937 lines
28 KiB
C++
937 lines
28 KiB
C++
/**************************************************************************/
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/* projection.cpp */
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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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#include "projection.h"
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#include "core/math/aabb.h"
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#include "core/math/math_funcs.h"
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#include "core/math/plane.h"
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#include "core/math/rect2.h"
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#include "core/math/transform_3d.h"
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#include "core/string/ustring.h"
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float Projection::determinant() const {
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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] -
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columns[0][3] * columns[1][1] * columns[2][2] * columns[3][0] + columns[0][1] * columns[1][3] * columns[2][2] * columns[3][0] +
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columns[0][2] * columns[1][1] * columns[2][3] * columns[3][0] - columns[0][1] * columns[1][2] * columns[2][3] * columns[3][0] -
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columns[0][3] * columns[1][2] * columns[2][0] * columns[3][1] + columns[0][2] * columns[1][3] * columns[2][0] * columns[3][1] +
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columns[0][3] * columns[1][0] * columns[2][2] * columns[3][1] - columns[0][0] * columns[1][3] * columns[2][2] * columns[3][1] -
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columns[0][2] * columns[1][0] * columns[2][3] * columns[3][1] + columns[0][0] * columns[1][2] * columns[2][3] * columns[3][1] +
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columns[0][3] * columns[1][1] * columns[2][0] * columns[3][2] - columns[0][1] * columns[1][3] * columns[2][0] * columns[3][2] -
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columns[0][3] * columns[1][0] * columns[2][1] * columns[3][2] + columns[0][0] * columns[1][3] * columns[2][1] * columns[3][2] +
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columns[0][1] * columns[1][0] * columns[2][3] * columns[3][2] - columns[0][0] * columns[1][1] * columns[2][3] * columns[3][2] -
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columns[0][2] * columns[1][1] * columns[2][0] * columns[3][3] + columns[0][1] * columns[1][2] * columns[2][0] * columns[3][3] +
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columns[0][2] * columns[1][0] * columns[2][1] * columns[3][3] - columns[0][0] * columns[1][2] * columns[2][1] * columns[3][3] -
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columns[0][1] * columns[1][0] * columns[2][2] * columns[3][3] + columns[0][0] * columns[1][1] * columns[2][2] * columns[3][3];
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}
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void Projection::set_identity() {
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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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columns[i][j] = (i == j) ? 1 : 0;
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}
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}
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}
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void Projection::set_zero() {
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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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columns[i][j] = 0;
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}
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}
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}
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Plane Projection::xform4(const Plane &p_vec4) const {
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Plane ret;
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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;
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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;
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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;
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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;
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return ret;
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}
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Vector4 Projection::xform(const Vector4 &p_vec4) const {
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return Vector4(
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columns[0][0] * p_vec4.x + columns[1][0] * p_vec4.y + columns[2][0] * p_vec4.z + columns[3][0] * p_vec4.w,
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columns[0][1] * p_vec4.x + columns[1][1] * p_vec4.y + columns[2][1] * p_vec4.z + columns[3][1] * p_vec4.w,
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columns[0][2] * p_vec4.x + columns[1][2] * p_vec4.y + columns[2][2] * p_vec4.z + columns[3][2] * p_vec4.w,
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columns[0][3] * p_vec4.x + columns[1][3] * p_vec4.y + columns[2][3] * p_vec4.z + columns[3][3] * p_vec4.w);
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}
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Vector4 Projection::xform_inv(const Vector4 &p_vec4) const {
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return Vector4(
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columns[0][0] * p_vec4.x + columns[0][1] * p_vec4.y + columns[0][2] * p_vec4.z + columns[0][3] * p_vec4.w,
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columns[1][0] * p_vec4.x + columns[1][1] * p_vec4.y + columns[1][2] * p_vec4.z + columns[1][3] * p_vec4.w,
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columns[2][0] * p_vec4.x + columns[2][1] * p_vec4.y + columns[2][2] * p_vec4.z + columns[2][3] * p_vec4.w,
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columns[3][0] * p_vec4.x + columns[3][1] * p_vec4.y + columns[3][2] * p_vec4.z + columns[3][3] * p_vec4.w);
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}
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void Projection::adjust_perspective_znear(real_t p_new_znear) {
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real_t zfar = get_z_far();
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real_t znear = p_new_znear;
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real_t deltaZ = zfar - znear;
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columns[2][2] = -(zfar + znear) / deltaZ;
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columns[3][2] = -2 * znear * zfar / deltaZ;
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}
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Projection Projection::create_depth_correction(bool p_flip_y) {
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Projection proj;
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proj.set_depth_correction(p_flip_y);
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return proj;
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}
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Projection Projection::create_light_atlas_rect(const Rect2 &p_rect) {
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Projection proj;
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proj.set_light_atlas_rect(p_rect);
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return proj;
