Fix Projection::invert on orthogonal projections and others.
Fixes #68878, specially when using orthographic projection. Also adds some tests.
This commit is contained in:
Álex Román
parent
739019e4e4
commit
3aa46b9036
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@ -596,101 +596,236 @@ Projection Projection::inverse() const {
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}
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void Projection::invert() {
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int i, j, k;
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int pvt_i[4], pvt_j[4]; /* Locations of pivot matrix */
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real_t pvt_val; /* Value of current pivot element */
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real_t hold; /* Temporary storage */
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real_t determinant = 1.0f;
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for (k = 0; k < 4; k++) {
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/** Locate k'th pivot element **/
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pvt_val = columns[k][k]; /** Initialize for search **/
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pvt_i[k] = k;
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pvt_j[k] = k;
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for (i = k; i < 4; i++) {
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for (j = k; j < 4; j++) {
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if (Math::abs(columns[i][j]) > Math::abs(pvt_val)) {
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pvt_i[k] = i;
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pvt_j[k] = j;
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pvt_val = columns[i][j];
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}
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}
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// Adapted from mesa's src/util/u_math.c util_invert_mat4x4
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// on commit 0d170a81288f2427425d53965a0daa57a57b110f
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Projection temp;
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real_t *out = (real_t *)temp.columns;
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real_t *m = (real_t *)columns;
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real_t wtmp[4][8];
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real_t m0, m1, m2, m3, s;
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real_t *r0, *r1, *r2, *r3;
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#define MAT(m, r, c) (m)[(c) * 4 + (r)]
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#define SWAP_ROWS(a, b) \
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{ \
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real_t *_tmp = a; \
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(a) = (b); \
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(b) = _tmp; \
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}
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/** Product of pivots, gives determinant when finished **/
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determinant *= pvt_val;
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if (Math::is_zero_approx(determinant)) {
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return; /** Matrix is singular (zero determinant). **/
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r0 = wtmp[0];
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r1 = wtmp[1];
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r2 = wtmp[2];
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r3 = wtmp[3];
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r0[0] = MAT(m, 0, 0);
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r0[1] = MAT(m, 0, 1);
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r0[2] = MAT(m, 0, 2);
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r0[3] = MAT(m, 0, 3);
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r0[4] = 1.0;
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r0[5] = 0.0;
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r0[6] = 0.0;
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r0[7] = 0.0;
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r1[0] = MAT(m, 1, 0);
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r1[1] = MAT(m, 1, 1);
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r1[2] = MAT(m, 1, 2);
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r1[3] = MAT(m, 1, 3);
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r1[5] = 1.0;
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r1[4] = 0.0;
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r1[6] = 0.0;
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r1[7] = 0.0;
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r2[0] = MAT(m, 2, 0);
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r2[1] = MAT(m, 2, 1);
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r2[2] = MAT(m, 2, 2);
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r2[3] = MAT(m, 2, 3);
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r2[6] = 1.0;
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r2[4] = 0.0;
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r2[5] = 0.0;
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r2[7] = 0.0;
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r3[0] = MAT(m, 3, 0);
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r3[1] = MAT(m, 3, 1);
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r3[2] = MAT(m, 3, 2);
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r3[3] = MAT(m, 3, 3);
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r3[7] = 1.0;
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r3[4] = 0.0;
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r3[5] = 0.0;
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r3[6] = 0.0;
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/* choose pivot - or die */
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if (Math::abs(r3[0]) > Math::abs(r2[0])) {
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SWAP_ROWS(r3, r2);
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}
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if (Math::abs(r2[0]) > Math::abs(r1[0])) {
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SWAP_ROWS(r2, r1);
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}
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if (Math::abs(r1[0]) > Math::abs(r0[0])) {
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SWAP_ROWS(r1, r0);
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}
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ERR_FAIL_COND(0.0 == r0[0]);
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/* eliminate first variable */
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m1 = r1[0] / r0[0];
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m2 = r2[0] / r0[0];
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m3 = r3[0] / r0[0];
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s = r0[1];
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r1[1] -= m1 * s;
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r2[1] -= m2 * s;
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r3[1] -= m3 * s;
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s = r0[2];
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r1[2] -= m1 * s;
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r2[2] -= m2 * s;
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r3[2] -= m3 * s;
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s = r0[3];
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r1[3] -= m1 * s;
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r2[3] -= m2 * s;
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r3[3] -= m3 * s;
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s = r0[4];
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if (s != 0.0) {
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r1[4] -= m1 * s;
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r2[4] -= m2 * s;
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r3[4] -= m3 * s;
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}
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s = r0[5];
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if (s != 0.0) {
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r1[5] -= m1 * s;
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r2[5] -= m2 * s;
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r3[5] -= m3 * s;
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}
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s = r0[6];
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if (s != 0.0) {
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r1[6] -= m1 * s;
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r2[6] -= m2 * s;
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r3[6] -= m3 * s;
