / root; // 1 / 4w
+ res->x = (m[6] - m[9]) * root;
+ res->y = (m[8] - m[2]) * root;
+ res->z = (m[1] - m[4]) * root;
+ } else {
+ // |w| <= 1/2
+ i = 0;
+ if(m[5] > m[0]) {
+ i = 1;
+ }
+ if(m[10] > m[i * 4 + i]) {
+ i = 2;
+ }
+ j = next[i];
+ k = next[j];
+
+ root = sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0f);
+ quat[i + 1] = 0.5f * root;
+ root = 0.5f / root;
+ quat[0] = (m[j + 4 + k] - m[k * 4 + j]) * root;
+ quat[j + 1] = (m[i * 4 + j] - m[j * 4 + i]) * root;
+ quat[k + 1] = (m[i * 4 + k] - m[k * 4 + i]) * root;
+ res->w = quat[0];
+ res->x = quat[1];
+ res->y = quat[2];
+ res->z = quat[3];
+ }
+}
+
+static inline void cgm_mget_scaling(const float *m, cgm_vec3 *res)
+{
+ res->x = sqrt(m[0] * m[0] + m[4] * m[4] + m[8] * m[8]);
+ res->y = sqrt(m[1] * m[1] + m[5] * m[5] + m[9] * m[9]);
+ res->z = sqrt(m[2] * m[2] + m[6] * m[6] + m[10] * m[10]);
+}
+
+static inline void cgm_mget_frustum_plane(const float *m, int p, cgm_vec4 *res)
+{
+ int row = p >> 1;
+ const float *rowptr = m + row * 4;
+
+ if((p & 1) == 0) {
+ res->x = m[12] + rowptr[0];
+ res->y = m[13] + rowptr[1];
+ res->z = m[14] + rowptr[2];
+ res->w = m[15] + rowptr[3];
+ } else {
+ res->x = m[12] - rowptr[0];
+ res->y = m[13] - rowptr[1];
+ res->z = m[14] - rowptr[2];
+ res->w = m[15] - rowptr[3];
+ }
+}
+
+static inline void cgm_mlookat(float *m, const cgm_vec3 *pos, const cgm_vec3 *targ,
+ const cgm_vec3 *up)
+{
+ float trans[16];
+ cgm_vec3 dir = *targ, right, vup;
+
+ cgm_vsub(&dir, pos);
+ cgm_vnormalize(&dir);
+ cgm_vcross(&right, &dir, up);
+ cgm_vnormalize(&right);
+ cgm_vcross(&vup, &right, &dir);
+ cgm_vnormalize(&vup);
+
+ cgm_midentity(m);
+ m[0] = right.x;
+ m[1] = right.y;
+ m[2] = right.z;
+ m[4] = vup.x;
+ m[5] = vup.y;
+ m[6] = vup.z;
+ m[8] = -dir.x;
+ m[9] = -dir.y;
+ m[10] = -dir.z;
+
+ cgm_mtranslation(trans, pos->x, pos->y, pos->z);
+ cgm_mmul(m, trans);
+}
+
+static inline void cgm_minv_lookat(float *m, const cgm_vec3 *pos, const cgm_vec3 *targ,
+ const cgm_vec3 *up)
+{
+ float rot[16];
+ cgm_vec3 dir = *targ, right, vup;
+
+ cgm_vsub(&dir, pos);
+ cgm_vnormalize(&dir);
+ cgm_vcross(&right, &dir, up);
+ cgm_vnormalize(&right);
+ cgm_vcross(&vup, &right, &dir);
+ cgm_vnormalize(&vup);
+
+ cgm_midentity(rot);
+ rot[0] = right.x;
+ rot[4] = right.y;
+ rot[8] = right.z;
+ rot[1] = vup.x;
+ rot[5] = vup.y;
+ rot[9] = vup.z;
+ rot[2] = -dir.x;
+ rot[6] = -dir.y;
+ rot[10] = -dir.z;
+
+ cgm_mtranslation(m, -pos->x, -pos->y, -pos->z);
+ cgm_mmul(m, rot);
+}
+
+static inline void cgm_mortho(float *m, float left, float right, float bot, float top,
+ float znear, float zfar)
+{
+ float dx = right - left;
+ float dy = top - bot;
+ float dz = zfar - znear;
+
+ cgm_midentity(m);
+ m[0] = 2.0f / dx;
+ m[5] = 2.0f / dy;
+ m[10] = -2.0f / dz;
+ m[12] = -(right + left) / dx;
+ m[13] = -(top + bot) / dy;
+ m[14] = -(zfar + znear) / dz;
+}
+
+static inline void cgm_mfrustum(float *m, float left, float right, float bot, float top,
+ float znear, float zfar)
+{
+ float dx = right - left;
+ float dy = top - bot;
+ float dz = zfar - znear;
+
+ cgm_mzero(m);
+ m[0] = 2.0f * znear / dx;
+ m[5] = 2.0f * znear / dy;
+ m[8] = (right + left) / dx;
+ m[9] = (top + bot) / dy;
+ m[10] = -(zfar + znear) / dz;
+ m[14] = -2.0f * zfar * znear / dz;
+ m[11] = -1.0f;
+}
+
+static inline void cgm_mperspective(float *m, float vfov, float aspect, float znear, float zfar)
+{
+ float s = 1.0f / (float)tan(vfov / 2.0f);
+ float range = znear - zfar;
+
+ cgm_mzero(m);
+ m[0] = s / aspect;
+ m[5] = s;
+ m[10] = (znear + zfar) / range;
+ m[14] = 2.0f * znear * zfar / range;
+ m[11] = -1.0f;
+}
+
+static inline void cgm_mmirror(float *m, float a, float b, float c, float d)
+{
+ m[0] = 1.0f - 2.0f * a * a;
+ m[5] = 1.0f - 2.0f * b * b;
+ m[10] = 1.0f - 2.0f * c * c;
+ m[15] = 1.0f;
+
+ m[1] = m[4] = -2.0f * a * b;
+ m[2] = m[8] = -2.0f * a * c;
+ m[6] = m[9] = -2.0f * b * c;
+
+ m[12] = -2.0f * a * d;
+ m[13] = -2.0f * b * d;
+ m[14] = -2.0f * c * d;
+
+ m[3] = m[7] = m[11] = 0.0f;
+}
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