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-rw-r--r--core/math/projection.cpp212
1 files changed, 107 insertions, 105 deletions
diff --git a/core/math/projection.cpp b/core/math/projection.cpp
index 863fe6ee79..d579b641a7 100644
--- a/core/math/projection.cpp
+++ b/core/math/projection.cpp
@@ -38,24 +38,24 @@
#include "core/string/print_string.h"
float Projection::determinant() const {
- return matrix[0][3] * matrix[1][2] * matrix[2][1] * matrix[3][0] - matrix[0][2] * matrix[1][3] * matrix[2][1] * matrix[3][0] -
- matrix[0][3] * matrix[1][1] * matrix[2][2] * matrix[3][0] + matrix[0][1] * matrix[1][3] * matrix[2][2] * matrix[3][0] +
- matrix[0][2] * matrix[1][1] * matrix[2][3] * matrix[3][0] - matrix[0][1] * matrix[1][2] * matrix[2][3] * matrix[3][0] -
- matrix[0][3] * matrix[1][2] * matrix[2][0] * matrix[3][1] + matrix[0][2] * matrix[1][3] * matrix[2][0] * matrix[3][1] +
- matrix[0][3] * matrix[1][0] * matrix[2][2] * matrix[3][1] - matrix[0][0] * matrix[1][3] * matrix[2][2] * matrix[3][1] -
- matrix[0][2] * matrix[1][0] * matrix[2][3] * matrix[3][1] + matrix[0][0] * matrix[1][2] * matrix[2][3] * matrix[3][1] +
- matrix[0][3] * matrix[1][1] * matrix[2][0] * matrix[3][2] - matrix[0][1] * matrix[1][3] * matrix[2][0] * matrix[3][2] -
- matrix[0][3] * matrix[1][0] * matrix[2][1] * matrix[3][2] + matrix[0][0] * matrix[1][3] * matrix[2][1] * matrix[3][2] +
- matrix[0][1] * matrix[1][0] * matrix[2][3] * matrix[3][2] - matrix[0][0] * matrix[1][1] * matrix[2][3] * matrix[3][2] -
- matrix[0][2] * matrix[1][1] * matrix[2][0] * matrix[3][3] + matrix[0][1] * matrix[1][2] * matrix[2][0] * matrix[3][3] +
- matrix[0][2] * matrix[1][0] * matrix[2][1] * matrix[3][3] - matrix[0][0] * matrix[1][2] * matrix[2][1] * matrix[3][3] -
- matrix[0][1] * matrix[1][0] * matrix[2][2] * matrix[3][3] + matrix[0][0] * matrix[1][1] * matrix[2][2] * matrix[3][3];
+ return columns[0][3] * columns[1][2] * columns[2][1] * columns[3][0] - columns[0][2] * columns[1][3] * columns[2][1] * columns[3][0] -
+ columns[0][3] * columns[1][1] * columns[2][2] * columns[3][0] + columns[0][1] * columns[1][3] * columns[2][2] * columns[3][0] +
+ columns[0][2] * columns[1][1] * columns[2][3] * columns[3][0] - columns[0][1] * columns[1][2] * columns[2][3] * columns[3][0] -
+ columns[0][3] * columns[1][2] * columns[2][0] * columns[3][1] + columns[0][2] * columns[1][3] * columns[2][0] * columns[3][1] +
+ columns[0][3] * columns[1][0] * columns[2][2] * columns[3][1] - columns[0][0] * columns[1][3] * columns[2][2] * columns[3][1] -
+ columns[0][2] * columns[1][0] * columns[2][3] * columns[3][1] + columns[0][0] * columns[1][2] * columns[2][3] * columns[3][1] +
+ columns[0][3] * columns[1][1] * columns[2][0] * columns[3][2] - columns[0][1] * columns[1][3] * columns[2][0] * columns[3][2] -
+ columns[0][3] * columns[1][0] * columns[2][1] * columns[3][2] + columns[0][0] * columns[1][3] * columns[2][1] * columns[3][2] +