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}
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s = r0[7];
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if (s != 0.0) {
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r1[7] -= m1 * s;
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r2[7] -= m2 * s;
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r3[7] -= m3 * s;
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}
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/** "Interchange" rows (with sign change stuff) **/
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i = pvt_i[k];
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if (i != k) { /** If rows are different **/
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for (j = 0; j < 4; j++) {
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hold = -columns[k][j];
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columns[k][j] = columns[i][j];
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columns[i][j] = hold;
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/* choose pivot - or die */
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if (Math::abs(r3[1]) > Math::abs(r2[1])) {
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SWAP_ROWS(r3, r2);
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}
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if (Math::abs(r2[1]) > Math::abs(r1[1])) {
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SWAP_ROWS(r2, r1);
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}
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ERR_FAIL_COND(0.0 == r1[1]);
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/* eliminate second variable */
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m2 = r2[1] / r1[1];
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m3 = r3[1] / r1[1];
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r2[2] -= m2 * r1[2];
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r3[2] -= m3 * r1[2];
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r2[3] -= m2 * r1[3];
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r3[3] -= m3 * r1[3];
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s = r1[4];
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if (0.0 != s) {
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r2[4] -= m2 * s;
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r3[4] -= m3 * s;
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}
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s = r1[5];
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if (0.0 != s) {
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r2[5] -= m2 * s;
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r3[5] -= m3 * s;
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}
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s = r1[6];
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if (0.0 != s) {
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r2[6] -= m2 * s;
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r3[6] -= m3 * s;
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}
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s = r1[7];
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if (0.0 != s) {
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r2[7] -= m2 * s;
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r3[7] -= m3 * s;
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}
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/** "Interchange" columns **/
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j = pvt_j[k];
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if (j != k) { /** If columns are different **/
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for (i = 0; i < 4; i++) {
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hold = -columns[i][k];
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columns[i][k] = columns[i][j];
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columns[i][j] = hold;
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}
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/* choose pivot - or die */
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if (Math::abs(r3[2]) > Math::abs(r2[2])) {
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SWAP_ROWS(r3, r2);
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}
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ERR_FAIL_COND(0.0 == r2[2]);
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/** Divide column by minus pivot value **/
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for (i = 0; i < 4; i++) {
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if (i != k) {
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columns[i][k] /= (-pvt_val);
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}
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}
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/* eliminate third variable */
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m3 = r3[2] / r2[2];
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r3[3] -= m3 * r2[3];
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r3[4] -= m3 * r2[4];
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r3[5] -= m3 * r2[5];
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r3[6] -= m3 * r2[6];
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r3[7] -= m3 * r2[7];
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/** Reduce the matrix **/
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for (i = 0; i < 4; i++) {
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hold = columns[i][k];
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for (j = 0; j < 4; j++) {
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if (i != k && j != k) {
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columns[i][j] += hold * columns[k][j];
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}
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}
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}
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/* last check */
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ERR_FAIL_COND(0.0 == r3[3]);
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/** Divide row by pivot **/
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for (j = 0; j < 4; j++) {
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if (j != k) {
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columns[k][j] /= pvt_val;
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}
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}
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s = 1.0 / r3[3]; /* now back substitute row 3 */
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r3[4] *= s;
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r3[5] *= s;
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r3[6] *= s;
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r3[7] *= s;
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/** Replace pivot by reciprocal (at last we can touch it). **/
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columns[k][k] = 1.0 / pvt_val;
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}
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m2 = r2[3]; /* now back substitute row 2 */
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s = 1.0 / r2[2];
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r2[4] = s * (r2[4] - r3[4] * m2);
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r2[5] = s * (r2[5] - r3[5] * m2);
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r2[6] = s * (r2[6] - r3[6] * m2);
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r2[7] = s * (r2[7] - r3[7] * m2);
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m1 = r1[3];
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r1[4] -= r3[4] * m1;
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r1[5] -= r3[5] * m1;
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r1[6] -= r3[6] * m1;
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r1[7] -= r3[7] * m1;
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m0 = r0[3];
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r0[4] -= r3[4] * m0;
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r0[5] -= r3[5] * m0;
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r0[6] -= r3[6] * m0;
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r0[7] -= r3[7] * m0;
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/* That was most of the work, one final pass of row/column interchange */
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/* to finish */
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for (k = 4 - 2; k >= 0; k--) { /* Don't need to work with 1 by 1 corner*/
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i = pvt_j[k]; /* Rows to swap correspond to pivot COLUMN */
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if (i != k) { /* If rows are different */
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for (j = 0; j < 4; j++) {
