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+/*************************************************************************/
+/* projection.cpp */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* https://godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+
+#include "projection.h"
+
+#include "core/math/aabb.h"
+#include "core/math/math_funcs.h"
+#include "core/math/plane.h"
+#include "core/math/rect2.h"
+#include "core/math/transform_3d.h"
+#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];
+}
+
+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;
+ }
+ }
+}
+
+void Projection::set_zero() {
+ for (int i = 0; i < 4; i++) {
+ for (int j = 0; j < 4; j++) {
+ matrix[i][j] = 0;
+ }
+ }
+}
+
+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;
+ 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);
+}
+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);
+}
+
+void Projection::adjust_perspective_znear(real_t p_new_znear) {
+ real_t zfar = get_z_far();
+ real_t znear = p_new_znear;
+
+ real_t deltaZ = zfar - znear;
+ matrix[2][2] = -(zfar + znear) / deltaZ;
+ matrix[3][2] = -2 * znear * zfar / deltaZ;
+}
+
+Projection Projection::create_depth_correction(bool p_flip_y) {
+ Projection proj;
+ proj.set_depth_correction(p_flip_y);
+ return proj;
+}
+
+Projection Projection::create_light_atlas_rect(const Rect2 &p_rect) {
+ Projection proj;
+ proj.set_light_atlas_rect(p_rect);
+ return proj;
+}
+
+Projection Projection::create_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov) {
+ Projection proj;
+ proj.set_perspective(p_fovy_degrees, p_aspect, p_z_near, p_z_far, p_flip_fov);
+ return proj;
+}
+
+Projection Projection::create_perspective_hmd(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) {
+ Projection proj;
+ proj.set_perspective(p_fovy_degrees, p_aspect, p_z_near, p_z_far, p_flip_fov, p_eye, p_intraocular_dist, p_convergence_dist);
+ return proj;
+}
+
+Projection Projection::create_for_hmd(int p_eye, real_t p_aspect, real_t p_intraocular_dist, real_t p_display_width, real_t p_display_to_lens, real_t p_oversample, real_t p_z_near, real_t p_z_far) {
+ Projection proj;
+ proj.set_for_hmd(p_eye, p_aspect, p_intraocular_dist, p_display_width, p_display_to_lens, p_oversample, p_z_near, p_z_far);
+ return proj;
+}
+
+Projection Projection::create_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) {
+ Projection proj;
+ proj.set_orthogonal(p_left, p_right, p_bottom, p_top, p_zfar, p_zfar);
+ return proj;
+}
+
+Projection Projection::create_orthogonal_aspect(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov) {
+ Projection proj;
+ proj.set_orthogonal(p_size, p_aspect, p_znear, p_zfar, p_flip_fov);
+ return proj;
+}
+
+Projection Projection::create_frustum(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far) {
+ Projection proj;
+ proj.set_frustum(p_left, p_right, p_bottom, p_top, p_near, p_far);
+ return proj;
+}
+
+Projection Projection::create_frustum_aspect(real_t p_size, real_t p_aspect, Vector2 p_offset, real_t p_near, real_t p_far, bool p_flip_fov) {
+ Projection proj;
+ proj.set_frustum(p_size, p_aspect, p_offset, p_near, p_far, p_flip_fov);
+ return proj;
+}
+
+Projection Projection::create_fit_aabb(const AABB &p_aabb) {
+ Projection proj;
+ proj.scale_translate_to_fit(p_aabb);
+ return proj;
+}
+
+Projection Projection::perspective_znear_adjusted(real_t p_new_znear) const {
+ Projection proj = *this;
+ proj.adjust_perspective_znear(p_new_znear);
+ return proj;
+}
+
+Plane Projection::get_projection_plane(Planes p_plane) const {
+ const real_t *matrix = (const real_t *)this->matrix;
+
+ switch (p_plane) {
+ case PLANE_NEAR: {
+ Plane new_plane = Plane(matrix[3] + matrix[2],
+ matrix[7] + matrix[6],
+ matrix[11] + matrix[10],