+ columns[0][1] * columns[1][0] * columns[2][3] * columns[3][2] - columns[0][0] * columns[1][1] * columns[2][3] * columns[3][2] -
+ columns[0][2] * columns[1][1] * columns[2][0] * columns[3][3] + columns[0][1] * columns[1][2] * columns[2][0] * columns[3][3] +
+ columns[0][2] * columns[1][0] * columns[2][1] * columns[3][3] - columns[0][0] * columns[1][2] * columns[2][1] * columns[3][3] -
+ columns[0][1] * columns[1][0] * columns[2][2] * columns[3][3] + columns[0][0] * columns[1][1] * columns[2][2] * columns[3][3];
}
void Projection::set_identity() {
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
- matrix[i][j] = (i == j) ? 1 : 0;
+ columns[i][j] = (i == j) ? 1 : 0;
}
}
}
@@ -63,7 +63,7 @@ void Projection::set_identity() {
void Projection::set_zero() {
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
- matrix[i][j] = 0;
+ columns[i][j] = 0;
}
}
}
@@ -71,26 +71,26 @@ void Projection::set_zero() {
Plane Projection::xform4(const Plane &p_vec4) const {
Plane ret;
- ret.normal.x = matrix[0][0] * p_vec4.normal.x + matrix[1][0] * p_vec4.normal.y + matrix[2][0] * p_vec4.normal.z + matrix[3][0] * p_vec4.d;
- ret.normal.y = matrix[0][1] * p_vec4.normal.x + matrix[1][1] * p_vec4.normal.y + matrix[2][1] * p_vec4.normal.z + matrix[3][1] * p_vec4.d;
- ret.normal.z = matrix[0][2] * p_vec4.normal.x + matrix[1][2] * p_vec4.normal.y + matrix[2][2] * p_vec4.normal.z + matrix[3][2] * p_vec4.d;
- ret.d = matrix[0][3] * p_vec4.normal.x + matrix[1][3] * p_vec4.normal.y + matrix[2][3] * p_vec4.normal.z + matrix[3][3] * p_vec4.d;
+ ret.normal.x = columns[0][0] * p_vec4.normal.x + columns[1][0] * p_vec4.normal.y + columns[2][0] * p_vec4.normal.z + columns[3][0] * p_vec4.d;
+ ret.normal.y = columns[0][1] * p_vec4.normal.x + columns[1][1] * p_vec4.normal.y + columns[2][1] * p_vec4.normal.z + columns[3][1] * p_vec4.d;
+ ret.normal.z = columns[0][2] * p_vec4.normal.x + columns[1][2] * p_vec4.normal.y + columns[2][2] * p_vec4.normal.z + columns[3][2] * p_vec4.d;
+ ret.d = columns[0][3] * p_vec4.normal.x + columns[1][3] * p_vec4.normal.y + columns[2][3] * p_vec4.normal.z + columns[3][3] * p_vec4.d;
return ret;
}
Vector4 Projection::xform(const Vector4 &p_vec4) const {
return Vector4(
- matrix[0][0] * p_vec4.x + matrix[1][0] * p_vec4.y + matrix[2][0] * p_vec4.z + matrix[3][0] * p_vec4.w,
- matrix[0][1] * p_vec4.x + matrix[1][1] * p_vec4.y + matrix[2][1] * p_vec4.z + matrix[3][1] * p_vec4.w,
- matrix[0][2] * p_vec4.x + matrix[1][2] * p_vec4.y + matrix[2][2] * p_vec4.z + matrix[3][2] * p_vec4.w,
- matrix[0][3] * p_vec4.x + matrix[1][3] * p_vec4.y + matrix[2][3] * p_vec4.z + matrix[3][3] * p_vec4.w);
+ columns[0][0] * p_vec4.x + columns[1][0] * p_vec4.y + columns[2][0] * p_vec4.z + columns[3][0] * p_vec4.w,
+ columns[0][1] * p_vec4.x + columns[1][1] * p_vec4.y + columns[2][1] * p_vec4.z + columns[3][1] * p_vec4.w,
+ columns[0][2] * p_vec4.x + columns[1][2] * p_vec4.y + columns[2][2] * p_vec4.z + columns[3][2] * p_vec4.w,
