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Fix Projection::invert on orthogonal projections and others.
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Fixes godotengine#68878, specially when using orthographic projection.

Also adds some tests.
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@EIREXE
Álex Román authored and EIREXE committed Nov 18, 2024
1 parent 739019e commit 02b2efc
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310 changes: 219 additions & 91 deletions core/math/projection.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -596,101 +596,229 @@ Projection Projection::inverse() const {
}

void Projection::invert() {
int i, j, k;
int pvt_i[4], pvt_j[4]; /* Locations of pivot matrix */
real_t pvt_val; /* Value of current pivot element */
real_t hold; /* Temporary storage */
real_t determinant = 1.0f;
for (k = 0; k < 4; k++) {
/** Locate k'th pivot element **/
pvt_val = columns[k][k]; /** Initialize for search **/
pvt_i[k] = k;
pvt_j[k] = k;
for (i = k; i < 4; i++) {
for (j = k; j < 4; j++) {
if (Math::abs(columns[i][j]) > Math::abs(pvt_val)) {
pvt_i[k] = i;
pvt_j[k] = j;
pvt_val = columns[i][j];
}
}
}

/** Product of pivots, gives determinant when finished **/
determinant *= pvt_val;
if (Math::is_zero_approx(determinant)) {
return; /** Matrix is singular (zero determinant). **/
}

/** "Interchange" rows (with sign change stuff) **/
i = pvt_i[k];
if (i != k) { /** If rows are different **/
for (j = 0; j < 4; j++) {
hold = -columns[k][j];
columns[k][j] = columns[i][j];
columns[i][j] = hold;
}
}

/** "Interchange" columns **/
j = pvt_j[k];
if (j != k) { /** If columns are different **/
for (i = 0; i < 4; i++) {
hold = -columns[i][k];
columns[i][k] = columns[i][j];
columns[i][j] = hold;
}
}

/** Divide column by minus pivot value **/
for (i = 0; i < 4; i++) {
if (i != k) {
columns[i][k] /= (-pvt_val);
}
}

/** Reduce the matrix **/
for (i = 0; i < 4; i++) {
hold = columns[i][k];
for (j = 0; j < 4; j++) {
if (i != k && j != k) {
columns[i][j] += hold * columns[k][j];
}
}
}

/** Divide row by pivot **/
for (j = 0; j < 4; j++) {
if (j != k) {
columns[k][j] /= pvt_val;
}
}

/** Replace pivot by reciprocal (at last we can touch it). **/
columns[k][k] = 1.0 / pvt_val;
// Adapted from Mesa's `src/util/u_math.c` `util_invert_mat4x4`.
// MIT licensed. Copyright 2008 VMware, Inc. Authored by Jacques Leroy.
Projection temp;
real_t *out = (real_t *)temp.columns;
real_t *m = (real_t *)columns;

real_t wtmp[4][8];
real_t m0, m1, m2, m3, s;
real_t *r0, *r1, *r2, *r3;

#define MAT(m, r, c) (m)[(c) * 4 + (r)]

r0 = wtmp[0];
r1 = wtmp[1];
r2 = wtmp[2];
r3 = wtmp[3];

r0[0] = MAT(m, 0, 0);
r0[1] = MAT(m, 0, 1);
r0[2] = MAT(m, 0, 2);
r0[3] = MAT(m, 0, 3);
r0[4] = 1.0;
r0[5] = 0.0;
r0[6] = 0.0;
r0[7] = 0.0;

r1[0] = MAT(m, 1, 0);
r1[1] = MAT(m, 1, 1);
r1[2] = MAT(m, 1, 2);
r1[3] = MAT(m, 1, 3);
r1[5] = 1.0;
r1[4] = 0.0;
r1[6] = 0.0;
r1[7] = 0.0;

r2[0] = MAT(m, 2, 0);
r2[1] = MAT(m, 2, 1);
r2[2] = MAT(m, 2, 2);
r2[3] = MAT(m, 2, 3);
r2[6] = 1.0;
r2[4] = 0.0;
r2[5] = 0.0;
r2[7] = 0.0;

r3[0] = MAT(m, 3, 0);
r3[1] = MAT(m, 3, 1);
r3[2] = MAT(m, 3, 2);
r3[3] = MAT(m, 3, 3);

r3[7] = 1.0;
r3[4] = 0.0;
r3[5] = 0.0;
r3[6] = 0.0;

/* choose pivot - or die */
if (Math::abs(r3[0]) > Math::abs(r2[0])) {
SWAP(r3, r2);
}
if (Math::abs(r2[0]) > Math::abs(r1[0])) {
SWAP(r2, r1);
}
if (Math::abs(r1[0]) > Math::abs(r0[0])) {
SWAP(r1, r0);
}
ERR_FAIL_COND(0.0 == r0[0]);