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}
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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) {
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Projection proj;
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proj.set_perspective(p_fovy_degrees, p_aspect, p_z_near, p_z_far, p_flip_fov);
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return proj;
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}
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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) {
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Projection proj;
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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);
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return proj;
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}
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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) {
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Projection proj;
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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);
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return proj;
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}
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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) {
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Projection proj;
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proj.set_orthogonal(p_left, p_right, p_bottom, p_top, p_znear, p_zfar);
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return proj;
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}
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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) {
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Projection proj;
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proj.set_orthogonal(p_size, p_aspect, p_znear, p_zfar, p_flip_fov);
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return proj;
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}
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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) {
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Projection proj;
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proj.set_frustum(p_left, p_right, p_bottom, p_top, p_near, p_far);
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return proj;
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}
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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) {
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Projection proj;
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proj.set_frustum(p_size, p_aspect, p_offset, p_near, p_far, p_flip_fov);
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return proj;
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}
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Projection Projection::create_fit_aabb(const AABB &p_aabb) {
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Projection proj;
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proj.scale_translate_to_fit(p_aabb);
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return proj;
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}
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Projection Projection::perspective_znear_adjusted(real_t p_new_znear) const {
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Projection proj = *this;
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proj.adjust_perspective_znear(p_new_znear);
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return proj;
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}
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Plane Projection::get_projection_plane(Planes p_plane) const {
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const real_t *matrix = (const real_t *)columns;
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switch (p_plane) {
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case PLANE_NEAR: {
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Plane new_plane = Plane(matrix[3] + matrix[2],
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matrix[7] + matrix[6],
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matrix[11] + matrix[10],
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matrix[15] + matrix[14]);
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new_plane.normal = -new_plane.normal;
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new_plane.normalize();
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return new_plane;
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}
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case PLANE_FAR: {
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Plane new_plane = Plane(matrix[3] - matrix[2],
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matrix[7] - matrix[6],
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matrix[11] - matrix[10],
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matrix[15] - matrix[14]);
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new_plane.normal = -new_plane.normal;
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new_plane.normalize();
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return new_plane;
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}
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case PLANE_LEFT: {
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Plane new_plane = Plane(matrix[3] + matrix[0],
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matrix[7] + matrix[4],
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matrix[11] + matrix[8],
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matrix[15] + matrix[12]);
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new_plane.normal = -new_plane.normal;
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new_plane.normalize();
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return new_plane;
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}
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case PLANE_TOP: {
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Plane new_plane = Plane(matrix[3] - matrix[1],
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matrix[7] - matrix[5],
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matrix[11] - matrix[9],
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matrix[15] - matrix[13]);
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new_plane.normal = -new_plane.normal;
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new_plane.normalize();
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return new_plane;
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}
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case PLANE_RIGHT: {
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Plane new_plane = Plane(matrix[3] - matrix[0],
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matrix[7] - matrix[4],
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matrix[11] - matrix[8],
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matrix[15] - matrix[12]);
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new_plane.normal = -new_plane.normal;
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new_plane.normalize();
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return new_plane;
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}
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case PLANE_BOTTOM: {
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Plane new_plane = Plane(matrix[3] + matrix[1],
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matrix[7] + matrix[5],