+ columns[0][3] * p_vec4.x + columns[1][3] * p_vec4.y + columns[2][3] * p_vec4.z + columns[3][3] * p_vec4.w);
}
Vector4 Projection::xform_inv(const Vector4 &p_vec4) const {
return Vector4(
- matrix[0][0] * p_vec4.x + matrix[0][1] * p_vec4.y + matrix[0][2] * p_vec4.z + matrix[0][3] * p_vec4.w,
- matrix[1][0] * p_vec4.x + matrix[1][1] * p_vec4.y + matrix[1][2] * p_vec4.z + matrix[1][3] * p_vec4.w,
- matrix[2][0] * p_vec4.x + matrix[2][1] * p_vec4.y + matrix[2][2] * p_vec4.z + matrix[2][3] * p_vec4.w,
- matrix[3][0] * p_vec4.x + matrix[3][1] * p_vec4.y + matrix[3][2] * p_vec4.z + matrix[3][3] * p_vec4.w);
+ columns[0][0] * p_vec4.x + columns[0][1] * p_vec4.y + columns[0][2] * p_vec4.z + columns[0][3] * p_vec4.w,
+ columns[1][0] * p_vec4.x + columns[1][1] * p_vec4.y + columns[1][2] * p_vec4.z + columns[1][3] * p_vec4.w,
+ columns[2][0] * p_vec4.x + columns[2][1] * p_vec4.y + columns[2][2] * p_vec4.z + columns[2][3] * p_vec4.w,
+ columns[3][0] * p_vec4.x + columns[3][1] * p_vec4.y + columns[3][2] * p_vec4.z + columns[3][3] * p_vec4.w);
}
void Projection::adjust_perspective_znear(real_t p_new_znear) {
@@ -98,8 +98,8 @@ void Projection::adjust_perspective_znear(real_t p_new_znear) {
real_t znear = p_new_znear;
real_t deltaZ = zfar - znear;
- matrix[2][2] = -(zfar + znear) / deltaZ;
- matrix[3][2] = -2 * znear * zfar / deltaZ;
+ columns[2][2] = -(zfar + znear) / deltaZ;
+ columns[3][2] = -2 * znear * zfar / deltaZ;
}
Projection Projection::create_depth_correction(bool p_flip_y) {
@@ -169,7 +169,7 @@ Projection Projection::perspective_znear_adjusted(real_t p_new_znear) const {
}
Plane Projection::get_projection_plane(Planes p_plane) const {
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
switch (p_plane) {
case PLANE_NEAR: {
@@ -267,12 +267,12 @@ void Projection::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t
set_identity();
- matrix[0][0] = cotangent / p_aspect;
- matrix[1][1] = cotangent;
- matrix[2][2] = -(p_z_far + p_z_near) / deltaZ;
- matrix[2][3] = -1;
- matrix[3][2] = -2 * p_z_near * p_z_far / deltaZ;
- matrix[3][3] = 0;
+ columns[0][0] = cotangent / p_aspect;
+ columns[1][1] = cotangent;
+ columns[2][2] = -(p_z_far + p_z_near) / deltaZ;
+ columns[2][3] = -1;
+ columns[3][2] = -2 * p_z_near * p_z_far / deltaZ;
+ columns[3][3] = 0;
}
void Projection::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov, int p_eye, real_t p_intraocular_dist, real_t p_convergence_dist) {
@@ -309,7 +309,7 @@ void Projection::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t
// translate matrix by (modeltranslation, 0.0, 0.0)
Projection cm;
cm.set_identity();
- cm.matrix[3][0] = modeltranslation;
+ cm.columns[3][0] = modeltranslation;
*this = *this * cm;
}
@@ -344,13 +344,13 @@ void Projection::set_for_hmd(int p_eye, real_t p_aspect, real_t p_intraocular_di
void Projection::set_orthogonal(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_znear, real_t p_zfar) {
