//[header] // A simple program that uses ray-tracing to render a single triangle //[/header] //[compile] // Download the raytri.cpp and geometry.h files to a folder. // Open a shell/terminal, and run the following command where the files is saved: // // c++ -o raytri raytri.cpp -O3 -std=c++11 -DMOLLER_TRUMBORE // // Run with: ./raytri. Open the file ./out.png in Photoshop or any program // reading PPM files. //[/compile] //[ignore] // Copyright (C) 2012 www.scratchapixel.com // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see <http://www.gnu.org/licenses/>. //[/ignore] // needed on Windows #define _USE_MATH_DEFINES #include <cstdio> #include <cstdlib> #include <memory> #include <vector> #include <utility> #include <cstdint> #include <iostream> #include <fstream> #include <cmath> #include <limits> #include <random> #include "geometry.h" constexpr float kEpsilon = 1e-8; inline float deg2rad(const float &deg) { return deg * M_PI / 180; } inline float clamp(const float &lo, const float &hi, const float &v) { return std::max(lo, std::min(hi, v)); } // [comment] // The main ray-triangle intersection routine. You can test both methoods: the // geometric method and the Moller-Trumbore algorithm (use the flag -DMOLLER_TRUMBORE // when you compile. // [/comment] bool rayTriangleIntersect( const Vec3f &orig, const Vec3f &dir, const Vec3f &v0, const Vec3f &v1, const Vec3f &v2, float &t, float &u, float &v) { #ifdef MOLLER_TRUMBORE Vec3f v0v1 = v1 - v0; Vec3f v0v2 = v2 - v0; Vec3f pvec = dir.crossProduct(v0v2); float det = v0v1.dotProduct(pvec); #ifdef CULLING // if the determinant is negative the triangle is backfacing // if the determinant is close to 0, the ray misses the triangle if (det < kEpsilon) return false; #else // ray and triangle are parallel if det is close to 0 if (fabs(det) < kEpsilon) return false; #endif float invDet = 1 / det; Vec3f tvec = orig - v0; u = tvec.dotProduct(pvec) * invDet; if (u < 0 || u > 1) return false; Vec3f qvec = tvec.crossProduct(v0v1); v = dir.dotProduct(qvec) * invDet; if (v < 0 || u + v > 1) return false; t = v0v2.dotProduct(qvec) * invDet; return true; #else // compute plane's normal Vec3f v0v1 = v1 - v0; Vec3f v0v2 = v2 - v0; // no need to normalize Vec3f N = v0v1.crossProduct(v0v2); // N float denom = N.dotProduct(N); // Step 1: finding P // check if ray and plane are parallel ? float NdotRayDirection = N.dotProduct(dir); if (fabs(NdotRayDirection) < kEpsilon) // almost 0 return false; // they are parallel so they don't intersect ! // compute d parameter using equation 2 float d = -N.dotProduct(v0); // compute t (equation 3) t = -(N.dotProduct(orig) + d) / NdotRayDirection; // check if the triangle is in behind the ray if (t < 0) return false; // the triangle is behind // compute the intersection point using equation 1 Vec3f P = orig + t * dir; // Step 2: inside-outside test Vec3f C; // vector perpendicular to triangle's plane // edge 0 Vec3f edge0 = v1 - v0; Vec3f vp0 = P - v0; C = edge0.crossProduct(vp0); if (N.dotProduct(C) < 0) return false; // P is on the right side // edge 1 Vec3f edge1 = v2 - v1; Vec3f vp1 = P - v1; C = edge1.crossProduct(vp1); if ((u = N.dotProduct(C)) < 0) return false; // P is on the right side // edge 2 Vec3f edge2 = v0 - v2; Vec3f vp2 = P - v2; C = edge2.crossProduct(vp2); if ((v = N.dotProduct(C)) < 0) return false; // P is on the right side; u /= denom; v /= denom; return true; // this ray hits the triangle #endif } int main(int argc, char **argv) { Vec3f v0(-1, -1, -5); Vec3f v1( 1, -1, -5); Vec3f v2( 0, 1, -5); const uint32_t width = 640; const uint32_t height = 480; Vec3f cols[3] = {{0.6, 0.4, 0.1}, {0.1, 0.5, 0.3}, {0.1, 0.3, 0.7}}; Vec3f *framebuffer = new Vec3f[width * height]; Vec3f *pix = framebuffer; float fov = 51.52; float scale = tan(deg2rad(fov * 0.5)); float imageAspectRatio = width / (float)height; Vec3f orig(0); for (uint32_t j = 0; j < height; ++j) { for (uint32_t i = 0; i < width; ++i) { // compute primary ray float x = (2 * (i + 0.5) / (float)width - 1) * imageAspectRatio * scale; float y = (1 - 2 * (j + 0.5) / (float)height) * scale; Vec3f dir(x, y, -1); dir.normalize(); float t, u, v; if (rayTriangleIntersect(orig, dir, v0, v1, v2, t, u, v)) { // [comment] // Interpolate colors using the barycentric coordinates // [/comment] *pix = u * cols[0] + v * cols[1] + (1 - u - v) * cols[2]; // uncomment this line if you want to visualize the row barycentric coordinates //*pix = Vec3f(u, v, 1 - u - v); } pix++; } } // Save result to a PPM image (keep these flags if you compile under Windows) std::ofstream ofs("./out.ppm", std::ios::out | std::ios::binary); ofs << "P6\n" << width << " " << height << "\n255\n"; for (uint32_t i = 0; i < height * width; ++i) { char r = (char)(255 * clamp(0, 1, framebuffer[i].x)); char g = (char)(255 * clamp(0, 1, framebuffer[i].y)); char b = (char)(255 * clamp(0, 1, framebuffer[i].z)); ofs << r << g << b; } ofs.close(); delete [] framebuffer; return 0; }