图像学基础之光线追踪(开篇)
图像学基础之光线追踪(开篇)
学习计算机图形学走路不少弯路，开始学习的都是OpenGL API库讲解的，只知道按部就班的做，不知道原理。直到当我看了 清华大学胡事民老师的清华大学-计算机图形学基础（国家级精品课）才感觉了解了真正的原理。看完这个教程在网上搜索到了tinyraytracer，一篇用256行c++代码实现光线追踪项目，项目不包含任何第三方库并配有wiki文章一步一步实现光线追踪的实现。本篇开篇主要解决下载代码后编译问题的。
因为笔者用的vs2015，下载源代码cmake构建项目编译报错。可能vs2015默认的c++ 11标准库，而tinyraytracer项目用到了c++17特性。
编译报错问题
1.auto相关地方报错
以一下代码为例说明
auto [hit, shadow_pt, trashnrm, trashmat] = scene_intersect(point, light_dir);
基本都是函数返回的std::tuple<>元组在用auto推测类型报错，查阅资料这个是C++17的特性。我们以上面最后一条语句为例只需要修改代码如下
auto tuplevalue = scene_intersect(orig, dir);
auto hit = std::get<0>(tuplevalue);
auto point = std::get<1>(tuplevalue);
auto N = std::get<2>(tuplevalue);
auto material = std::get<3>(tuplevalue);
2.无法从“initializer list”转换为“Material ”
以一下代码为例说明
struct Material {
float refractive_index = 1;
float albedo[4] = { 2,0,0,0 };
vec3 diffuse_color = { 0,0,0 };
float specular_exponent = 0;
};
主要是列表初始化问题.C++11中列表初始化是不能就地赋值的,具体可以查阅c++11新特性列表初始化，改成如下的即可
struct Material {
float refractive_index;
float albedo[4] ;
vec3 diffuse_color ;
float specular_exponent ;
};
注意改成这样后直接使用会有问题,本来需要的初始化值会丢弃.
Material material;
在使用之前需要初始化
Material material = { 1,{ 2,0,0,0 },{ 0,0,0 },0 };
3.从“double”转换到“float”需要收缩转换
将以下代码
material.diffuse_color = (int(.5*pt.x+1000) + int(.5*pt.z)) & 1 ? vec3{.3, .3, .3} : vec3{.3, .2, .1};
改为如下代码
material.diffuse_color = (int(.5f*pt.x+1000) + int(.5f*pt.z)) & 1 ? vec3{.3f, .3f, .3f} : vec3{.3f, .2f, .1f};
修改后的完整代码如下
#include <tuple>
#include <vector>
#include <fstream>
#include <algorithm>
#include <cmath>
struct vec3 {
//float x=0, y=0, z=0;
float x, y, z;
float& operator[](const int i) { return i==0 ? x : (1==i ? y : z); }
const float& operator[](const int i) const { return i==0 ? x : (1==i ? y : z); }
vec3 operator*(const float v) const { return {x*v, y*v, z*v}; }
float operator*(const vec3& v) const { return x*v.x + y*v.y + z*v.z; }
vec3 operator+(const vec3& v) const { return {x+v.x, y+v.y, z+v.z}; }
vec3 operator-(const vec3& v) const { return {x-v.x, y-v.y, z-v.z}; }
vec3 operator-() const { return {-x, -y, -z}; }
float norm() const { return std::sqrt(x*x+y*y+z*z); }
vec3 normalized() const { return (*this)*(1.f/norm()); }
};
vec3 cross(const vec3 v1, const vec3 v2) {
return { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x };
}
struct Material {
/*float refractive_index = 1;
float albedo[4] = { 2,0,0,0 };
vec3 diffuse_color = { 0,0,0 };
float specular_exponent = 0;*/
float refractive_index;
float albedo[4] ;
vec3 diffuse_color ;
float specular_exponent ;
};
struct Sphere {
vec3 center;
float radius;
Material material;
};
constexpr Material ivory = {1.0, {0.9, 0.5, 0.1, 0.0}, {0.4, 0.4, 0.3}, 50.};
constexpr Material glass = {1.5, {0.0, 0.9, 0.1, 0.8}, {0.6, 0.7, 0.8}, 125.};
constexpr Material red_rubber = {1.0, {1.4, 0.3, 0.0, 0.0}, {0.3, 0.1, 0.1}, 10.};
constexpr Material mirror = {1.0, {0.0, 16.0, 0.8, 0.0}, {1.0, 1.0, 1.0}, 1425.};
constexpr Sphere spheres[] = {
{{-3, 0, -16}, 2, ivory},
{{-1.0, -1.5, -12}, 2, glass},
{{ 1.5, -0.5, -18}, 3, red_rubber},
{{ 7, 5, -18}, 4, mirror}
};
constexpr vec3 lights[] = {
{-20, 20, 20},
{ 30, 50, -25},
{ 30, 20, 30}
};
vec3 reflect(const vec3 &I, const vec3 &N) {
return I - N*2.f*(I*N);
}
vec3 refract(const vec3 &I, const vec3 &N, const float eta_t, const float eta_i=1.f) { // Snell's law
float cosi = - std::max(-1.f, std::min(1.f, I*N));
if (cosi<0) return refract(I, -N, eta_i, eta_t); // if the ray comes from the inside the object, swap the air and the media
float eta = eta_i / eta_t;
float k = 1 - eta*eta*(1 - cosi*cosi);
return k<0 ? vec3{1,0,0} : I*eta + N*(eta*cosi - std::sqrt(k)); // k<0 = total reflection, no ray to refract. I refract it anyways, this has no physical meaning
}
std::tuple<bool,float> ray_sphere_intersect(const vec3 &orig, const vec3 &dir, const Sphere &s) { // ret value is a pair [intersection found, distance]
vec3 L = s.center - orig;
float tca = L*dir;