set_identity();
- matrix[0][0] = 2.0 / (p_right - p_left);
- matrix[3][0] = -((p_right + p_left) / (p_right - p_left));
- matrix[1][1] = 2.0 / (p_top - p_bottom);
- matrix[3][1] = -((p_top + p_bottom) / (p_top - p_bottom));
- matrix[2][2] = -2.0 / (p_zfar - p_znear);
- matrix[3][2] = -((p_zfar + p_znear) / (p_zfar - p_znear));
- matrix[3][3] = 1.0;
+ columns[0][0] = 2.0 / (p_right - p_left);
+ columns[3][0] = -((p_right + p_left) / (p_right - p_left));
+ columns[1][1] = 2.0 / (p_top - p_bottom);
+ columns[3][1] = -((p_top + p_bottom) / (p_top - p_bottom));
+ columns[2][2] = -2.0 / (p_zfar - p_znear);
+ columns[3][2] = -((p_zfar + p_znear) / (p_zfar - p_znear));
+ columns[3][3] = 1.0;
}
void Projection::set_orthogonal(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov) {
@@ -366,7 +366,7 @@ void Projection::set_frustum(real_t p_left, real_t p_right, real_t p_bottom, rea
ERR_FAIL_COND(p_top <= p_bottom);
ERR_FAIL_COND(p_far <= p_near);
- real_t *te = &matrix[0][0];
+ real_t *te = &columns[0][0];
real_t x = 2 * p_near / (p_right - p_left);
real_t y = 2 * p_near / (p_top - p_bottom);
@@ -402,7 +402,7 @@ void Projection::set_frustum(real_t p_size, real_t p_aspect, Vector2 p_offset, r
}
real_t Projection::get_z_far() const {
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
Plane new_plane = Plane(matrix[3] - matrix[2],
matrix[7] - matrix[6],
matrix[11] - matrix[10],
@@ -415,7 +415,7 @@ real_t Projection::get_z_far() const {
}
real_t Projection::get_z_near() const {
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
Plane new_plane = Plane(matrix[3] + matrix[2],
matrix[7] + matrix[6],
matrix[11] + matrix[10],
@@ -426,7 +426,7 @@ real_t Projection::get_z_near() const {
}
Vector2 Projection::get_viewport_half_extents() const {
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
///////--- Near Plane ---///////
Plane near_plane = Plane(matrix[3] + matrix[2],
matrix[7] + matrix[6],
@@ -454,7 +454,7 @@ Vector2 Projection::get_viewport_half_extents() const {
}
Vector2 Projection::get_far_plane_half_extents() const {
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
///////--- Far Plane ---///////
Plane far_plane = Plane(matrix[3] - matrix[2],
matrix[7] - matrix[6],
@@ -514,7 +514,7 @@ Vector<Plane> Projection::get_projection_planes(const Transform3D &p_transform)
Vector<Plane> planes;
planes.resize(6);
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
Plane new_plane;
@@ -601,15 +601,15 @@ void Projection::invert() {
real_t determinant = 1.0f;
for (k = 0; k < 4; k++) {
/** Locate k'th pivot element **/
- pvt_val = matrix[k][k]; /** Initialize for search **/
+ 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(matrix[i][j]) > Math::abs(pvt_val)) {
+ if (Math::abs(columns[i][j]) > Math::abs(pvt_val)) {
pvt_i[k] = i;
pvt_j[k] = j;
- pvt_val = matrix[i][j];
+ pvt_val = columns[i][j];
}
}
}
@@ -624,9 +624,9 @@ void Projection::invert() {
