RTIOW-ch5：Surface normals and multiple objects

法向量，垂直于表面，方向为相交点p减去球心点c的方向向量。用色彩表可视化单位法向量，让法向量的XYZ值映射到RGB值，使得球有一个渐变的效果，具体做法：考虑x/y/z在[-1,1]，r/g/b在[0,1]，怎么映射？x/y/z分别+1然后/2 [

](http://www.wjgbaby.com/wp-content/uploads/2018/05/18051503-300x137.png)

cpp:

#include
#include
#include “ray.h”
using namespace std;

//此时该函数的返回值从ch4的bool变为float
float hit_sphere(const vec3& center, float radius, const ray& r)
{
vec3 oc = r.origin() - center;
float a = dot(r.direction(), r.direction());
float b = 2.0f * dot(oc, r.direction());
float c = dot(oc, oc) - radius * radius;
//判断这个方程有没有根，如果有2个根就是击中
float discrimiant = b * b - 4.0f * a * c;
if (discrimiant < 0.0f)
{
return -1.0f;
}
else
{
return (-b - sqrt(discrimiant)) / (2.0f * a);
}
}

vec3 Color(const ray& r)
{
float t = hit_sphere(vec3(0.0f, 0.0f, -1.0f), 0.5, r);
if (t > 0.0f)
{
//法向量
vec3 N = unit_vector(r.point_at_parameter(t) - vec3(0.0f, 0.0f, -1.0f));
return 0.5f * vec3(N.x() + 1.0f, N.y() + 1.0f, N.z() + 1.0f);
}
//绘制背景
vec3 unit_direction = unit_vector(r.direction());
//t从0到1
t = 0.5f * (unit_direction.y() + 1.0f);

//blended\_value = (1-t)\*start\_value + t\*end\_value
//线性混合，t=1时蓝色，t=0时白色，t介于中间时是混合颜色
return (1.0f - t) \* vec3(1.0f, 1.0f, 1.0f) + t \* vec3(0.5f, 0.7f, 1.0f);

}

int main()
{
ofstream outfile;
outfile.open(“IMG.ppm”);

int nx = 800;
int ny = 400;
outfile << "P3\\n" << nx << " " << ny << "\\n255\\n";

//视锥体左下角
vec3 lower\_left\_corner(-2.0f, -1.0f, -1.0f);
//距离左下角的水平距离
vec3 horizontal(4.0f, 0.0f, 0.0f);
//距离左下角的垂直距离
vec3 vertical(0.0f, 2.0f, 0.0f);
//起始点
vec3 origin(0.0f, 0.0f, 0.0f);

for (int j = ny - 1; j >= 0; j--)
{
    for (int i = 0; i < nx; i++)
    {
        //u从0开始越来越接近1；v从无限接近1开始，越来越接近0
        float u = float(i) / float(nx);
        float v = float(j) / float(ny);

        ray r(origin, lower\_left\_corner +u \* horizontal + v \* vertical);
        vec3 col = Color(r);

        int ir = int(255.99 \* col\[0\]);
        int ig = int(255.99 \* col\[1\]);
        int ib = int(255.99 \* col\[2\]);
        outfile << ir << " " << ig << " " << ib << "\\n";
    }
}
outfile.close();
return 0;

}

运行效果： [

](http://www.wjgbaby.com/wp-content/uploads/2018/05/18051501.jpg)

下面是多个球的出现： hitable.h 抽象类：

#ifndef hitableH
#define hitableH

#include “ray.h”
class material;

//撞击点信息
struct hit_record
{
//射线参数t
float t;
//撞击点位置向量p
vec3 p;
//撞击点位置向量N
vec3 normal;
material* mat_ptr;
};

//所有能被射线撞击的物体的父类
class hitable
{
public:
//hit()虚函数
virtual bool hit(const ray& r, float t_min, float t_max, hit_record& rec) const = 0;
};

