路径追踪 低差异序列 sobol序列采样

sobol 是一种均匀数组替代随机半球采样，对降噪非常好

引用如下
vec2 ua=sobolVec2(int(frameCounter)+1,maxBounce);
vec3 L = SampleCosineHemisphere(ua.x, ua.y, N);

完整项目代码https://blog.youkuaiyun.com/asaqlp/article/details/120828724
fshader.fsh

#version 330 core

in vec3 pix;
out vec4 fragColor;

// ----------------------------------------------------------------------------- //

uniform uint frameCounter;
uniform int nTriangles;
uniform int nNodes;
uniform int width;
uniform int height;

uniform samplerBuffer triangles;
uniform samplerBuffer nodes;

uniform sampler2D lastFrame;
uniform sampler2D hdrMap;

uniform vec3 eye;
uniform mat4 cameraRotate;

// ----------------------------------------------------------------------------- //

#define PI              3.1415926
#define INF             114514.0
#define SIZE_TRIANGLE   12
#define SIZE_BVHNODE    4

// ----------------------------------------------------------------------------- //

// Triangle 数据格式
struct Triangle {
   
   
    vec3 p1, p2, p3;    // 顶点坐标
    vec3 n1, n2, n3;    // 顶点法线
};

// BVH 树节点
struct BVHNode {
   
   
    int left;           // 左子树
    int right;          // 右子树
    int n;              // 包含三角形数目
    int index;          // 三角形索引
    vec3 AA, BB;        // 碰撞盒
};

// 物体表面材质定义
struct Material {
   
   
    vec3 emissive;          // 作为光源时的发光颜色
    vec3 baseColor;
    float subsurface;
    float metallic;
    float specular;
    float specularTint;
    float roughness;
    float anisotropic;
    float sheen;
    float sheenTint;
    float clearcoat;
    float clearcoatGloss;
    float IOR;
    float transmission;
};

// 光线
struct Ray {
   
   
    vec3 startPoint;
    vec3 direction;
};

// 光线求交结果
struct HitResult {
   
   
    bool isHit;             // 是否命中
    bool isInside;          // 是否从内部命中
    float distance;         // 与交点的距离
    vec3 hitPoint;          // 光线命中点
    vec3 normal;            // 命中点法线
    vec3 viewDir;           // 击中该点的光线的方向
    Material material;      // 命中点的表面材质
};

// ----------------------------------------------------------------------------- //

/*
 * 生成随机向量，依赖于 frameCounter 帧计数器
 * 代码来源：https://blog.demofox.org/2020/05/25/casual-shadertoy-path-tracing-1-basic-camera-diffuse-emissive/
*/

uint seed = uint(
    uint((pix.x * 0.5 + 0.5) * width)  * uint(1973) + 
    uint((pix.y * 0.5 + 0.5) * height) * uint(9277) + 
    uint(frameCounter) * uint(26699)) | uint(1);

uint wang_hash(inout uint seed) {
   
   
    seed = uint(seed ^ uint(61)) ^ uint(seed >> uint(16));
    seed *= uint(9);
    seed = seed ^ (seed >> 4);
    seed *= uint(0x27d4eb2d);
    seed = seed ^ (seed >> 15);
    return seed;
}
 
float rand() {
   
   
    return float(wang_hash(seed)) / 4294967296.0;
}

// ----------------------------------------------------------------------------- //

// 半球均匀采样
vec3 SampleHemisphere() {
   
   
    float z = rand();
    float r = max(0, sqrt(1.0 - z*z));
    float phi = 2.0 * PI * rand();
    return vec3(r * cos(phi), r * sin(phi), z);
}

/*
vec3 toNormalHemisphere(vec3 v, vec3 N) {
    vec3 tangent = vec3(0);
    if(N.yz==vec2(0)) tangent = vec3(0, 0, -N.x);
    else if(N.xz==vec2(0)) tangent = vec3(0, 0, N.y);
    else if(N.xy==vec2(0)) tangent = vec3(-N.z, 0, 0);
    else if(abs(N.x)>abs(N.y)) tangent = normalize(vec3(0, N.z, -N.y));
    else tangent = normalize(vec3(-N.z, 0, N.x)); 
    vec3 bitangent = cross(N, tangent);
    return normalize(v.x * tangent + v.y * bitangent + v.z * N);
}
*/

// 将向量 v 投影到 N 的法向半球
vec3 toNormalHemisphere(vec3 v, vec3 N) {
   
   
    vec3 helper = vec3(1, 0, 0);
    if(abs(N.x)>0.999) helper = vec3(0, 0, 1);
    vec3 tangent = normalize(cross(N, helper));
    vec3 bitangent = normalize(cross(N, tangent));
    return v.x * tangent + v.y * bitangent + v.z * N;
}

// ----------------------------------------------------------------------------- //

// 将三维向量 v 转为 HDR map 的纹理坐标 uv
vec2 SampleSphericalMap(vec3 v) {
   
   
    vec2 uv = vec2(atan(v.z, v.x), asin(v.y));
    uv /= vec2(2.0 * PI, PI);
    uv += 0.5;
    uv.y = 1.0 - uv.y;
    return uv;
}

// 获取 HDR 环境颜色
vec3 sampleHdr(vec3 v) {
   
   
    vec2 uv = SampleSphericalMap(normalize(v));
    vec3 color = texture2D(hdrMap, uv).rgb;
    color = min(color, vec3(10));
    return color;
}

// ----------------------------------------------------------------------------- //

// 获取第 i 下标的三角形
Triangle getTriangle(int i) {
   
   
    int offset = i * SIZE_TRIANGLE;
    Triangle t;

    // 顶点坐标
    t.p1 = texelFetch(triangles, offset + 0).xyz;
    t.p2 = texelFetch(triangles, offset + 1).xyz;
    t.p3 = texelFetch(triangles, offset + 2).xyz;
    // 法线
    t.n1 = texelFetch(triangles, offset + 3).xyz;
    t.n2 = texelFetch(triangles, offset + 4).xyz;
    t.n3 = texelFetch(triangles, offset + 5).xyz;

    return t;
}

// 获取第 i 下标的三角形的材质
Material getMaterial(int i) {
   
   
    Material m;

    int offset = i * SIZE_TRIANGLE;
    vec3 param1 = texelFetch(triangles, offset + 8).xyz;
    vec3 param2 = texelFetch(triangles, offset + 9).xyz;
    vec3 param3 = texelFetch(triangles, offset + 10).xyz;
    vec3 param4 = texelFetch(triangles, offset + 11).xyz;
    
    m.emissive = texelFetch(triangles, offset + 6).xyz;
    m.baseColor = texelFetch(triangles, offset + 7).xyz;
    m.subsurface = param1.x;
    m.metallic = param1.y;
    m.specular = param1.z;
    m.specularTint = param2.x;
    m.roughness = param2.y;
    m.anisotropic = param2.z;
    m.sheen = param3.x;
    m.sheenTint = param3.y;
    m.clearcoat = param3.z;
    m.clearcoatGloss = param4.x;
    m.IOR = param4.y;
    m.transmission = param4.z;

    return m;
}

// 获取第 i 下标的 BVHNode 对象
BVHNode getBVHNode(int i) {
   
   
    BVHNode node;

    // 左右子树
    int offset = i * SIZE_BVHNODE;
    ivec3 childs = ivec3(texelFetch(nodes, offset + 0).xyz);
    ivec3 leafInfo = ivec3(texelFetch(nodes, offset + 1).xyz);
    node.left = int(childs.x);
    node.right = int(childs.y);
    node.n = int(leafInfo.x);
    node.index = int(leafInfo.y);

    //