+ matrix[15] + matrix[14]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+ return new_plane;
+ } break;
+ case PLANE_FAR: {
+ Plane new_plane = Plane(matrix[3] - matrix[2],
+ matrix[7] - matrix[6],
+ matrix[11] - matrix[10],
+ matrix[15] - matrix[14]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+ return new_plane;
+ } break;
+ case PLANE_LEFT: {
+ Plane new_plane = Plane(matrix[3] + matrix[0],
+ matrix[7] + matrix[4],
+ matrix[11] + matrix[8],
+ matrix[15] + matrix[12]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+ return new_plane;
+ } break;
+ case PLANE_TOP: {
+ Plane new_plane = Plane(matrix[3] - matrix[1],
+ matrix[7] - matrix[5],
+ matrix[11] - matrix[9],
+ matrix[15] - matrix[13]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+ return new_plane;
+ } break;
+ case PLANE_RIGHT: {
+ Plane new_plane = Plane(matrix[3] - matrix[0],
+ matrix[7] - matrix[4],
+ matrix[11] - matrix[8],
+ matrix[15] - matrix[12]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+ return new_plane;
+ } break;
+ case PLANE_BOTTOM: {
+ Plane new_plane = Plane(matrix[3] + matrix[1],
+ matrix[7] + matrix[5],
+ matrix[11] + matrix[9],
+ matrix[15] + matrix[13]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+ return new_plane;
+ } break;
+ }
+
+ return Plane();
+}
+
+Projection Projection::flipped_y() const {
+ Projection proj = *this;
+ proj.flip_y();
+ return proj;
+}
+
+Projection Projection ::jitter_offseted(const Vector2 &p_offset) const {
+ Projection proj = *this;
+ proj.add_jitter_offset(p_offset);
+ return proj;
+}
+
+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) {
+ if (p_flip_fov) {
+ p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect);
+ }
+
+ real_t sine, cotangent, deltaZ;
+ real_t radians = Math::deg2rad(p_fovy_degrees / 2.0);
+
+ deltaZ = p_z_far - p_z_near;
+ sine = Math::sin(radians);
+
+ if ((deltaZ == 0) || (sine == 0) || (p_aspect == 0)) {
+ return;
+ }
+ cotangent = Math::cos(radians) / sine;
+
+ 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;
+}
+
+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) {
+ if (p_flip_fov) {
+ p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect);
+ }
+
+ real_t left, right, modeltranslation, ymax, xmax, frustumshift;
+
+ ymax = p_z_near * tan(Math::deg2rad(p_fovy_degrees / 2.0));
+ xmax = ymax * p_aspect;
+ frustumshift = (p_intraocular_dist / 2.0) * p_z_near / p_convergence_dist;
+
+ switch (p_eye) {
+ case 1: { // left eye
+ left = -xmax + frustumshift;
+ right = xmax + frustumshift;
+ modeltranslation = p_intraocular_dist / 2.0;
+ } break;
+ case 2: { // right eye
+ left = -xmax - frustumshift;
+ right = xmax - frustumshift;
+ modeltranslation = -p_intraocular_dist / 2.0;
+ } break;
+ default: { // mono, should give the same result as set_perspective(p_fovy_degrees,p_aspect,p_z_near,p_z_far,p_flip_fov)
+ left = -xmax;
+ right = xmax;
+ modeltranslation = 0.0;
+ } break;
+ }
+
+ set_frustum(left, right, -ymax, ymax, p_z_near, p_z_far);
+
+ // translate matrix by (modeltranslation, 0.0, 0.0)
+ Projection cm;
+ cm.set_identity();
+ cm.matrix[3][0] = modeltranslation;
+ *this = *this * cm;
+}
+
+void Projection::set_for_hmd(int p_eye, real_t p_aspect, real_t p_intraocular_dist, real_t p_display_width, real_t p_display_to_lens, real_t p_oversample, real_t p_z_near, real_t p_z_far) {
+ // we first calculate our base frustum on our values without taking our lens magnification into account.
+ real_t f1 = (p_intraocular_dist * 0.5) / p_display_to_lens;
+ real_t f2 = ((p_display_width - p_intraocular_dist) * 0.5) / p_display_to_lens;
+ real_t f3 = (p_display_width / 4.0) / p_display_to_lens;
+
+ // now we apply our oversample factor to increase our FOV. how much we oversample is always a balance we strike between performance and how much
+ // we're willing to sacrifice in FOV.
