问题三十六：ray tracing中的Inverse Mapping（5）——圆锥面Inverse Mapping
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36.5 圆锥面Inverse Mapping
36.5.1 数学推导
36.5.2 看C++代码实现
----------------------------------------------quadratic.cpp ------------------------------------------
quadratic.cpp
#include "quadratic.h"#include <iostream>using namespace std;bool quadratic::hit(const ray& r, float t_min, float t_max, hit_record& rec) const {#if QUADRATIC_LOG == 1 std::cout << "-------------quadratic::hit----------------" << endl;#endif // QUADRATIC_LOG float ab_square = intercept_x*intercept_x*intercept_y*intercept_y; float bc_square = intercept_y*intercept_y*intercept_z*intercept_z; float ac_square = sign1*intercept_x*intercept_x*intercept_z*intercept_z; float abc_square = sign2*intercept_x*intercept_x*intercept_y*intercept_y*intercept_z*intercept_z; vec3 inter_square = vec3(bc_square, ac_square, ab_square); vec3 rd_square = vec3(r.direction().x()*r.direction().x(), r.direction().y()*r.direction().y(), r.direction().z()*r.direction().z()); float A = dot(inter_square, rd_square); vec3 r0_c = r.origin() - center; vec3 r0_c_rd = vec3(r0_c.x()*r.direction().x(), r0_c.y()*r.direction().y(), r0_c.z()*r.direction().z()); float B = 2*dot(r0_c_rd, inter_square); vec3 r0_c_square = vec3(r0_c.x()*r0_c.x(), r0_c.y()*r0_c.y(), r0_c.z()*r0_c.z()); float C = dot(r0_c_square, inter_square) - abc_square; float temp, temp1, temp2; vec3 pc; if(A == 0) { if (B == 0) { return false; } else { temp = -C/B; if (temp < t_max && temp > t_min) { rec.t = temp; rec.p = r.point_at_parameter(rec.t); if (((rec.p.y()-center.y()) > -height_half_y) && ((rec.p.y()-center.y()) < height_half_y)) { pc = rec.p - center; rec.normal = unit_vector(vec3(2*bc_square*pc.x(), 2*ac_square*pc.y(), 2*ab_square*pc.z())); if (dot(rec.normal, r.direction()) > 0) { rec.normal = -rec.normal; } rec.mat_ptr = ma; if ((sign1 == 0) && (sign2 == 1) && (intercept_x == intercept_y) && (intercept_y == intercept_z)) {//cylinder rec.v = (rec.p.y() - (center.y() - height_half_y)) / (2*height_half_y); float u = acos((rec.p.x() - center.x()) / intercept_x) / (2*M_PI); if ((rec.p.z() - center.z()) < 0) { rec.u = 1-u; } else { rec.u = u; } return true; } else if ((sign1 == -1) && (sign2 == 0) && (intercept_x == intercept_z)) {//cone if (((rec.p.y()-center.y()) > -height_half_y) && ((rec.p.y()-center.y()) < 0)) { pc = rec.p - center; rec.normal = unit_vector(vec3(2*bc_square*pc.x(), 2*ac_square*pc.y(), 2*ab_square*pc.z())); if (dot(rec.normal, r.direction()) > 0) { rec.normal = -rec.normal; } rec.mat_ptr = ma; rec.v = (rec.p.y() - (center.y() - height_half_y)) / (height_half_y);// float rate = intercept_y / intercept_x; vec3 pc1 = vec3(rec.p.x()-center.x(), 0, rec.p.z()-center.z()); vec3 vx = vec3(0, 0, 1); float u = acos(dot(pc1, vx) / (pc1.length()*vx.length())) / (2*M_PI); // float u = acos((rec.p.x() - center.x()) / ((center.y() - rec.p.y()) / rate)) / (2*M_PI); if ((rec.p.x() - center.x()) < 0) { rec.u = 1-u; } else { rec.u = u; } return true; } else { rec.u = -1.0; rec.v = -1.0; } } else { rec.u = -1.0; rec.v = -1.0; return true; } } else { return false; } } } } else { float discriminant = B*B - 4*A*C; if (discriminant >= 0) { temp1 = (-B - sqrt(discriminant)) / (2.0*A); temp2 = (-B + sqrt(discriminant)) / (2.0*A); if (temp1 > temp2) {//make sure that temp1 is smaller than temp2 temp = temp1; temp1 = temp2; temp2 = temp; } if (temp1 < t_max && temp1 > t_min) { rec.t = temp1; rec.p = r.point_at_parameter(rec.t); if (((rec.p.y()-center.y()) > -height_half_y) && ((rec.p.y()-center.y()) < height_half_y)) { pc = rec.p - center; rec.normal = unit_vector(vec3(2*bc_square*pc.x(), 2*ac_square*pc.y(), 2*ab_square*pc.z())); if (dot(rec.normal, r.direction()) > 0) { rec.normal = -rec.normal; } rec.mat_ptr = ma; if ((sign1 == 0) && (sign2 == 1) && (intercept_x == intercept_y) && (intercept_y == intercept_z)) {//cylinder rec.v = (rec.p.y() - (center.y() - height_half_y)) / (2*height_half_y); float u = acos((rec.p.x() - center.x()) / intercept_x) / (2*M_PI); if ((rec.p.z() - center.z()) < 0) { rec.u = 1-u; } else { rec.u = u; } return true; } else if ((sign1 == -1) && (sign2 == 0) && (intercept_x == intercept_z)) {//cone if (((rec.p.y()-center.y()) > -height_half_y) && ((rec.p.y()-center.y()) < 0)) { pc = rec.p - center; rec.normal = unit_vector(vec3(2*bc_square*pc.x(), 2*ac_square*pc.y(), 2*ab_square*pc.z())); if (dot(rec.normal, r.direction()) > 0) { rec.normal = -rec.normal; } rec.mat_ptr = ma; rec.v = (rec.p.y() - (center.y() - height_half_y)) / (height_half_y);// float rate = intercept_y / intercept_x; vec3 pc1 = vec3(rec.p.x()-center.x(), 0, rec.p.z()-center.z()); vec3 vx = vec3(0, 0, 1); float u = acos(dot(pc1, vx) / (pc1.length()*vx.length())) / (2*M_PI); // float u = acos((rec.p.x() - center.x()) / ((center.y() - rec.p.y()) / rate)) / (2*M_PI); if ((rec.p.x() - center.x()) < 0) { rec.u = 1-u; } else { rec.u = u; } return true; } else { rec.u = -1.0; rec.v = -1.0; } } else { rec.u = -1.0; rec.v = -1.0; return true; } } else {// return false; } } if (temp2 < t_max && temp2 > t_min) { rec.t = temp2; rec.p = r.point_at_parameter(rec.t); if (((rec.p.y()-center.y()) > -height_half_y) && ((rec.p.y()-center.y()) < height_half_y)) { pc = rec.p - center; rec.normal = unit_vector(vec3(2*bc_square*pc.x(), 2*ac_square*pc.y(), 2*ab_square*pc.z())); if (dot(rec.normal, r.direction()) > 0) { rec.normal = -rec.normal; } rec.mat_ptr = ma; if ((sign1 == 0) && (sign2 == 1) && (intercept_x == intercept_y) && (intercept_y == intercept_z)) {//cylinder rec.v = (rec.p.y() - (center.y() - height_half_y)) / (2*height_half_y); float u = acos((rec.p.x() - center.x()) / intercept_x) / (2*M_PI); if ((rec.p.z() - center.z()) < 0) { rec.u = 1-u; } else { rec.u = u; } return true; } else if ((sign1 == -1) && (sign2 == 0) && (intercept_x == intercept_z)) {//cone if (((rec.p.y()-center.y()) > -height_half_y) && ((rec.p.y()-center.y()) < 0)) { pc = rec.p - center; rec.normal = unit_vector(vec3(2*bc_square*pc.x(), 2*ac_square*pc.y(), 2*ab_square*pc.z())); if (dot(rec.normal, r.direction()) > 0) { rec.normal = -rec.normal; } rec.mat_ptr = ma; rec.v = (rec.p.y() - (center.y() - height_half_y)) / (height_half_y);// float rate = intercept_y / intercept_x; vec3 pc1 = vec3(rec.p.x()-center.x(), 0, rec.p.z()-center.z()); vec3 vx = vec3(0, 0, 1); float u = acos(dot(pc1, vx) / (pc1.length()*vx.length())) / (2*M_PI); // float u = acos((rec.p.x() - center.x()) / ((center.y() - rec.p.y()) / rate)) / (2*M_PI); if ((rec.p.x() - center.x()) < 0) { rec.u = 1-u; } else { rec.u = u; } return true; } else { rec.u = -1.0; rec.v = -1.0; } } else { rec.u = -1.0; rec.v = -1.0; return true; } } else {// return false; } } } return false; }}
----------------------------------------------main.cpp ------------------------------------------
main.cpp
hitable *list[2]; list[0] = new sphere(vec3(0.0,-100,0), 100, new lambertian(vec3(0.8, 0.8, 0.0))); list[1] = new quadratic(vec3(0, 5, 0), 2.5, 5, 2.5, -1, 0, 5, new lambertian(vec3(0.8, 0.8, 0.0))); hitable *world = new hitable_list(list,2); vec3 lookfrom(0, 10, 20); vec3 lookat(0, 2.5, 0); float dist_to_focus = (lookfrom - lookat).length(); float aperture = 0.0; camera cam(lookfrom, lookat, vec3(0,1,0), 20, float(nx)/float(ny), aperture, 0.7*dist_to_focus);
输出图片如下：
vec3 lookfrom(0, 10, 20);
vec3 lookfrom(0, 10, -20);
uv原图：
4 0
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