光线追踪(RayTracing)算法理论与实践(三)光照

提要

经过之前的学习,我们已经可以在利用光线追踪实现一些简单的场景。今天我们要探讨的是图形学里面的三种基本光源:方向光源,点光源,聚光灯。

不同于利用现成的Api,这次会从理论到实际一步步用C++实现。


前提工作

在老师的建议下,我将图形引擎换成了SDL,最终的渲染效果比之前的好了很多,原来的GLFW虽然能够很好的兼容OpenGL,但并没提供对像素的控制,而SDL有Surface。

对与GLFW,本人觉得其终究只能算是glut的替代品,而SDL应当是一个完善的游戏引擎,而且文档和教程都非常地丰富。

有关SDL的文章,请猛击这里。


方向光源

方向光源是一组平行光。所以方向光源类只有方向和颜色两个属性。用一个向量对象来表示方向,颜色对象表示光的颜色。


阴影

回忆一下入门文章的第一幅图片,在有光的情况下,判断某一点是否是阴影,即判断是否能够从那一点看到光。

那么光线追踪的过程就是:

从摄像机产生光线->投射场景->若与物体相交,从该点产生光线,方向为光源方向的饭方向->投射场景->若与场景中的物体相交,则属于阴影区域。


方向光源的实现:

/***************************************************************************** Copyright: 2012, ustc All rights reserved. contact:[email protected] File name: directlight.h Description:directlight's h doc. Author:Silang Quan Version: 1.0 Date: 2012.12.04 *****************************************************************************/ #ifndef DIRECTLIGHT_H #define DIRECTLIGHT_H #include "color.h" #include "gvector3.h" #include "union.h" class DirectLight {     public:         DirectLight();         DirectLight(Color _color,GVector3 _direction,bool _isShadow);         virtual ~DirectLight();         Color intersect(Union &scence,IntersectResult &result);     protected:     private:         bool isShadow;         Color color;         GVector3 direction; }; #endif // DIRECTLIGHT_H

/***************************************************************************** Copyright: 2012, ustc All rights reserved. contact:[email protected] File name: directlight.cpp Description:directlight's cpp doc. Author:Silang Quan Version: 1.0 Date: 2012.12.04 *****************************************************************************/ #include "directlight.h"  DirectLight::DirectLight() {     //ctor } DirectLight::DirectLight(Color _color,GVector3 _direction,bool _isShadow) {     color=_color;     direction=_direction;     isShadow=_isShadow; } DirectLight::~DirectLight() {     //dtor } //通过光线与场景的相交结果计算光照结果 Color DirectLight::intersect(Union &scence,IntersectResult &rayResult) {     //生产shadowRay的修正值     const float k=1e-4;     //生成与光照相反方向的shadowRay     GVector3 shadowDir=direction.normalize().negate();     CRay shadowRay=CRay(rayResult.position+rayResult.normal*k,shadowDir);     //计算shadowRay是否与场景相交     IntersectResult lightResult = scence.isIntersected(shadowRay);     Color resultColor = Color::black();     if(isShadow)     {         if(lightResult.object)         {         return resultColor;         }     }      //计算光强     float NdotL=rayResult.normal.dotMul(shadowDir);     if (NdotL >= 0)     resultColor=resultColor.add(this->color.multiply(NdotL));     //return this->color;      return resultColor; } 


需要注意的是intersect函数,输入的参数是场景的引用和光线和场景相交结果的引用,返回一个Color。

若shadowRay没有与场景相交,那么就要对那一点接收到的光强进行计算。

与之有关的就是平面法向量与光的方向的夹角,当这个夹角约大,接受的光强就越小,想想看,中午太阳光是不是最强,傍晚是不是比较弱一些:0).