+ real_t add = ((f1 + f2) * (p_oversample - 1.0)) / 2.0;
+ f1 += add;
+ f2 += add;
+ f3 *= p_oversample;
+
+ // always apply KEEP_WIDTH aspect ratio
+ f3 /= p_aspect;
+
+ switch (p_eye) {
+ case 1: { // left eye
+ set_frustum(-f2 * p_z_near, f1 * p_z_near, -f3 * p_z_near, f3 * p_z_near, p_z_near, p_z_far);
+ } break;
+ case 2: { // right eye
+ set_frustum(-f1 * p_z_near, f2 * p_z_near, -f3 * p_z_near, f3 * p_z_near, p_z_near, p_z_far);
+ } break;
+ default: { // mono, does not apply here!
+ } break;
+ }
+}
+
+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;
+}
+
+void Projection::set_orthogonal(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov) {
+ if (!p_flip_fov) {
+ p_size *= p_aspect;
+ }
+
+ set_orthogonal(-p_size / 2, +p_size / 2, -p_size / p_aspect / 2, +p_size / p_aspect / 2, p_znear, p_zfar);
+}
+
+void Projection::set_frustum(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far) {
+ ERR_FAIL_COND(p_right <= p_left);
+ ERR_FAIL_COND(p_top <= p_bottom);
+ ERR_FAIL_COND(p_far <= p_near);
+
+ real_t *te = &matrix[0][0];
+ real_t x = 2 * p_near / (p_right - p_left);
+ real_t y = 2 * p_near / (p_top - p_bottom);
+
+ real_t a = (p_right + p_left) / (p_right - p_left);
+ real_t b = (p_top + p_bottom) / (p_top - p_bottom);
+ real_t c = -(p_far + p_near) / (p_far - p_near);
+ real_t d = -2 * p_far * p_near / (p_far - p_near);
+
+ te[0] = x;
+ te[1] = 0;
+ te[2] = 0;
+ te[3] = 0;
+ te[4] = 0;
+ te[5] = y;
+ te[6] = 0;
+ te[7] = 0;
+ te[8] = a;
+ te[9] = b;
+ te[10] = c;
+ te[11] = -1;
+ te[12] = 0;
+ te[13] = 0;
+ te[14] = d;
+ te[15] = 0;
+}
+
+void Projection::set_frustum(real_t p_size, real_t p_aspect, Vector2 p_offset, real_t p_near, real_t p_far, bool p_flip_fov) {
+ if (!p_flip_fov) {
+ p_size *= p_aspect;
+ }
+
+ set_frustum(-p_size / 2 + p_offset.x, +p_size / 2 + p_offset.x, -p_size / p_aspect / 2 + p_offset.y, +p_size / p_aspect / 2 + p_offset.y, p_near, p_far);
+}
+
+real_t Projection::get_z_far() const {
+ const real_t *matrix = (const real_t *)this->matrix;
+ Plane new_plane = Plane(matrix[3] - matrix[2],
+ matrix[7] - matrix[6],
+ matrix[11] - matrix[10],
+ matrix[15] - matrix[14]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ return new_plane.d;
+}
+
+real_t Projection::get_z_near() const {
+ const real_t *matrix = (const real_t *)this->matrix;
+ Plane new_plane = Plane(matrix[3] + matrix[2],
+ matrix[7] + matrix[6],
+ matrix[11] + matrix[10],
+ -matrix[15] - matrix[14]);
+
+ new_plane.normalize();
+ return new_plane.d;
+}
+
+Vector2 Projection::get_viewport_half_extents() const {
+ const real_t *matrix = (const real_t *)this->matrix;
+ ///////--- Near Plane ---///////
+ Plane near_plane = Plane(matrix[3] + matrix[2],
+ matrix[7] + matrix[6],
+ matrix[11] + matrix[10],
+ -matrix[15] - matrix[14]);
+ near_plane.normalize();
+
+ ///////--- Right Plane ---///////
+ Plane right_plane = Plane(matrix[3] - matrix[0],
+ matrix[7] - matrix[4],
+ matrix[11] - matrix[8],
+ -matrix[15] + matrix[12]);
+ right_plane.normalize();
+
+ Plane top_plane = Plane(matrix[3] - matrix[1],
+ matrix[7] - matrix[5],
+ matrix[11] - matrix[9],
+ -matrix[15] + matrix[13]);
+ top_plane.normalize();
+
+ Vector3 res;
