光线步进——RayMarching入门

入门实现

先用RayMarching描绘一个球体，最后在进行光照计算
参考：https://www.shadertoy.com/view/llt3R4

模拟摄像机射线
float3 rayDirection(float filedOfView, float2 size, float2 fragCoord){
float2 xy=fragCoord-size/2;
float z=size.y/tan(radians(filedOfView)/2.0);
return normalize(float3(xy,-z));
}
1
2
3
4
5
首先，把屏幕中心设置为坐标原点（0.0,0.0），射线的z值都是固定的，其中filedOfView可以看成视椎体两条棱的夹角，返回归一化的射线向量。

对射线进行碰撞检测
float sphereSDF(float3 samplePoint){
return length(samplePoint) - 1.0;
}
1
2
3
float shortestDistanceToSurface(float3 eye,float3 marchingDirection,float start,float end){
float depth = start;
for(int i=0;i<maxMarchingSteps;i++){
float dist=sphereSDF(eye+depth*marchingDirection);
if(dist < epsilon){
return depth;
}

depth+=dist;
if(depth>=end){
return end;
}
}
return end;
}
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
以eye坐标为起点，沿着模拟射线的方向进行碰撞检测，返回碰撞点的深度，如果到最大深度仍然没有碰撞，则发挥最大深度

根据深度返回颜色
float dist=shortestDistanceToSurface(eye,dir,minDist,maxDist);
if(dist>=maxDist-epsilon){
return float4(0.0,0.0,0.0,0.0);
}
float value=floor(dist*10.0)*_StepValue;
return float4(1-value,sin(value*10.0),0.0,1.0);
1
2
3
4
5
6
存在问题
球体的碰撞检测是比较容易的，如果我们想放一个立方体到“场景”里，怎么搞？

float cubeSDF(float3 samplePoint){
float3 d=abs(samplePoint)-float3(0.5,0.5,0.5);
return length(max(d,0.0));
}
1
2
3
4

感觉绘制什么样的物体并不是特别容易控制，需要使用一些数学手段，真佩服哪些用RayMarching画画的那些老哥。

计算法线方向
现在，我们知道顶点坐标，通过计算 xyz 三个方向的差值（梯度），归一化后得到一个近似的法线方向

float3 normalCalculate(float3 p){
return normalize(float3(
sphereSDF(float3(p.x + epsilon, p.y, p.z)) - sphereSDF(float3(p.x - epsilon, p.y, p.z)),
sphereSDF(float3(p.x, p.y + epsilon, p.z)) - sphereSDF(float3(p.x, p.y - epsilon, p.z)),
sphereSDF(float3(p.x, p.y, p.z + epsilon)) - sphereSDF(float3(p.x, p.y, p.z - epsilon))
));
}
1
2
3
4
5
6
7
可以利用matlab进行检验，绘制一个曲面，计算它的表面法线

clear;
[X Y]=meshgrid(-0.5:0.05:0.5, -0.5:0.05:0.5);
Z=0.25-X.^2-Y.^2;
vecX=sqrt(((X+0.0001).^2+Y.^2+Z))-sqrt(((X-0.0001).^2+Y.^2+Z));
vecY=sqrt((X.^2+(Y+0.0001).^2+Z))-sqrt((X.^2+(Y-0.0001).^2+Z));
%mesh(X,Y,Z);
quiver(X,Y,vecX,vecY);
1
2
3
4
5
6
7
根据法线方向计算光照
设定光源位置，环境光，漫反射颜色，高光颜色，高光系数等信息，计算光照即可

代码部分
Shader "Unlit/RayMarching_1"
{
Properties
{
_MainTex ("Texture", 2D) = "white" {}
_StepValue("StepValue",Range(0.001,0.025))=0.001
_LightPos("LightPos",vector)=(0,0,0,0)
_AmbientCol("AmbientCol",Color)=(1,1,1,1)
_DiffuseCol("DiffuseCol",Color)=(1,1,1,1)
_SpecularCol("SpecularCol",Color)=(1,1,1,1)
_Gloss("Gloss",Range(0.1,255))=10
}
SubShader
{
Pass
{
ZTest Always Cull Off ZWrite Off
CGPROGRAM
#pragma vertex vert
#pragma fragment frag
#include "UnityCG.cginc"

#define maxMarchingSteps 255
#define minDist 0.0
#define maxDist 1000.0
#define epsilon 0.00001
#define sizeX (_ScreenParams.x/_ScreenParams.y)

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

sampler2D _MainTex;
float4 _MainTex_ST;
float _StepValue;
float4 _LightPos;
float4 _AmbientCol;
float4 _DiffuseCol;
float4 _SpecularCol;
float _Gloss;

float cubeSDF(float3 samplePoint){
float3 d=abs(samplePoint)-float3(0.5,0.5,0.5);
return length(max(d,0.0));
}

float sphereSDF(float3 samplePoint){
return length(samplePoint) - 0.7;
}

float sceneSDF(float3 samplePoint){
return sphereSDF(samplePoint);
}

float3 rayDirection(float filedOfView, float2 size, float2 fragCoord){
float2 xy=fragCoord-size/2;
float z=size.y/tan(radians(filedOfView)/2.0);
return normalize(float3(xy,-z));
}

float shortestDistanceToSurface(float3 eye,float3 marchingDirection,float start,float end){
float depth = start;
for(int i=0;i<maxMarchingSteps;i++){
float dist=sceneSDF(eye+depth*marchingDirection);
if(dist < epsilon){
return depth;
}

depth+=dist;
if(depth>=end){
return end;
}
}
return end;
}

float3 normalCalculate(float3 p){
return normalize(float3(
sceneSDF(float3(p.x + epsilon, p.y, p.z)) - sceneSDF(float3(p.x - epsilon, p.y, p.z)),
sceneSDF(float3(p.x, p.y + epsilon, p.z)) - sceneSDF(float3(p.x, p.y - epsilon, p.z)),
sceneSDF(float3(p.x, p.y, p.z + epsilon)) - sceneSDF(float3(p.x, p.y, p.z - epsilon))
));
}

float3 LightCalculate(float3 eyePos,float3 pos,float3 lightPos,float3 ambientCol,float3 diffuseColor){
float3 normal = normalCalculate(pos);
float3 col=diffuseColor*max(dot(normal,normalize(lightPos-pos)),0);
col+=ambientCol;
float3 halfDir = normalize(lightPos-pos + eyePos-pos);
float3 specular = _SpecularCol.rgb * pow(max(0, dot(normal, halfDir)), _Gloss);
col+=specular;
return col;
}

v2f vert (appdata v)
{
v2f o;
o.vertex = UnityObjectToClipPos(v.vertex);
o.uv = TRANSFORM_TEX(v.uv, _MainTex);
return o;
}

float4 frag (v2f i) : SV_Target
{
i.uv.x*=_ScreenParams.x/_ScreenParams.y;
float3 dir=rayDirection(45.0,float2(sizeX,1.0),i.uv);
float3 eye= float3(0.0,0.0,5.0);
float dist=shortestDistanceToSurface(eye,dir,minDist,maxDist);
if(dist>=maxDist-epsilon){
return float4(0.0,0.0,0.0,1.0);
}
float3 pos=eye+dist*dir;

float3 col=LightCalculate(eye,pos,_LightPos.xyz,_AmbientCol.xyz,_DiffuseCol.xyz);
return float4(col,1);
//return float4(0.5,0.5,0.5,1);
//float value=floor(dist*10.0)*_StepValue;
//return float4(sin(value*1000),1-value,0.0,1.0);
}

ENDCG
}
}
}

---------------------