674 lines
18 KiB
C++
674 lines
18 KiB
C++
/*************************************************************************/
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/* camera_matrix.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) 2007-2017 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2017 Godot Engine contributors (cf. AUTHORS.md) */
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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 "camera_matrix.h"
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#include "math_funcs.h"
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#include "print_string.h"
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void CameraMatrix::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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matrix[i][j] = (i == j) ? 1 : 0;
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}
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}
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}
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void CameraMatrix::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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matrix[i][j] = 0;
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}
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}
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}
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Plane CameraMatrix::xform4(const Plane &p_vec4) const {
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Plane ret;
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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;
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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;
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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;
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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;
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return ret;
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}
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void CameraMatrix::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 = p_fovy_degrees / 2.0 * Math_PI / 180.0;
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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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matrix[0][0] = cotangent / p_aspect;
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matrix[1][1] = cotangent;
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matrix[2][2] = -(p_z_far + p_z_near) / deltaZ;
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matrix[2][3] = -1;
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matrix[3][2] = -2 * p_z_near * p_z_far / deltaZ;
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matrix[3][3] = 0;
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}
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void CameraMatrix::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(p_fovy_degrees * Math_PI / 360.0f);
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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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CameraMatrix cm;
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cm.set_identity();
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cm.matrix[3][0] = modeltranslation;
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*this = *this * cm;
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}
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void CameraMatrix::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 CameraMatrix::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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matrix[0][0] = 2.0 / (p_right - p_left);
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matrix[3][0] = -((p_right + p_left) / (p_right - p_left));
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matrix[1][1] = 2.0 / (p_top - p_bottom);
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matrix[3][1] = -((p_top + p_bottom) / (p_top - p_bottom));
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matrix[2][2] = -2.0 / (p_zfar - p_znear);
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matrix[3][2] = -((p_zfar + p_znear) / (p_zfar - p_znear));
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matrix[3][3] = 1.0;
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}
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void CameraMatrix::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 CameraMatrix::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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real_t *te = &matrix[0][0];
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real_t x = 2 * p_near / (p_right - p_left);
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real_t y = 2 * p_near / (p_top - p_bottom);
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real_t a = (p_right + p_left) / (p_right - p_left);
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real_t b = (p_top + p_bottom) / (p_top - p_bottom);
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real_t c = -(p_far + p_near) / (p_far - p_near);
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real_t d = -2 * p_far * p_near / (p_far - p_near);
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te[0] = x;
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te[1] = 0;
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te[2] = 0;
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te[3] = 0;
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te[4] = 0;
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te[5] = y;
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te[6] = 0;
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te[7] = 0;
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te[8] = a;
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te[9] = b;
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te[10] = c;
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te[11] = -1;
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te[12] = 0;
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te[13] = 0;
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te[14] = d;
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te[15] = 0;
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}
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real_t CameraMatrix::get_z_far() const {
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const real_t *matrix = (const real_t *)this->matrix;
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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.d;
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}
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real_t CameraMatrix::get_z_near() const {
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const real_t *matrix = (const real_t *)this->matrix;
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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.normalize();
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return new_plane.d;
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}
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void CameraMatrix::get_viewport_size(real_t &r_width, real_t &r_height) const {
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const real_t *matrix = (const real_t *)this->matrix;
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///////--- Near Plane ---///////
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Plane near_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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near_plane.normalize();
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///////--- Right Plane ---///////
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Plane right_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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right_plane.normalize();
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Plane top_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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top_plane.normalize();
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Vector3 res;
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near_plane.intersect_3(right_plane, top_plane, &res);
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r_width = res.x;
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r_height = res.y;
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}
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bool CameraMatrix::get_endpoints(const Transform &p_transform, Vector3 *p_8points) const {
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Vector<Plane> planes = get_projection_planes(Transform());
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const Planes intersections[8][3] = {
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{ PLANE_FAR, PLANE_LEFT, PLANE_TOP },
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{ PLANE_FAR, PLANE_LEFT, PLANE_BOTTOM },
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{ PLANE_FAR, PLANE_RIGHT, PLANE_TOP },
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{ PLANE_FAR, PLANE_RIGHT, PLANE_BOTTOM },
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{ PLANE_NEAR, PLANE_LEFT, PLANE_TOP },
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{ PLANE_NEAR, PLANE_LEFT, PLANE_BOTTOM },
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{ PLANE_NEAR, PLANE_RIGHT, PLANE_TOP },
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{ PLANE_NEAR, PLANE_RIGHT, PLANE_BOTTOM },
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};
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for (int i = 0; i < 8; i++) {
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Vector3 point;
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bool res = planes[intersections[i][0]].intersect_3(planes[intersections[i][1]], planes[intersections[i][2]], &point);
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ERR_FAIL_COND_V(!res, false);
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p_8points[i] = p_transform.xform(point);
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}
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return true;
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}
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Vector<Plane> CameraMatrix::get_projection_planes(const Transform &p_transform) const {
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/** Fast Plane Extraction from combined modelview/projection matrices.