+ near_plane.intersect_3(right_plane, top_plane, &res);
+
+ return Vector2(res.x, res.y);
+}
+
+Vector2 Projection::get_far_plane_half_extents() const {
+ const real_t *matrix = (const real_t *)this->matrix;
+ ///////--- Far Plane ---///////
+ Plane far_plane = Plane(matrix[3] - matrix[2],
+ matrix[7] - matrix[6],
+ matrix[11] - matrix[10],
+ -matrix[15] + matrix[14]);
+ far_plane.normalize();
+
+ ///////--- Right Plane ---///////
+ Plane right_plane = Plane(matrix[3] - matrix[0],
+ matrix[7] - matrix[4],
+ matrix[11] - matrix[8],
+ -matrix[15] + matrix[12]);
+ right_plane.normalize();
+
+ Plane top_plane = Plane(matrix[3] - matrix[1],
+ matrix[7] - matrix[5],
+ matrix[11] - matrix[9],
+ -matrix[15] + matrix[13]);
+ top_plane.normalize();
+
+ Vector3 res;
+ far_plane.intersect_3(right_plane, top_plane, &res);
+
+ return Vector2(res.x, res.y);
+}
+
+bool Projection::get_endpoints(const Transform3D &p_transform, Vector3 *p_8points) const {
+ Vector<Plane> planes = get_projection_planes(Transform3D());
+ const Planes intersections[8][3] = {
+ { PLANE_FAR, PLANE_LEFT, PLANE_TOP },
+ { PLANE_FAR, PLANE_LEFT, PLANE_BOTTOM },
+ { PLANE_FAR, PLANE_RIGHT, PLANE_TOP },
+ { PLANE_FAR, PLANE_RIGHT, PLANE_BOTTOM },
+ { PLANE_NEAR, PLANE_LEFT, PLANE_TOP },
+ { PLANE_NEAR, PLANE_LEFT, PLANE_BOTTOM },
+ { PLANE_NEAR, PLANE_RIGHT, PLANE_TOP },
+ { PLANE_NEAR, PLANE_RIGHT, PLANE_BOTTOM },
+ };
+
+ for (int i = 0; i < 8; i++) {
+ Vector3 point;
+ bool res = planes[intersections[i][0]].intersect_3(planes[intersections[i][1]], planes[intersections[i][2]], &point);
+ ERR_FAIL_COND_V(!res, false);
+ p_8points[i] = p_transform.xform(point);
+ }
+
+ return true;
+}
+
+Vector<Plane> Projection::get_projection_planes(const Transform3D &p_transform) const {
+ /** Fast Plane Extraction from combined modelview/projection matrices.
+ * References:
+ * https://web.archive.org/web/20011221205252/https://www.markmorley.com/opengl/frustumculling.html
+ * https://web.archive.org/web/20061020020112/https://www2.ravensoft.com/users/ggribb/plane%20extraction.pdf
+ */
+
+ Vector<Plane> planes;
+ planes.resize(6);
+
+ const real_t *matrix = (const real_t *)this->matrix;
+
+ Plane new_plane;
+
+ ///////--- Near Plane ---///////
+ new_plane = Plane(matrix[3] + matrix[2],
+ matrix[7] + matrix[6],
+ matrix[11] + matrix[10],
+ matrix[15] + matrix[14]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ planes.write[0] = p_transform.xform(new_plane);
+
+ ///////--- Far Plane ---///////
+ new_plane = Plane(matrix[3] - matrix[2],
+ matrix[7] - matrix[6],
+ matrix[11] - matrix[10],
+ matrix[15] - matrix[14]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ planes.write[1] = p_transform.xform(new_plane);
+
+ ///////--- Left Plane ---///////
+ new_plane = Plane(matrix[3] + matrix[0],
+ matrix[7] + matrix[4],
+ matrix[11] + matrix[8],
+ matrix[15] + matrix[12]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ planes.write[2] = p_transform.xform(new_plane);
+
+ ///////--- Top Plane ---///////
+ new_plane = Plane(matrix[3] - matrix[1],
+ matrix[7] - matrix[5],
+ matrix[11] - matrix[9],
+ matrix[15] - matrix[13]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ planes.write[3] = p_transform.xform(new_plane);