float d2 = L*L - tca*tca;
if (d2 > s.radius*s.radius) return {false, 0};
float thc = std::sqrt(s.radius*s.radius - d2);
float t0 = tca-thc, t1 = tca+thc;
if (t0>.001) return {true, t0}; // offset the original point by .001 to avoid occlusion by the object itself
if (t1>.001) return {true, t1};
return {false, 0};
}
std::tuple<bool,vec3,vec3,Material> scene_intersect(const vec3 &orig, const vec3 &dir) {
vec3 pt, N;
//Material material;
Material material = { 1,{ 2,0,0,0 },{ 0,0,0 },0 };
float nearest_dist = 1e10;
if (std::abs(dir.y)>.001) { // intersect the ray with the checkerboard, avoid division by zero
float d = -(orig.y+4)/dir.y; // the checkerboard plane has equation y = -4
vec3 p = orig + dir*d;
if (d>.001 && d<nearest_dist && std::abs(p.x)<10 && p.z<-10 && p.z>-30) {
nearest_dist = d;
pt = p;
N = {0,1,0};
material.diffuse_color = (int(.5f*pt.x+1000) + int(.5f*pt.z)) & 1 ? vec3{.3f, .3f, .3f} : vec3{.3f, .2f, .1f};
}
}
for (const Sphere &s : spheres) { // intersect the ray with all spheres
// auto [intersection, d] = ray_sphere_intersect(orig, dir, s);
auto tuplevalue = ray_sphere_intersect(orig, dir, s);
auto intersection =std::get<0>(tuplevalue);
auto d = std::get<1>(tuplevalue);
if (!intersection || d > nearest_dist) continue;
nearest_dist = d;
pt = orig + dir*nearest_dist;
N = (pt - s.center).normalized();
material = s.material;
}
return { nearest_dist<1000, pt, N, material };
}
vec3 cast_ray(const vec3 &orig, const vec3 &dir, const int depth=0) {
//auto [hit, point, N, material] = scene_intersect(orig, dir);
auto tuplevalue = scene_intersect(orig, dir);
auto hit = std::get<0>(tuplevalue);
auto point = std::get<1>(tuplevalue);
auto N = std::get<2>(tuplevalue);
auto material = std::get<3>(tuplevalue);
if (depth>4 || !hit)
return {0.2f, 0.7f, 0.8f}; // background color
vec3 reflect_dir = reflect(dir, N).normalized();
vec3 refract_dir = refract(dir, N, material.refractive_index).normalized();
vec3 reflect_color = cast_ray(point, reflect_dir, depth + 1);
vec3 refract_color = cast_ray(point, refract_dir, depth + 1);
float diffuse_light_intensity = 0, specular_light_intensity = 0;
for (const vec3 &light : lights) { // checking if the point lies in the shadow of the light
vec3 light_dir = (light - point).normalized();
//auto [hit, shadow_pt, trashnrm, trashmat] = scene_intersect(point, light_dir);
auto tuplevalue = scene_intersect(point, light_dir);
auto hit = std::get<0>(tuplevalue);
auto shadow_pt = std::get<1>(tuplevalue);
auto trashnrm = std::get<2>(tuplevalue);
auto trashmat = std::get<3>(tuplevalue);
if (hit && (shadow_pt-point).norm() < (light-point).norm()) continue;
diffuse_light_intensity += std::max(0.f, light_dir*N);
specular_light_intensity += std::pow(std::max(0.f, -reflect(-light_dir, N)*dir), material.specular_exponent);
}
return material.diffuse_color * diffuse_light_intensity * material.albedo[0] + vec3{1., 1., 1.}*specular_light_intensity * material.albedo[1] + reflect_color*material.albedo[2] + refract_color*material.albedo[3];
}
int main() {
constexpr int width = 1024;
constexpr int height = 768;
constexpr float fov = 1.05; // 60 degrees field of view in radians
std::vector<vec3> framebuffer(width*height);
#pragma omp parallel for
for (int pix = 0; pix<width*height; pix++) { // actual rendering loop
float dir_x = (pix%width + 0.5) - width/2.;
float dir_y = -(pix/width + 0.5) + height/2.; // this flips the image at the same time
float dir_z = -height/(2.*tan(fov/2.));
framebuffer[pix] = cast_ray(vec3{0,0,0}, vec3{dir_x, dir_y, dir_z}.normalized());
}
std::ofstream ofs("./out.ppm", std::ios::binary);
ofs << "P6\n" << width << " " << height << "\n255\n";
for (vec3 &color : framebuffer) {
float max = std::max(1.f, std::max(color[0], std::max(color[1], color[2])));
for (int chan : {0,1,2})
ofs << (char)(255 * color[chan]/max);
}
return 0;
}
参考
https://github.com/ssloy/tinyraytracer
浙公网安备 33010602011771号