/*************************************************************************/ /* camera_matrix.cpp */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2019 Juan Linietsky, Ariel Manzur. */ /* Copyright (c) 2014-2019 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 "camera_matrix.h" #include "core/math/math_funcs.h" #include "core/print_string.h" void CameraMatrix::set_identity() { for (int i = 0; i < 4; i++) { for (int j = 0; j < 4; j++) { matrix[i][j] = (i == j) ? 1 : 0; } } } void CameraMatrix::set_zero() { for (int i = 0; i < 4; i++) { for (int j = 0; j < 4; j++) { matrix[i][j] = 0; } } } Plane CameraMatrix::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; } 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) { if (p_flip_fov) { p_fovy_degrees = get_fovy(p_fovy_degrees, 1.0 / p_aspect); } real_t sine, cotangent, deltaZ; real_t radians = p_fovy_degrees / 2.0 * Math_PI / 180.0; 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 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) { 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(p_fovy_degrees * Math_PI / 360.0f); 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) CameraMatrix cm; cm.set_identity(); cm.matrix[3][0] = modeltranslation; *this = *this * cm; } 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) { // 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 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) { 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 CameraMatrix::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 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) { 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 CameraMatrix::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 CameraMatrix::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 CameraMatrix::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; } void CameraMatrix::get_viewport_size(real_t &r_width, real_t &r_height) 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); r_width = res.x; r_height = res.y; } bool CameraMatrix::get_endpoints(const Transform &p_transform, Vector3 *p_8points) const { Vector<Plane> planes = get_projection_planes(Transform()); 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> CameraMatrix::get_projection_planes(const Transform &p_transform) const { /** Fast Plane Extraction from combined modelview/projection matrices. * References: * https://web.archive.org/web/20011221205252/http://www.markmorley.com/opengl/frustumculling.html * https://web.archive.org/web/20061020020112/http://www2.ravensoft.com/users/ggribb/plane%20extraction.pdf */ Vector<Plane> planes; 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.push_back(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.push_back(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.push_back(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.push_back(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.push_back(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.push_back(p_transform.xform(new_plane)); return planes; } CameraMatrix CameraMatrix::inverse() const { CameraMatrix cm = *this; cm.invert(); return cm; } void CameraMatrix::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 determinat; /* Determinant */ determinat = 1.0; 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::absd(matrix[i][j]) > Math::absd(pvt_val)) { pvt_i[k] = i; pvt_j[k] = j; pvt_val = matrix[i][j]; } } } /** Product of pivots, gives determinant when finished **/ determinat *= pvt_val; if (Math::absd(determinat) < 1e-7) { return; //(false); /** 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; } } } 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() { }