/* eliminate first variable */
m1 = r1[0] / r0[0];
m2 = r2[0] / r0[0];
m3 = r3[0] / r0[0];
s = r0[1];
r1[1] -= m1 * s;
r2[1] -= m2 * s;
r3[1] -= m3 * s;
s = r0[2];
r1[2] -= m1 * s;
r2[2] -= m2 * s;
r3[2] -= m3 * s;
s = r0[3];
r1[3] -= m1 * s;
r2[3] -= m2 * s;
r3[3] -= m3 * s;
s = r0[4];
if (s != 0.0) {
r1[4] -= m1 * s;
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r0[5];
if (s != 0.0) {
r1[5] -= m1 * s;
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r0[6];
if (s != 0.0) {
r1[6] -= m1 * s;
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r0[7];
if (s != 0.0) {
r1[7] -= m1 * s;
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}

/* That was most of the work, one final pass of row/column interchange */
/* to finish */
for (k = 4 - 2; k >= 0; k--) { /* Don't need to work with 1 by 1 corner*/
i = pvt_j[k]; /* Rows to swap correspond to pivot COLUMN */
if (i != k) { /* If rows are different */
for (j = 0; j < 4; j++) {
hold = columns[k][j];
columns[k][j] = -columns[i][j];
columns[i][j] = hold;
}
}
/* choose pivot - or die */
if (Math::abs(r3[1]) > Math::abs(r2[1])) {
SWAP(r3, r2);
}
if (Math::abs(r2[1]) > Math::abs(r1[1])) {
SWAP(r2, r1);
}
ERR_FAIL_COND(0.0 == r1[1]);

/* eliminate second variable */
m2 = r2[1] / r1[1];
m3 = r3[1] / r1[1];
r2[2] -= m2 * r1[2];
r3[2] -= m3 * r1[2];
r2[3] -= m2 * r1[3];
r3[3] -= m3 * r1[3];
s = r1[4];
if (0.0 != s) {
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r1[5];
if (0.0 != s) {
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r1[6];
if (0.0 != s) {
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r1[7];
if (0.0 != s) {
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}

j = pvt_i[k]; /* Columns to swap correspond to pivot ROW */
if (j != k) { /* If columns are different */
for (i = 0; i < 4; i++) {
hold = columns[i][k];
columns[i][k] = -columns[i][j];
columns[i][j] = hold;
}
}
/* choose pivot - or die */
if (Math::abs(r3[2]) > Math::abs(r2[2])) {
SWAP(r3, r2);
}
ERR_FAIL_COND(0.0 == r2[2]);

/* eliminate third variable */
m3 = r3[2] / r2[2];
r3[3] -= m3 * r2[3];
r3[4] -= m3 * r2[4];
r3[5] -= m3 * r2[5];
r3[6] -= m3 * r2[6];
r3[7] -= m3 * r2[7];

/* last check */
ERR_FAIL_COND(0.0 == r3[3]);

s = 1.0 / r3[3]; /* now back substitute row 3 */
r3[4] *= s;
r3[5] *= s;
r3[6] *= s;
r3[7] *= s;

m2 = r2[3]; /* now back substitute row 2 */
s = 1.0 / r2[2];
r2[4] = s * (r2[4] - r3[4] * m2);
r2[5] = s * (r2[5] - r3[5] * m2);
r2[6] = s * (r2[6] - r3[6] * m2);
r2[7] = s * (r2[7] - r3[7] * m2);
m1 = r1[3];
r1[4] -= r3[4] * m1;
r1[5] -= r3[5] * m1;
r1[6] -= r3[6] * m1;
r1[7] -= r3[7] * m1;
m0 = r0[3];
r0[4] -= r3[4] * m0;
r0[5] -= r3[5] * m0;
r0[6] -= r3[6] * m0;
r0[7] -= r3[7] * m0;

m1 = r1[2]; /* now back substitute row 1 */
s = 1.0 / r1[1];
r1[4] = s * (r1[4] - r2[4] * m1);
r1[5] = s * (r1[5] - r2[5] * m1),
r1[6] = s * (r1[6] - r2[6] * m1);
r1[7] = s * (r1[7] - r2[7] * m1);
m0 = r0[2];
r0[4] -= r2[4] * m0;
r0[5] -= r2[5] * m0;
r0[6] -= r2[6] * m0;
r0[7] -= r2[7] * m0;

m0 = r0[1]; /* now back substitute row 0 */
s = 1.0 / r0[0];
r0[4] = s * (r0[4] - r1[4] * m0);
r0[5] = s * (r0[5] - r1[5] * m0),
r0[6] = s * (r0[6] - r1[6] * m0);
r0[7] = s * (r0[7] - r1[7] * m0);

MAT(out, 0, 0) = r0[4];
MAT(out, 0, 1) = r0[5];
MAT(out, 0, 2) = r0[6];
MAT(out, 0, 3) = r0[7];
MAT(out, 1, 0) = r1[4];
MAT(out, 1, 1) = r1[5];
MAT(out, 1, 2) = r1[6];
MAT(out, 1, 3) = r1[7];
MAT(out, 2, 0) = r2[4];
MAT(out, 2, 1) = r2[5];
MAT(out, 2, 2) = r2[6];
MAT(out, 2, 3) = r2[7];
MAT(out, 3, 0) = r3[4];
MAT(out, 3, 1) = r3[5];
MAT(out, 3, 2) = r3[6];
MAT(out, 3, 3) = r3[7];

#undef MAT

*this = temp;
}

void Projection::flip_y() {
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