问题三十六：ray tracing中的Inverse Mapping（4）—

36.4 圆柱面Inverse Mapping

36.4.1 数学推导

36.4.2 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 == 1std::cout << "-------------quadratic::hit----------------" << endl;
#endif // QUADRATIC_LOGfloat 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)) {//cylinderrec.v = (rec.p.y() - (center.y() - height_half_y)) / (2*height_half_y);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()) / intercept_x) / (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;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 temp2temp = 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)) {//cylinderrec.v = (rec.p.y() - (center.y() - height_half_y)) / (2*height_half_y);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()) / intercept_x) / (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;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)) {//cylinderrec.v = (rec.p.y() - (center.y() - height_half_y)) / (2*height_half_y);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()) / intercept_x) / (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;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, 2.5, 0), 2.5, 2.5, 2.5, 0, 1, 2.5, 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：

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问题三十六：ray tracing中的Inverse Mapping（4）——圆柱面Inverse Mapping

36.4 圆柱面Inverse Mapping

36.4.2 看C++代码实现

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