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* References:
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* http://www.markmorley.com/opengl/frustumculling.html
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* http://www2.ravensoft.com/users/ggribb/plane%20extraction.pdf
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*/
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Vector<Plane> planes;
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const real_t *matrix = (const real_t *)this->matrix;
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Plane new_plane;
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///////--- Near Plane ---///////
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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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planes.push_back(p_transform.xform(new_plane));
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///////--- Far Plane ---///////
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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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planes.push_back(p_transform.xform(new_plane));
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///////--- Left Plane ---///////
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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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planes.push_back(p_transform.xform(new_plane));
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///////--- Top Plane ---///////
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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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planes.push_back(p_transform.xform(new_plane));
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///////--- Right Plane ---///////
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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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planes.push_back(p_transform.xform(new_plane));
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///////--- Bottom Plane ---///////
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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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planes.push_back(p_transform.xform(new_plane));
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return planes;
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}
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CameraMatrix CameraMatrix::inverse() const {
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CameraMatrix cm = *this;
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cm.invert();
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return cm;
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}
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void CameraMatrix::invert() {
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int i, j, k;
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int pvt_i[4], pvt_j[4]; /* Locations of pivot matrix */
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real_t pvt_val; /* Value of current pivot element */
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real_t hold; /* Temporary storage */
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real_t determinat; /* Determinant */
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determinat = 1.0;
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for (k = 0; k < 4; k++) {
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/** Locate k'th pivot element **/
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pvt_val = matrix[k][k]; /** Initialize for search **/
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pvt_i[k] = k;
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pvt_j[k] = k;
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for (i = k; i < 4; i++) {
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for (j = k; j < 4; j++) {
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if (Math::absd(matrix[i][j]) > Math::absd(pvt_val)) {
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pvt_i[k] = i;
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pvt_j[k] = j;
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pvt_val = matrix[i][j];
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}
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}
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}
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/** Product of pivots, gives determinant when finished **/
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determinat *= pvt_val;
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if (Math::absd(determinat) < 1e-7) {
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return; //(false); /** Matrix is singular (zero determinant). **/
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}
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/** "Interchange" rows (with sign change stuff) **/
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i = pvt_i[k];
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if (i != k) { /** If rows are different **/
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for (j = 0; j < 4; j++) {
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hold = -matrix[k][j];
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matrix[k][j] = matrix[i][j];
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matrix[i][j] = hold;
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}
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}
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/** "Interchange" columns **/
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j = pvt_j[k];
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if (j != k) { /** If columns are different **/
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for (i = 0; i < 4; i++) {
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hold = -matrix[i][k];
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matrix[i][k] = matrix[i][j];
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matrix[i][j] = hold;
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}
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}
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/** Divide column by minus pivot value **/
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for (i = 0; i < 4; i++) {
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if (i != k) matrix[i][k] /= (-pvt_val);
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}
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/** Reduce the matrix **/
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for (i = 0; i < 4; i++) {
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hold = matrix[i][k];
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for (j = 0; j < 4; j++) {
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if (i != k && j != k) matrix[i][j] += hold * matrix[k][j];
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}
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}
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/** Divide row by pivot **/
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for (j = 0; j < 4; j++) {
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if (j != k) matrix[k][j] /= pvt_val;
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}
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/** Replace pivot by reciprocal (at last we can touch it). **/
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matrix[k][k] = 1.0 / pvt_val;
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}
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/* That was most of the work, one final pass of row/column interchange */
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/* to finish */
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for (k = 4 - 2; k >= 0; k--) { /* Don't need to work with 1 by 1 corner*/
|
|
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;
|
|
}
|
|
}
|
|
}
|
|
|
|
CameraMatrix::CameraMatrix() {
|
|
|
|
set_identity();
|
|
}
|
|
|
|
CameraMatrix CameraMatrix::operator*(const CameraMatrix &p_matrix) const {
|
|
|
|
CameraMatrix 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 CameraMatrix::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 CameraMatrix::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;
|
|
}
|
|
|
|
CameraMatrix::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 CameraMatrix::get_aspect() const {
|
|
|
|
real_t w, h;
|
|
get_viewport_size(w, h);
|
|
return w / h;
|
|
}
|
|
|
|
int CameraMatrix::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 CameraMatrix::is_orthogonal() const {
|
|
|
|
return matrix[3][3] == 1.0;
|
|
}
|
|
|
|
real_t CameraMatrix::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)));
|
|
}
|
|
}
|
|
|
|
void CameraMatrix::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 CameraMatrix::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;
|
|
}
|
|
|
|
CameraMatrix::operator Transform() const {
|
|
|
|
Transform tr;
|
|
const real_t *m = &matrix[0][0];
|
|
|
|
tr.basis.elements[0][0] = m[0];
|
|
tr.basis.elements[1][0] = m[1];
|
|
tr.basis.elements[2][0] = m[2];
|
|
|
|
tr.basis.elements[0][1] = m[4];
|
|
tr.basis.elements[1][1] = m[5];
|
|
tr.basis.elements[2][1] = m[6];
|
|
|
|
tr.basis.elements[0][2] = m[8];
|
|
tr.basis.elements[1][2] = m[9];
|
|
tr.basis.elements[2][2] = m[10];
|
|
|
|
tr.origin.x = m[12];
|
|
tr.origin.y = m[13];
|
|
tr.origin.z = m[14];
|
|
|
|
return tr;
|
|
}
|
|
|
|
CameraMatrix::CameraMatrix(const Transform &p_transform) {
|
|
|
|
const Transform &tr = p_transform;
|
|
real_t *m = &matrix[0][0];
|
|
|
|
m[0] = tr.basis.elements[0][0];
|
|
m[1] = tr.basis.elements[1][0];
|
|
m[2] = tr.basis.elements[2][0];
|
|
m[3] = 0.0;
|
|
m[4] = tr.basis.elements[0][1];
|
|
m[5] = tr.basis.elements[1][1];
|
|
m[6] = tr.basis.elements[2][1];
|
|
m[7] = 0.0;
|
|
m[8] = tr.basis.elements[0][2];
|
|
m[9] = tr.basis.elements[1][2];
|
|
m[10] = tr.basis.elements[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;
|
|
}
|
|
|
|
CameraMatrix::~CameraMatrix() {
|
|
}
|