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hold = columns[k][j];
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columns[k][j] = -columns[i][j];
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columns[i][j] = hold;
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}
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}
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m1 = r1[2]; /* now back substitute row 1 */
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s = 1.0 / r1[1];
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r1[4] = s * (r1[4] - r2[4] * m1);
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r1[5] = s * (r1[5] - r2[5] * m1),
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r1[6] = s * (r1[6] - r2[6] * m1);
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r1[7] = s * (r1[7] - r2[7] * m1);
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m0 = r0[2];
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r0[4] -= r2[4] * m0;
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r0[5] -= r2[5] * m0;
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r0[6] -= r2[6] * m0;
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r0[7] -= r2[7] * m0;
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j = pvt_i[k]; /* Columns to swap correspond to pivot ROW */
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if (j != k) { /* If columns are different */
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for (i = 0; i < 4; i++) {
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hold = columns[i][k];
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columns[i][k] = -columns[i][j];
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columns[i][j] = hold;
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}
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}
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}
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m0 = r0[1]; /* now back substitute row 0 */
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s = 1.0 / r0[0];
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r0[4] = s * (r0[4] - r1[4] * m0);
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r0[5] = s * (r0[5] - r1[5] * m0),
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r0[6] = s * (r0[6] - r1[6] * m0);
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r0[7] = s * (r0[7] - r1[7] * m0);
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MAT(out, 0, 0) = r0[4];
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MAT(out, 0, 1) = r0[5];
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MAT(out, 0, 2) = r0[6];
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MAT(out, 0, 3) = r0[7];
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MAT(out, 1, 0) = r1[4];
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MAT(out, 1, 1) = r1[5];
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MAT(out, 1, 2) = r1[6];
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MAT(out, 1, 3) = r1[7];
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MAT(out, 2, 0) = r2[4];
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MAT(out, 2, 1) = r2[5];
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MAT(out, 2, 2) = r2[6];
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MAT(out, 2, 3) = r2[7];
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MAT(out, 3, 0) = r3[4];
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MAT(out, 3, 1) = r3[5];
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MAT(out, 3, 2) = r3[6];
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MAT(out, 3, 3) = r3[7];
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#undef MAT
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#undef SWAP_ROWS
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*this = temp;
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}
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void Projection::flip_y() {
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@ -0,0 +1,87 @@
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/**************************************************************************/
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/* test_projection.h */
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/**************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/**************************************************************************/
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#ifndef TEST_PROJECTION_H
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#define TEST_PROJECTION_H
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#include "core/math/projection.h"
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#include "core/string/print_string.h"
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#include "tests/test_macros.h"
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namespace TestProjection {
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TEST_CASE("[Projection] Default construct") {
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Projection p;
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CHECK(p.columns[0][0] == 1.0);
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CHECK(p.columns[0][1] == 0.0);
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CHECK(p.columns[0][2] == 0.0);
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CHECK(p.columns[0][3] == 0.0);
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CHECK(p.columns[1][0] == 0.0);
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CHECK(p.columns[1][1] == 1.0);
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CHECK(p.columns[1][2] == 0.0);
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CHECK(p.columns[1][3] == 0.0);
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CHECK(p.columns[2][0] == 0.0);
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CHECK(p.columns[2][1] == 0.0);
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CHECK(p.columns[2][2] == 1.0);
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CHECK(p.columns[2][3] == 0.0);
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CHECK(p.columns[3][0] == 0.0);
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CHECK(p.columns[3][1] == 0.0);
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CHECK(p.columns[3][2] == 0.0);
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CHECK(p.columns[3][3] == 1.0);
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}
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bool projection_is_equal_approx(const Projection &p_a, const Projection &p_b) {
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for (int i = 0; i < 4; i++) {
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for (int j = 0; j < 4; j++) {
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if (!Math::is_equal_approx(p_a.columns[i][j], p_b.columns[i][j])) {
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return false;
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}
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}
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}
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return true;
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}
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TEST_CASE("[Projection] Orthogonal projection matrix inversion") {
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Projection p = Projection::create_orthogonal(-125.0f, 125.0f, -125.0f, 125.0f, 0.01f, 25.0f);
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CHECK(projection_is_equal_approx(p.inverse() * p, Projection()));
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}
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TEST_CASE("[Projection] Perspective projection matrix inversion") {
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Projection p = Projection::create_perspective(90.0f, 1.77777f, 0.05f, 4000.0f);
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CHECK(projection_is_equal_approx(p.inverse() * p, Projection()));
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}
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} //namespace TestProjection
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#endif // TEST_PROJECTION_H
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@ -61,6 +61,7 @@
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#include "tests/core/math/test_geometry_3d.h"
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#include "tests/core/math/test_math_funcs.h"
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#include "tests/core/math/test_plane.h"
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#include "tests/core/math/test_projection.h"
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#include "tests/core/math/test_quaternion.h"
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#include "tests/core/math/test_random_number_generator.h"
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#include "tests/core/math/test_rect2.h"
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