i = pvt_i[k];
if (i != k) { /** If rows are different **/
for (j = 0; j < 4; j++) {
- hold = -matrix[k][j];
- matrix[k][j] = matrix[i][j];
- matrix[i][j] = hold;
+ hold = -columns[k][j];
+ columns[k][j] = columns[i][j];
+ columns[i][j] = hold;
}
}
@@ -634,25 +634,25 @@ void Projection::invert() {
j = pvt_j[k];
if (j != k) { /** If columns are different **/
for (i = 0; i < 4; i++) {
- hold = -matrix[i][k];
- matrix[i][k] = matrix[i][j];
- matrix[i][j] = hold;
+ 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) {
- matrix[i][k] /= (-pvt_val);
+ columns[i][k] /= (-pvt_val);
}
}
/** Reduce the matrix **/
for (i = 0; i < 4; i++) {
- hold = matrix[i][k];
+ hold = columns[i][k];
for (j = 0; j < 4; j++) {
if (i != k && j != k) {
- matrix[i][j] += hold * matrix[k][j];
+ columns[i][j] += hold * columns[k][j];
}
}
}
@@ -660,12 +660,12 @@ void Projection::invert() {
/** Divide row by pivot **/
for (j = 0; j < 4; j++) {
if (j != k) {
- matrix[k][j] /= pvt_val;
+ columns[k][j] /= pvt_val;
}
}
/** Replace pivot by reciprocal (at last we can touch it). **/
- matrix[k][k] = 1.0 / pvt_val;
+ columns[k][k] = 1.0 / pvt_val;
}
/* That was most of the work, one final pass of row/column interchange */
@@ -674,18 +674,18 @@ void Projection::invert() {
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 = matrix[k][j];
- matrix[k][j] = -matrix[i][j];
- matrix[i][j] = hold;
+ hold = columns[k][j];
+ columns[k][j] = -columns[i][j];
+ columns[i][j] = hold;
}
}
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 = matrix[i][k];
- matrix[i][k] = -matrix[i][j];
- matrix[i][j] = hold;
+ hold = columns[i][k];
+ columns[i][k] = -columns[i][j];
+ columns[i][j] = hold;
}
}
}
@@ -693,7 +693,7 @@ void Projection::invert() {
void Projection::flip_y() {
for (int i = 0; i < 4; i++) {
- matrix[1][i] = -matrix[1][i];
+ columns[1][i] = -columns[1][i];
}
}
@@ -708,9 +708,9 @@ Projection Projection::operator*(const Projection &p_matrix) const {
for (int i = 0; i < 4; i++) {
real_t ab = 0;
for (int k = 0; k < 4; k++) {
- ab += matrix[k][i] * p_matrix.matrix[j][k];
+ ab += columns[k][i] * p_matrix.columns[j][k];
}
- new_matrix.matrix[j][i] = ab;
+ new_matrix.columns[j][i] = ab;
}
}
@@ -718,7 +718,7 @@ Projection Projection::operator*(const Projection &p_matrix) const {
}
void Projection::set_depth_correction(bool p_flip_y) {
- real_t *m = &matrix[0][0];
+ real_t *m = &columns[0][0];
m[0] = 1;
m[1] = 0.0;
@@ -739,7 +739,7 @@ void Projection::set_depth_correction(bool p_flip_y) {
}
void Projection::set_light_bias() {
- real_t *m = &matrix[0][0];
+ real_t *m = &columns[0][0];
m[0] = 0.5;
m[1] = 0.0;
@@ -760,7 +760,7 @@ void Projection::set_light_bias() {
}
void Projection::set_light_atlas_rect(const Rect2 &p_rect) {
- real_t *m = &matrix[0][0];
+ real_t *m = &columns[0][0];
m[0] = p_rect.size.width;
m[1] = 0.0;
@@ -784,7 +784,7 @@ Projection::operator String() const {
String str;