计算夹角利用的是向量的点乘。

渲染一下:

void renderLight() {     Uint32 pixelColor;     Union scene;     PerspectiveCamera camera( GVector3(0, 10, 10),GVector3(0, 0, -1),GVector3(0, 1, 0), 90);     Plane* plane1=new Plane(GVector3(0, 1, 0),0.0);     Plane* plane2=new Plane(GVector3(0, 0, 1),-50);     Plane* plane3=new Plane(GVector3(1, 0, 0),-20);     CSphere* sphere1=new CSphere(GVector3(0, 10, -10), 10.0);     DirectLight light1(Color::white().multiply(10), GVector3(-1.75, -2, -1.5),true);     scene.push(plane1);     scene.push(plane2);     scene.push(plane3);     scene.push(sphere1);     long maxDepth=20;     float dx=1.0f/WINDOW_WIDTH;     float dy=1.0f/WINDOW_HEIGHT;     float dD=255.0f/maxDepth;     for (long y = 0; y < WINDOW_HEIGHT; ++y)     {         float sy = 1 - dy*y;         for (long x = 0; x < WINDOW_WIDTH; ++x)         {             float sx =dx*x;             CRay ray(camera.generateRay(sx, sy));             IntersectResult result = scene.isIntersected(ray);              if (result.isHit)             {                 Color color=light1.intersect(scene,result);                 pixelColor=SDL_MapRGB(screen->format,std::min(color.r*255,(float)255),std::min(color.g*255,(float)255.0),std::min(color.b*255,(float)255.0));                 drawPixel(screen, x, y,pixelColor);             }         }     } }


点光源

点光源/点光灯(point light),又称全向光源/泛光源/泛光灯(omnidirectional light/omni light),是指一个无限小的点,向所有光向平均地散射光。最常见的点光源就是电灯泡了,需要确定光源的位置,还有就是光的颜色。


在计算光强的时候,需要乘以一个衰减系数,接收到的能量和距离的关系,是成平方反比定律的:


点光源的实现:

/***************************************************************************** Copyright: 2012, ustc All rights reserved. contact:[email protected] File name: pointlight.h Description:pointlight's h doc. Author:Silang Quan Version: 1.0 Date: 2012.12.04 *****************************************************************************/ #ifndef POINTLIGHT_H #define POINTLIGHT_H #include "color.h" #include "gvector3.h" #include "union.h"  class PointLight {     public:         PointLight();         PointLight(Color _color,GVector3 _position,bool _isShadow);         virtual ~PointLight();         Color intersect(Union &scence,IntersectResult &result);     protected:     private:         bool isShadow;         Color color;         GVector3 position; };  #endif // POINTLIGHT_H 

/***************************************************************************** Copyright: 2012, ustc All rights reserved. contact:[email protected] File name: pointlight.cpp Description:pointlight's cpp doc. Author:Silang Quan Version: 1.0 Date: 2012.12.04 *****************************************************************************/ #include "pointlight.h"  PointLight::PointLight() {     //ctor }  PointLight::~PointLight() {     //dtor } PointLight::PointLight(Color _color,GVector3 _position,bool _isShadow) {     color=_color;     position=_position;     isShadow=_isShadow; } //通过光线与场景的相交结果计算光照结果 Color PointLight::intersect(Union &scence,IntersectResult &rayResult) {     //生产shadowRay的修正值     const float k=1e-4;     GVector3 delta=this->position-rayResult.position;     float distance=delta.getLength();     //生成与光照相反方向的shadowRay     CRay shadowRay=CRay(rayResult.position,delta.normalize());     GVector3 shadowDir=delta.normalize();     //计算shadowRay是否与场景相交     IntersectResult lightResult = scence.isIntersected(shadowRay);     Color resultColor = Color::black();     Color returnColor=Color::black();     //如果shadowRay与场景中的物体相交     if(lightResult.object&&(lightResult.distance<=distance))     {         return resultColor;;     }     else     {         resultColor=this->color.divide(distance*distance);         float NdotL=rayResult.normal.dotMul(shadowDir);         if (NdotL >= 0)         returnColor=returnColor.add(resultColor.multiply(NdotL));          return returnColor;     }  } 

渲染一下:

在rendeLight函数中初始化点光源:

PointLight light2(Color::white().multiply(200), GVector3(10,20,10),true);



聚光灯

聚光灯点光源的基础上,加入圆锥形的范围,最常见的聚光灯就是手电了,或者舞台的投射灯。聚光灯可以有不同的模型,以下采用Direct3D固定功能管道(fixed-function pipeline)用的模型做示范。


聚光灯有一个主要方向s,再设置两个圆锥范围,称为内圆锥和外圆锥,两圆锥之间的范围称为半影(penumbra)。内外圆锥的内角分别为和。聚光灯可计算一个聚光灯系数,范围为[0,1],代表某方向的放射比率。内圆锥中系数为1(最亮),内圆锥和外圆锥之间系数由1逐渐变成0。另外,可用另一参数p代表衰减(falloff),决定内圆锥和外圆锥之间系数变化。方程式如下:


聚光灯的实现

/***************************************************************************** Copyright: 2012, ustc All rights reserved. contact:[email protected] File name: spotlight.h Description:spotlight's h doc. Author:Silang Quan Version: 1.0 Date: 2012.12.04 *****************************************************************************/ #ifndef SPOTLIGHT_H #define SPOTLIGHT_H #include "color.h" #include "gvector3.h" #include "union.h" #include <math.h>  class SpotLight {     public:         SpotLight();         SpotLight(Color _color,GVector3 _position,GVector3 _direction,float _theta,float _phi,float _fallOff,bool _isShadow);         virtual ~SpotLight();         Color intersect(Union &scence,IntersectResult &result);     protected:     private:         Color color;         GVector3 position;         GVector3 direction;         bool isShadow;         float theta;         float phi;         float fallOff;         //negate the Direction         GVector3 directionN;         float cosTheta;         float cosPhi;         float baseMultiplier; };  #endif // SPOTLIGHT_H 

/***************************************************************************** Copyright: 2012, ustc All rights reserved. contact:[email protected] File name: pointlight.cpp Description:pointlight's cpp doc. Author:Silang Quan Version: 1.0 Date: 2012.12.04 *****************************************************************************/ #include "pointlight.h"  PointLight::PointLight() {     //ctor }  PointLight::~PointLight() {     //dtor } PointLight::PointLight(Color _color,GVector3 _position,bool _isShadow) {     color=_color;     position=_position;     isShadow=_isShadow; } //通过光线与场景的相交结果计算光照结果 Color PointLight::intersect(Union &scence,IntersectResult &rayResult) {     //生产shadowRay的修正值     const float k=1e-4;     GVector3 delta=this->position-rayResult.position;     float distance=delta.getLength();     //生成与光照相反方向的shadowRay     CRay shadowRay=CRay(rayResult.position,delta.normalize());     GVector3 shadowDir=delta.normalize();     //计算shadowRay是否与场景相交     IntersectResult lightResult = scence.isIntersected(shadowRay);     Color resultColor = Color::black();     Color returnColor=Color::black();     //如果shadowRay与场景中的物体相交     if(lightResult.object&&(lightResult.distance<=distance))     {         return resultColor;;     }     else     {         resultColor=this->color.divide(distance*distance);         float NdotL=rayResult.normal.dotMul(shadowDir);         if (NdotL >= 0)         returnColor=returnColor.add(resultColor.multiply(NdotL));          return returnColor;     }  } 

渲染一下:

在场景中初始化一个聚光灯:

SpotLight light3(Color::white().multiply(1350),GVector3(30, 30, 20),GVector3(-1, -0.7, -1), 20, 30, 0.5,true);