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matrix[11] + matrix[9],
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matrix[15] + matrix[13]);
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new_plane.normal = -new_plane.normal;
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new_plane.normalize();
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return new_plane;
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}
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}
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return Plane();
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}
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Projection Projection::flipped_y() const {
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Projection proj = *this;
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proj.flip_y();
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return proj;
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}
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Projection Projection ::jitter_offseted(const Vector2 &p_offset) const {
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Projection proj = *this;
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proj.add_jitter_offset(p_offset);
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return proj;
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}
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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) {
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if (p_flip_fov) {
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p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect);
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}
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real_t sine, cotangent, deltaZ;
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real_t radians = Math::deg_to_rad(p_fovy_degrees / 2.0);
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deltaZ = p_z_far - p_z_near;
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sine = Math::sin(radians);
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if ((deltaZ == 0) || (sine == 0) || (p_aspect == 0)) {
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return;
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}
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cotangent = Math::cos(radians) / sine;
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set_identity();
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columns[0][0] = cotangent / p_aspect;
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columns[1][1] = cotangent;
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columns[2][2] = -(p_z_far + p_z_near) / deltaZ;
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columns[2][3] = -1;
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columns[3][2] = -2 * p_z_near * p_z_far / deltaZ;
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columns[3][3] = 0;
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}
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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) {
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if (p_flip_fov) {
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p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect);
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}
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real_t left, right, modeltranslation, ymax, xmax, frustumshift;
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ymax = p_z_near * tan(Math::deg_to_rad(p_fovy_degrees / 2.0));
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xmax = ymax * p_aspect;
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frustumshift = (p_intraocular_dist / 2.0) * p_z_near / p_convergence_dist;
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switch (p_eye) {
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case 1: { // left eye
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left = -xmax + frustumshift;
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right = xmax + frustumshift;
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modeltranslation = p_intraocular_dist / 2.0;
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} break;
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case 2: { // right eye
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left = -xmax - frustumshift;
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right = xmax - frustumshift;
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modeltranslation = -p_intraocular_dist / 2.0;
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} break;
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default: { // mono, should give the same result as set_perspective(p_fovy_degrees,p_aspect,p_z_near,p_z_far,p_flip_fov)
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left = -xmax;
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right = xmax;
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modeltranslation = 0.0;
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} break;
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}
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set_frustum(left, right, -ymax, ymax, p_z_near, p_z_far);
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// translate matrix by (modeltranslation, 0.0, 0.0)
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Projection cm;
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cm.set_identity();
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cm.columns[3][0] = modeltranslation;
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*this = *this * cm;
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}
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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) {
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// we first calculate our base frustum on our values without taking our lens magnification into account.
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real_t f1 = (p_intraocular_dist * 0.5) / p_display_to_lens;
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real_t f2 = ((p_display_width - p_intraocular_dist) * 0.5) / p_display_to_lens;
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real_t f3 = (p_display_width / 4.0) / p_display_to_lens;
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// 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
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// we're willing to sacrifice in FOV.
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real_t add = ((f1 + f2) * (p_oversample - 1.0)) / 2.0;
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f1 += add;
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f2 += add;
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f3 *= p_oversample;
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// always apply KEEP_WIDTH aspect ratio
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f3 /= p_aspect;
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switch (p_eye) {
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case 1: { // left eye
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set_frustum(-f2 * p_z_near, f1 * p_z_near, -f3 * p_z_near, f3 * p_z_near, p_z_near, p_z_far);
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} break;
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case 2: { // right eye
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set_frustum(-f1 * p_z_near, f2 * p_z_near, -f3 * p_z_near, f3 * p_z_near, p_z_near, p_z_far);
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} break;
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default: { // mono, does not apply here!