#endif

sphere.h：

#ifndef sphereH
#define sphereH

#include “hitable.h”

class sphere : public hitable {
public:
sphere(){ }
//sphere(vec3 cen, float r, material *m) : center(cen), radius(r), mat_ptr(m) {};
sphere(vec3 cen, float r) : center(cen), radius(r) { };
virtual bool hit(const ray& r, float tmin, float tmax, hit_record& rec) const;
vec3 center;
float radius;
material* mat_ptr;
};

bool sphere::hit(const ray& r, float t_min, float t_max, hit_record& rec) const {
vec3 oc = r.origin() - center;
float a = dot(r.direction(), r.direction());
float b = dot(oc, r.direction());
float c = dot(oc, oc) - radius * radius;
float discriminant = b * b - a * c;
if (discriminant > 0) {
float temp = (-b - sqrt(discriminant)) / a;
if (temp<t_max && temp> t_min) {
rec.t = temp;
rec.p = r.point_at_parameter(rec.t);
rec.normal = (rec.p - center) / radius;
rec.mat_ptr = mat_ptr;
return true;
}
temp = (-b + sqrt(discriminant)) / a;
if (temp<t_max && temp> t_min) {
rec.t = temp;
rec.p = r.point_at_parameter(rec.t);
rec.normal = (rec.p - center) / radius;
rec.mat_ptr = mat_ptr;
return true;
}
}
return false;
}

#endif

hitable_list.h：

#ifndef hitableLISTH
#define hitableLISTH

#include “hitable.h”

class hitable_list : public hitable {
public:
hitable_list(){ }
hitable_list(hitable** l, int n){ list = l; list_size = n; }
virtual bool hit(const ray& r, float tmin, float tmax, hit_record& rec) const;
hitable** list;
int list_size;
};

bool hitable_list::hit(const ray& r, float t_min, float t_max, hit_record& rec) const {
hit_record temp_rec;
bool hit_anything = false;
double closest_so_far = t_max;
//依次判断列表中所有物体是否被光线撞到
for (int i = 0; i<list_size; i++) {
if (list[i]->hit(r, t_min, closest_so_far, temp_rec)) {
hit_anything = true;
closest_so_far = temp_rec.t;
rec = temp_rec;
}
}
return hit_anything;
}

#endif

cpp：

#include
#include
#include “sphere.h”
#include “hitable_list.h”

using namespace std;

vec3 Color(const ray& r, hitable* world)
{
hit_record rec;
if (world->hit(r, 0.0, FLT_MAX, rec))
{
return 0.5f * vec3(rec.normal.x() + 1.0f, rec.normal.y() + 1.0f, rec.normal.z() + 1.0f);
}
else
{
vec3 unit_direction = unit_vector(r.direction());
float t = 0.5f * (unit_direction.y() + 1.0f);
return (1.0f - t) * vec3(1.0f, 1.0f, 1.0f) + t * vec3(0.5f, 0.7f, 1.0f);
}
}

int main()
{
ofstream outfile;
outfile.open(“IMG2.ppm”);

int nx = 800;
int ny = 400;
outfile << "P3\\n" << nx << " " << ny << "\\n255\\n";

vec3 lower\_left\_corner(-2.0f, -1.0f, -1.0f);
vec3 horizontal(4.0f, 0.0f, 0.0f);
vec3 vertical(0.0f, 2.0f, 0.0f);
vec3 origin(0.0f, 0.0f, 0.0f);

hitable\* list\[2\];
list\[0\] = new sphere(vec3(0.0f, 0.0f, -1.0f), 0.5f);
list\[1\] = new sphere(vec3(0.0f, -100.5f, -1.0f), 100.0f);
hitable\* world = new hitable\_list(list, 2);

for (int j = ny - 1; j >= 0; j--)
{
    for (int i = 0; i < nx; i++)
    {
        float u = float(i) / float(nx);
        float v = float(j) / float(ny);
        ray r(origin, lower\_left\_corner +u \* horizontal + v \* vertical);

        vec3 p = r.point\_at\_parameter(2.0);
        vec3 col = Color(r, world);

        int ir = int(255.99 \* col\[0\]);
        int ig = int(255.99 \* col\[1\]);
        int ib = int(255.99 \* col\[2\]);
        outfile << ir << " " << ig << " " << ib << "\\n";
    }
}
outfile.close();
return 0;

}

最终效果：参考书籍：《Ray Tracing in One Weekend》 RTIOW系列项目地址：GitHub RTIOW系列笔记： RTIOW-ch1：Output an image RTIOW-ch2：The vec3 class RTIOW-ch3：Rays, a simple camera, and background RTIOW-ch4：Adding a sphere RTIOW-ch5：Surface normals and multiple objects RTIOW-ch6：Antialiasing RTIOW-ch7：Diffuse Materials RTIOW-ch8：Metal RTIOW-ch9：Dielectrics RTIOW-ch10：Positionable camera RTIOW-ch11：Defocus Blur RTIOW-ch12：Where next