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
- str += String((j > 0) ? ", " : "\n") + rtos(matrix[i][j]);
+ str += String((j > 0) ? ", " : "\n") + rtos(columns[i][j]);
}
}
@@ -803,11 +803,11 @@ int Projection::get_pixels_per_meter(int p_for_pixel_width) const {
}
bool Projection::is_orthogonal() const {
- return matrix[3][3] == 1.0;
+ return columns[3][3] == 1.0;
}
real_t Projection::get_fov() const {
- const real_t *matrix = (const real_t *)this->matrix;
+ const real_t *matrix = (const real_t *)this->columns;
Plane right_plane = Plane(matrix[3] - matrix[0],
matrix[7] - matrix[4],
@@ -842,44 +842,44 @@ float Projection::get_lod_multiplier() const {
}
void Projection::make_scale(const Vector3 &p_scale) {
set_identity();
- matrix[0][0] = p_scale.x;
- matrix[1][1] = p_scale.y;
- matrix[2][2] = p_scale.z;
+ columns[0][0] = p_scale.x;
+ columns[1][1] = p_scale.y;
+ columns[2][2] = p_scale.z;
}
void Projection::scale_translate_to_fit(const AABB &p_aabb) {
Vector3 min = p_aabb.position;
Vector3 max = p_aabb.position + p_aabb.size;
- matrix[0][0] = 2 / (max.x - min.x);
- matrix[1][0] = 0;
- matrix[2][0] = 0;
- matrix[3][0] = -(max.x + min.x) / (max.x - min.x);
+ columns[0][0] = 2 / (max.x - min.x);
+ columns[1][0] = 0;
+ columns[2][0] = 0;
+ columns[3][0] = -(max.x + min.x) / (max.x - min.x);
- matrix[0][1] = 0;
- matrix[1][1] = 2 / (max.y - min.y);
- matrix[2][1] = 0;
- matrix[3][1] = -(max.y + min.y) / (max.y - min.y);
+ columns[0][1] = 0;
+ columns[1][1] = 2 / (max.y - min.y);
+ columns[2][1] = 0;
+ columns[3][1] = -(max.y + min.y) / (max.y - min.y);
- matrix[0][2] = 0;
- matrix[1][2] = 0;
- matrix[2][2] = 2 / (max.z - min.z);
- matrix[3][2] = -(max.z + min.z) / (max.z - min.z);
+ columns[0][2] = 0;
+ columns[1][2] = 0;
+ columns[2][2] = 2 / (max.z - min.z);
+ columns[3][2] = -(max.z + min.z) / (max.z - min.z);
- matrix[0][3] = 0;
- matrix[1][3] = 0;
- matrix[2][3] = 0;
- matrix[3][3] = 1;
+ columns[0][3] = 0;
+ columns[1][3] = 0;
+ columns[2][3] = 0;
+ columns[3][3] = 1;
}
void Projection::add_jitter_offset(const Vector2 &p_offset) {
- matrix[3][0] += p_offset.x;
- matrix[3][1] += p_offset.y;
+ columns[3][0] += p_offset.x;
+ columns[3][1] += p_offset.y;
}
Projection::operator Transform3D() const {
Transform3D tr;
- const real_t *m = &matrix[0][0];
+ const real_t *m = &columns[0][0];
tr.basis.rows[0][0] = m[0];
tr.basis.rows[1][0] = m[1];
@@ -899,15 +899,17 @@ Projection::operator Transform3D() const {
return tr;
}
+
Projection::Projection(const Vector4 &p_x, const Vector4 &p_y, const Vector4 &p_z, const Vector4 &p_w) {
- matrix[0] = p_x;
- matrix[1] = p_y;
- matrix[2] = p_z;
- matrix[3] = p_w;
+ columns[0] = p_x;
+ columns[1] = p_y;
+ columns[2] = p_z;
+ columns[3] = p_w;
}
+
Projection::Projection(const Transform3D &p_transform) {
const Transform3D &tr = p_transform;
- real_t *m = &matrix[0][0];
+ real_t *m = &columns[0][0];
m[0] = tr.basis.rows[0][0];
m[1] = tr.basis.rows[1][0];