渲染多个灯

这里用到了vector容器。场景中布置了很多个点光源,渲染耗时将近半分钟。

void renderLights() {     Uint32 pixelColor;     Union scene;     PerspectiveCamera camera( GVector3(0, 10, 10),GVector3(0, 0, -1),GVector3(0, 1, 0), 90);     Plane* plane1=new Plane(GVector3(0, 1, 0),0.0);     Plane* plane2=new Plane(GVector3(0, 0, 1),-50);     Plane* plane3=new Plane(GVector3(1, 0, 0),-20);     CSphere* sphere1=new CSphere(GVector3(0, 10, -10), 10.0);     CSphere* sphere2=new CSphere(GVector3(5, 5, -7), 3.0);      PointLight *light2;     vector<PointLight> lights;     for (int x = 10; x <= 30; x += 4)         for (int z = 20; z <= 40; z += 4)         {             light2=new PointLight(Color::white().multiply(80),GVector3(x, 50, z),true);             lights.push_back(*light2);         }      scene.push(plane1);     scene.push(plane2);     scene.push(plane3);     scene.push(sphere1);     //scene.push(sphere2);     long maxDepth=20;     float dx=1.0f/WINDOW_WIDTH;     float dy=1.0f/WINDOW_HEIGHT;     float dD=255.0f/maxDepth;     for (long y = 0; y < WINDOW_HEIGHT; ++y)     {         float sy = 1 - dy*y;         for (long x = 0; x < WINDOW_WIDTH; ++x)         {             float sx =dx*x;             CRay ray(camera.generateRay(sx, sy));             IntersectResult result = scene.isIntersected(ray);              if (result.isHit)             {                 Color color=Color::black();                  for(vector<PointLight>::iterator iter=lights.begin();iter!=lights.end();++iter)                 {                     color=color.add(iter->intersect(scene,result));                 }                 pixelColor=SDL_MapRGB(screen->format,std::min(color.r*255,(float)255),std::min(color.g*255,(float)255.0),std::min(color.b*255,(float)255.0));                 drawPixel(screen, x, y,pixelColor);             }         }     } }


渲染结果:


渲染三原色

把原先场景中的球体去掉,布置3盏聚光动,发射红绿蓝,可以很清晰地看见它们融合之后的颜色。

void renderTriColor() {       Uint32 pixelColor;     Union scene;     PerspectiveCamera camera( GVector3(0, 40, 15),GVector3(0, -1.25, -1),GVector3(0, 1, 0), 60);     Plane* plane1=new Plane(GVector3(0, 1, 0),0.0);     Plane* plane2=new Plane(GVector3(0, 0, 1),-50);     Plane* plane3=new Plane(GVector3(1, 0, 0),-20);      PointLight light0(Color::white().multiply(1000), GVector3(30,40,20),true);     SpotLight light1(Color::red().multiply(2000),GVector3(0, 30, 10),GVector3(0, -1, -1), 20, 30, 1,true);     SpotLight light2(Color::green().multiply(2000),GVector3(6, 30, 20),GVector3(0, -1, -1), 20, 30, 1,true);     SpotLight light3(Color::blue().multiply(2000),GVector3(-6, 30, 20),GVector3(0, -1, -1), 20, 30, 1,true);     scene.push(plane1);     scene.push(plane2);     scene.push(plane3);      long maxDepth=20;     float dx=1.0f/WINDOW_WIDTH;     float dy=1.0f/WINDOW_HEIGHT;     float dD=255.0f/maxDepth;     for (long y = 0; y < WINDOW_HEIGHT; ++y)     {         float sy = 1 - dy*y;         for (long x = 0; x < WINDOW_WIDTH; ++x)         {             float sx =dx*x;             CRay ray(camera.generateRay(sx, sy));             IntersectResult result = scene.isIntersected(ray);             if (result.isHit)             {                 Color color=light0.intersect(scene,result);                 color=color.add(light1.intersect(scene,result));                 color=color.add(light2.intersect(scene,result));                 color=color.add(light3.intersect(scene,result));                 pixelColor=SDL_MapRGB(screen->format,std::min(color.r*255,(float)255),std::min(color.g*255,(float)255.0),std::min(color.b*255,(float)255.0));                 drawPixel(screen, x, y,pixelColor);             }         }     } } 

渲染结果



结语

花了大概一周的时间来实现这个光照效果,虽然网上有相关文章,但亲自动手来实现又是另外一回事了。

当然,这都没有结束,期待后续。

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