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} break;
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}
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}
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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) {
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set_identity();
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columns[0][0] = 2.0 / (p_right - p_left);
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columns[3][0] = -((p_right + p_left) / (p_right - p_left));
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columns[1][1] = 2.0 / (p_top - p_bottom);
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columns[3][1] = -((p_top + p_bottom) / (p_top - p_bottom));
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columns[2][2] = -2.0 / (p_zfar - p_znear);
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columns[3][2] = -((p_zfar + p_znear) / (p_zfar - p_znear));
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columns[3][3] = 1.0;
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}
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void Projection::set_orthogonal(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov) {
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if (!p_flip_fov) {
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p_size *= p_aspect;
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}
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set_orthogonal(-p_size / 2, +p_size / 2, -p_size / p_aspect / 2, +p_size / p_aspect / 2, p_znear, p_zfar);
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}
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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) {
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ERR_FAIL_COND(p_right <= p_left);
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ERR_FAIL_COND(p_top <= p_bottom);
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ERR_FAIL_COND(p_far <= p_near);
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|
|
|
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);
|
|
|
|
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 *)columns;
|
|
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;
|
|
}
|
|
|
|
real_t Projection::get_z_near() const {
|
|
const real_t *matrix = (const real_t *)columns;
|
|
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 *)columns;
|
|
///////--- 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 *)columns;
|
|
///////--- 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;
|
|
Plane a = planes[intersections[i][0]];
|
|
Plane b = planes[intersections[i][1]];
|
|
Plane c = planes[intersections[i][2]];
|
|
bool res = a.intersect_3(b, c, &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 *)columns;
|
|
|
|
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 = 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;
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
}
|
|
|
|
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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void Projection::flip_y() {
|
|
for (int i = 0; i < 4; i++) {
|
|
columns[1][i] = -columns[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 += columns[k][i] * p_matrix.columns[j][k];
|
|
}
|
|
new_matrix.columns[j][i] = ab;
|
|
}
|
|
}
|
|
|
|
return new_matrix;
|
|
}
|
|
|
|
void Projection::set_depth_correction(bool p_flip_y) {
|
|
real_t *m = &columns[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 = &columns[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 = &columns[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(columns[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 columns[3][3] == 1.0;
|
|
}
|
|
|
|
real_t Projection::get_fov() const {
|
|
const real_t *matrix = (const real_t *)columns;
|
|
|
|
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::rad_to_deg(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::rad_to_deg(Math::acos(Math::abs(left_plane.normal.x))) + Math::rad_to_deg(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();
|
|
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;
|
|
|
|
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);
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columns[0][1] = 0;
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columns[1][1] = 2 / (max.y - min.y);
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columns[2][1] = 0;
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columns[3][1] = -(max.y + min.y) / (max.y - min.y);
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|
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columns[0][2] = 0;
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columns[1][2] = 0;
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columns[2][2] = 2 / (max.z - min.z);
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columns[3][2] = -(max.z + min.z) / (max.z - min.z);
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|
|
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columns[0][3] = 0;
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columns[1][3] = 0;
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columns[2][3] = 0;
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columns[3][3] = 1;
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}
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void Projection::add_jitter_offset(const Vector2 &p_offset) {
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columns[3][0] += p_offset.x;
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columns[3][1] += p_offset.y;
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}
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Projection::operator Transform3D() const {
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Transform3D tr;
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const real_t *m = &columns[0][0];
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tr.basis.rows[0][0] = m[0];
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tr.basis.rows[1][0] = m[1];
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tr.basis.rows[2][0] = m[2];
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|
|
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tr.basis.rows[0][1] = m[4];
|
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tr.basis.rows[1][1] = m[5];
|
|
tr.basis.rows[2][1] = m[6];
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|
|
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tr.basis.rows[0][2] = m[8];
|
|
tr.basis.rows[1][2] = m[9];
|
|
tr.basis.rows[2][2] = m[10];
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|
|
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tr.origin.x = m[12];
|
|
tr.origin.y = m[13];
|
|
tr.origin.z = m[14];
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|
|
|
return tr;
|
|
}
|
|
|
|
Projection::Projection(const Vector4 &p_x, const Vector4 &p_y, const Vector4 &p_z, const Vector4 &p_w) {
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|
columns[0] = p_x;
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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 = &columns[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;
|
|
}
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|
|
|
Projection::~Projection() {
|
|
}
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