GLSL 大气散射不随变换缩放

我正在尝试在 GLSL 版本 4.10 中实现大气散射。我正在改编此 Shadertoy 着色器中的着色器https://www.shadertoy.com/view/lslXDr https://www.shadertoy.com/view/lslXDr。我的程序中的大气层是根据行星球体的缩放版本创建的。

我有实际的散射方程，但对于大多数相机位置来说，大气的内半径与球体的外半径并不对齐。我知道这是因为大气层的半径比行星球体大，但我似乎无法让它正确缩放。

我的问题在这里得到了最好的说明。这些图片中的模型是按比例放大的。可以看出，大气层内半径与行星（深蓝色球体）的半径不匹配。

这里模型被缩放和平移。大气层偏离了相机的中心，内部大气层仍然没有与行星对齐。

这是顶点着色器，它本质上是一个直通着色器

#version 410

in vec4 vPosition;
in vec3 vNormal;

out vec3 fPosition;
out mat3 m;

uniform mat4 model;
uniform mat4 view;
uniform mat4 projection;

void main()
{   
    fPosition = vec3(vPosition);
    m = mat3(model);

    gl_Position = projection*view*model*vPosition;
}

还有片段着色器。

#version 410

uniform float time;
uniform vec3 camPosition;
uniform float fInnerRadius;
uniform float fOuterRadius;

in vec3 fPosition;
in mat3 m;

out vec4 FragColor;

const float PI = 3.14159265359;
const float degToRad = PI / 180.0;
const float MAX = 10000.0;

float K_R = 0.166;
const float K_M = 0.0025;
const float E = 14.3;
const vec3 C_R = vec3(0.3, 0.7, 1.0);
const float G_M = -0.85;

float SCALE_H = 4.0 / (fOuterRadius - fInnerRadius);
float SCALE_L = 1.0 / (fOuterRadius - fInnerRadius);

const int numOutScatter = 10;
const float fNumOutScatter = 10.0;
const int numInScatter = 10;
const float fNumInScatter = 10.0;

vec3 rayDirection(vec3 camPosition) {
    vec3 ray = m*fPosition - camPosition;
    float far = length(ray);
    return ray /= far;
}

vec2 rayIntersection(vec3 p, vec3 dir, float radius ) {
    float b = dot( p, dir );
    float c = dot( p, p ) - radius * radius;

    float d = b * b - c;
    if ( d < 0.0 ) {
        return vec2( MAX, -MAX );
    }
    d = sqrt( d );

    float near = -b - d;
    float far = -b + d;

    return vec2(near, far);
 }

// Mie
// g : ( -0.75, -0.999 )
//      3 * ( 1 - g^2 )               1 + c^2
// F = ----------------- * -------------------------------
//      2 * ( 2 + g^2 )     ( 1 + g^2 - 2 * g * c )^(3/2)
float miePhase( float g, float c, float cc ) {
    float gg = g * g;

    float a = ( 1.0 - gg ) * ( 1.0 + cc );

    float b = 1.0 + gg - 2.0 * g * c;
    b *= sqrt( b );
    b *= 2.0 + gg;  

    return 1.5 * a / b;
}

// Reyleigh
// g : 0
// F = 3/4 * ( 1 + c^2 )
float rayleighPhase( float cc ) {
    return 0.75 * ( 1.0 + cc );
}


float density(vec3 p) {
    return exp(-(length(p) - fInnerRadius) * SCALE_H);
}

float optic(vec3 p, vec3 q) {
    vec3 step = (q - p) / fNumOutScatter;
    vec3 v = p + step * 0.5;

    float sum = 0.0;
    for(int i = 0; i < numOutScatter; i++) {
        sum += density(v);
        v += step;
    }
    sum *= length(step)*SCALE_L;
    return sum;
}

vec3 inScatter(vec3 o, vec3 dir, vec2 e, vec3 l) {
    float len = (e.y - e.x) / fNumInScatter;
    vec3 step = dir * len;
    vec3 p = o + dir * e.x;
    vec3 v = p + dir * (len * 0.5);

    vec3 sum = vec3(0.0);
    for(int i = 0; i < numInScatter; i++) {
        vec2 f = rayIntersection(v, l, fOuterRadius);
        vec3 u = v + l * f.y;
        float n = (optic(p, v) + optic(v, u))*(PI * 4.0);
        sum += density(v)* exp(-n * ( K_R * C_R + K_M ));
        v += step;
    }
    sum *= len * SCALE_L;
    float c = dot(dir, -l);
    float cc = c * c;
    return sum * ( K_R * C_R * rayleighPhase( cc ) + K_M * miePhase( G_M, c, cc ) ) * E;
}

void main (void)
{
    vec3 dir = rayDirection(vec3(camPosition.x, 0.0, camPosition.z));
    vec3 eye = vec3(camPosition.x, 0.0, camPosition.z);

    vec3 l = normalize(vec3(0.0, 0.0, 1.0));

    vec2 e = rayIntersection(eye, dir, fOuterRadius);
    if ( e.x > e.y ) {
        discard;
    }
    vec2 f = rayIntersection(eye, dir, fInnerRadius);
    e.y = min(e.y, f.x);

    vec3 I = inScatter(eye, dir, e, l);

    FragColor = vec4(I, 1.0);
}

如果需要的话，这里是绘制气氛的代码。绘制行星的代码基本上具有相同的转换（没有比例因子）。

void drawAtmosphere()
{
    glUseProgram(atmosphereShader);

    v = getViewMatrix();
    vec3 Position = getCameraPosition();

    float scaleFactor = 1.25;
    m = multiplymat4(translate(0.0, 0.0, -10), scale(fScale*scaleFactor));
    float fOuter = (fScale*scaleFactor);
    float fInner = fScale;

    glUniform1f(glGetUniformLocation(atmosphereShader, "fInnerRadius"), fInner);
    glUniform1f(glGetUniformLocation(atmosphereShader, "fOuterRadius"), fOuter);
    glUniform3f(glGetUniformLocation(atmosphereShader, "camPosition"), Position.x, Position.y, Position.z);
    glUniform1f(glGetUniformLocation(atmosphereShader, "time"), glfwGetTime());

    initMVP(atmosphereShader, m, v);

    glBindVertexArray (atmosphereVAO);
    glDrawArrays( GL_TRIANGLES, 0, planet.vertexNumber);
    glBindVertexArray(0);

}

任何帮助，或者任何可以指引我正确方向的事情，我都会感激不尽。

发现问题是由于相机位置计算不正确并且没有考虑物体的模型空间引起的。我上传了代码的精简版本here https://github.com/TJGreen0211/gl_tests/tree/master/atmosphere.

希望这能帮助任何尝试实施 Sean O'Neil 的大气代码的人。