+
+ ///////--- Right Plane ---///////
+ new_plane = Plane(matrix[3] - matrix[0],
+ matrix[7] - matrix[4],
+ matrix[11] - matrix[8],
+ matrix[15] - matrix[12]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ planes.write[4] = p_transform.xform(new_plane);
+
+ ///////--- Bottom Plane ---///////
+ new_plane = Plane(matrix[3] + matrix[1],
+ matrix[7] + matrix[5],
+ matrix[11] + matrix[9],
+ matrix[15] + matrix[13]);
+
+ new_plane.normal = -new_plane.normal;
+ new_plane.normalize();
+
+ planes.write[5] = p_transform.xform(new_plane);
+
+ return planes;
+}
+
+Projection Projection::inverse() const {
+ Projection cm = *this;
+ cm.invert();
+ return cm;
+}
+
+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 = matrix[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)) {
+ pvt_i[k] = i;
+ pvt_j[k] = j;
+ pvt_val = matrix[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 = -matrix[k][j];
+ matrix[k][j] = matrix[i][j];
+ matrix[i][j] = hold;
+ }
+ }
+
+ /** "Interchange" columns **/
+ 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;
+ }
+ }
+
+ /** Divide column by minus pivot value **/
+ for (i = 0; i < 4; i++) {
+ if (i != k) {
+ matrix[i][k] /= (-pvt_val);
+ }
+ }
+
+ /** Reduce the matrix **/
+ for (i = 0; i < 4; i++) {
+ hold = matrix[i][k];
+ for (j = 0; j < 4; j++) {
+ if (i != k && j != k) {
+ matrix[i][j] += hold * matrix[k][j];
+ }
+ }
+ }
+
+ /** Divide row by pivot **/
+ for (j = 0; j < 4; j++) {
+ if (j != k) {
+ matrix[k][j] /= pvt_val;
+ }
+ }
+
+ /** Replace pivot by reciprocal (at last we can touch it). **/
+ matrix[k][k] = 1.0 / pvt_val;
+ }
+
+ /* 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 = matrix[k][j];
+ matrix[k][j] = -matrix[i][j];
+ matrix[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;
+ }
+ }
+ }
+}
+
+void Projection::flip_y() {
+ for (int i = 0; i < 4; i++) {
+ matrix[1][i] = -matrix[1][i];
+ }
+}
+
+Projection::Projection() {
+ set_identity();
+}
+
+Projection Projection::operator*(const Projection &p_matrix) const {
+ Projection new_matrix;
+
+ for (int j = 0; j < 4; j++) {
+ 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];
+ }
+ new_matrix.matrix[j][i] = ab;
+ }
+ }
+
+ return new_matrix;
+}
+
+void Projection::set_depth_correction(bool p_flip_y) {
+ real_t *m = &matrix[0][0];
+
+ m[0] = 1;
+ m[1] = 0.0;
+ m[2] = 0.0;
+ m[3] = 0.0;
+ m[4] = 0.0;
+ m[5] = p_flip_y ? -1 : 1;
+ m[6] = 0.0;
+ m[7] = 0.0;
+ m[8] = 0.0;
+ m[9] = 0.0;
+ m[10] = 0.5;
+ m[11] = 0.0;
+ m[12] = 0.0;
+ m[13] = 0.0;
+ m[14] = 0.5;
+ m[15] = 1.0;
+}
+
+void Projection::set_light_bias() {
+ real_t *m = &matrix[0][0];
+
+ m[0] = 0.5;
+ m[1] = 0.0;
+ m[2] = 0.0;
+ m[3] = 0.0;
+ m[4] = 0.0;
+ m[5] = 0.5;
+ m[6] = 0.0;
+ m[7] = 0.0;
+ m[8] = 0.0;
+ m[9] = 0.0;
+ m[10] = 0.5;
+ m[11] = 0.0;
+ m[12] = 0.5;
+ m[13] = 0.5;
+ m[14] = 0.5;
+ m[15] = 1.0;
+}
+
+void Projection::set_light_atlas_rect(const Rect2 &p_rect) {
+ real_t *m = &matrix[0][0];
+
+ m[0] = p_rect.size.width;
+ m[1] = 0.0;
+ m[2] = 0.0;
+ m[3] = 0.0;
+ m[4] = 0.0;
+ m[5] = p_rect.size.height;
+ m[6] = 0.0;
+ m[7] = 0.0;
+ m[8] = 0.0;
+ m[9] = 0.0;
+ m[10] = 1.0;
+ m[11] = 0.0;
+ m[12] = p_rect.position.x;
+ m[13] = p_rect.position.y;
+ m[14] = 0.0;
+ m[15] = 1.0;
+}
+
+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]);
+ }
+ }
+
+ return str;
+}
+
+real_t Projection::get_aspect() const {
+ Vector2 vp_he = get_viewport_half_extents();
+ return vp_he.x / vp_he.y;
+}
+
+int Projection::get_pixels_per_meter(int p_for_pixel_width) const {
+ Vector3 result = xform(Vector3(1, 0, -1));
+
+ return int((result.x * 0.5 + 0.5) * p_for_pixel_width);
+}
+
+bool Projection::is_orthogonal() const {
+ return matrix[3][3] == 1.0;
+}
+
+real_t Projection::get_fov() const {
+ const real_t *matrix = (const real_t *)this->matrix;
+
+ Plane right_plane = Plane(matrix[3] - matrix[0],
+ matrix[7] - matrix[4],
+ matrix[11] - matrix[8],
+ -matrix[15] + matrix[12]);
+ right_plane.normalize();
+
+ if ((matrix[8] == 0) && (matrix[9] == 0)) {
+ return Math::rad2deg(Math::acos(Math::abs(right_plane.normal.x))) * 2.0;
+ } else {
+ // our frustum is asymmetrical need to calculate the left planes angle separately..
+ Plane left_plane = Plane(matrix[3] + matrix[0],
+ matrix[7] + matrix[4],
+ matrix[11] + matrix[8],
+ matrix[15] + matrix[12]);
+ left_plane.normalize();
+
+ return Math::rad2deg(Math::acos(Math::abs(left_plane.normal.x))) + Math::rad2deg(Math::acos(Math::abs(right_plane.normal.x)));
+ }
+}
+
+float Projection::get_lod_multiplier() const {
+ if (is_orthogonal()) {
+ return get_viewport_half_extents().x;
+ } else {
+ float zn = get_z_near();
+ float width = get_viewport_half_extents().x * 2.0;
+ return 1.0 / (zn / width);
+ }
+
+ //usage is lod_size / (lod_distance * multiplier) < threshold
+}
+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;
+}
+
+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);
+
+ 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);
+
+ 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);
+
+ matrix[0][3] = 0;
+ matrix[1][3] = 0;
+ matrix[2][3] = 0;
+ matrix[3][3] = 1;
+}
+
+void Projection::add_jitter_offset(const Vector2 &p_offset) {
+ matrix[3][0] += p_offset.x;
+ matrix[3][1] += p_offset.y;
+}
+
+Projection::operator Transform3D() const {
+ Transform3D tr;
+ const real_t *m = &matrix[0][0];
+
+ tr.basis.rows[0][0] = m[0];
+ tr.basis.rows[1][0] = m[1];
+ tr.basis.rows[2][0] = m[2];
+
+ tr.basis.rows[0][1] = m[4];
+ tr.basis.rows[1][1] = m[5];
+ tr.basis.rows[2][1] = m[6];
+
+ tr.basis.rows[0][2] = m[8];
+ tr.basis.rows[1][2] = m[9];
+ tr.basis.rows[2][2] = m[10];
+
+ tr.origin.x = m[12];
+ tr.origin.y = m[13];
+ tr.origin.z = m[14];
+
+ 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;
+}
+Projection::Projection(const Transform3D &p_transform) {
+ const Transform3D &tr = p_transform;
+ real_t *m = &matrix[0][0];
+
+ m[0] = tr.basis.rows[0][0];
+ m[1] = tr.basis.rows[1][0];
+ m[2] = tr.basis.rows[2][0];
+ m[3] = 0.0;
+ m[4] = tr.basis.rows[0][1];
+ m[5] = tr.basis.rows[1][1];
+ m[6] = tr.basis.rows[2][1];
+ m[7] = 0.0;
+ m[8] = tr.basis.rows[0][2];
+ m[9] = tr.basis.rows[1][2];
+ m[10] = tr.basis.rows[2][2];
+ m[11] = 0.0;
+ m[12] = tr.origin.x;
+ m[13] = tr.origin.y;
+ m[14] = tr.origin.z;
+ m[15] = 1.0;
+}
+
+Projection::~Projection() {
+}
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