javascript - 如何在 Three.js 中渲染地球时渲染 'atmosphere'？

Question

在过去的几天里，我一直在努力让 Three.js 纹理发挥作用。我一直遇到的问题是我的浏览器阻止加载纹理，按照说明解决了这个问题 here .

无论如何，我正在为我的一门类(class)制作一个太空导航游戏，演示如何在太空中驾驶航天器。所以，我正在渲染一堆行星，地球就是其中之一。我在下面附上了我的地球渲染图。看起来不错，但我想做的是通过在地球周围添加“气氛”来让它看起来更逼真。

我环顾四周，发现了一些真正的 neat looking creations处理发光，但不幸的是，我认为它们不适用于我的情况。

下面是将地球添加到我的场景中的代码(它是我从 Three.js 教程中获得的代码的修改版本):

    function addEarth(x,y){

        var sphereMaterial =
        new THREE.MeshLambertMaterial({
            //color: 0x0000ff,
            map: earthTexture
        });

        // set up the sphere vars
        var radius = 75;
        segments = 16;
        rings = 16;

        // create a new mesh with
        // sphere geometry - we will cover
        // the sphereMaterial next!
        earth = new THREE.Mesh(

        new THREE.SphereGeometry(
        radius,
        segments,
        rings),

        sphereMaterial);

        earth.position.x = x;
        earth.position.y = y;

        // add the sphere to the scene
        scene.add(earth);
    }

Answer 1

好吧，这是一个已经回答过的老问题，但我想添加我的解决方案以供初学者考虑。长期研究大气散射和 GLSL 并开发了这个 VEEERRRYYY 大气散射的简化版本(如果动画停止刷新页面或以更合适的方式查看 GIF):

[

1. 行星是椭圆体(中心 x,y, z 和半径 rx,ry,rz )
2. 大气层也是椭圆体(相同但大气层高度更大)
3. 所有渲染都正常完成，但最重要的是为近观察者行星添加了 1 次渲染
4. 那个 channel 是覆盖整个屏幕的单个四边形
5. 在片段内部它计算像素射线与这 2 个椭圆体的交点
6. 取可见部分(不在后面，不在地面之后)
7. 计算大气中的射线长度
8. 根据 r,g,b 扭曲原始颜色按射线长度缩放参数(类似于沿路径积分)
   • 一些颜色是给定的...
   • 极大地影响颜色，因此可以通过几个属性来模拟不同的气氛
9. 它在大气层内和大气层外(从远处)都能很好地工作
10. 可以添加附近的星星作为光源(我使用最多 3 星系统)

结果令人惊叹，请参见下图:

顶点:

/* SSH GLSL Atmospheric Ray light scattering ver 3.0

    glEnable(GL_BLEND);
    glBlendFunc(GL_ONE,GL_ONE);
    use with single quad covering whole screen

    no Modelview/Projection/Texture matrixes used

    gl_Normal   is camera direction in ellipsoid space
    gl_Vertex   is pixel in ellipsoid space
    gl_Color    is pixel pos in screen space <-1,+1>

    const int _lights=3;
    uniform vec3 light_dir[_lights];     // direction to local star in ellipsoid space
    uniform vec3 light_col[_lights];     // local star color * visual intensity
    uniform vec4 light_posr[_lights];    // local star position and radius^-2 in ellipsoid space
    uniform vec4 B0;                     // atmosphere scattering coefficient (affects color) (r,g,b,-)

    [ToDo:]
    add light map texture for light source instead of uniform star colide parameters
    - all stars and distant planets as dots
    - near planets ??? maybe too slow for reading pixels
    aspect ratio correction
*/

varying vec3 pixel_nor;       // camera direction in ellipsoid space
varying vec4 pixel_pos;       // pixel in ellipsoid space

void main(void)
    {
    pixel_nor=gl_Normal;
    pixel_pos=gl_Vertex;
    gl_Position=gl_Color;
    }

片段:

varying vec3 pixel_nor;              // camera direction in ellipsoid space
varying vec4 pixel_pos;              // pixel in ellipsoid space

uniform vec3 planet_r;               // rx^-2,ry^-2,rz^-2 - surface
uniform vec3 planet_R;               // Rx^-2,Ry^-2,Rz^-2 - atmosphere
uniform float planet_h;              // atmoshere height [m]
uniform float view_depth;            // max. optical path length [m] ... saturation

// lights are only for local stars-atmosphere ray colision to set start color to star color
const int _lights=3;
uniform vec3 light_dir[_lights];     // direction to local star in ellipsoid space
uniform vec3 light_col[_lights];     // local star color * visual intensity
uniform vec4 light_posr[_lights];    // local star position and radius^-2 in ellipsoid space
uniform vec4 B0;                     // atmosphere scattering coefficient (affects color) (r,g,b,-)

// compute length of ray(p0,dp) to intersection with ellipsoid((0,0,0),r) -> view_depth_l0,1
// where r.x is elipsoid rx^-2, r.y = ry^-2 and r.z=rz^-2
float view_depth_l0=-1.0,view_depth_l1=-1.0;
bool _view_depth(vec3 p0,vec3 dp,vec3 r)
    {
    float a,b,c,d,l0,l1;
    view_depth_l0=-1.0;
    view_depth_l1=-1.0;
    a=(dp.x*dp.x*r.x)
     +(dp.y*dp.y*r.y)
     +(dp.z*dp.z*r.z); a*=2.0;
    b=(p0.x*dp.x*r.x)
     +(p0.y*dp.y*r.y)
     +(p0.z*dp.z*r.z); b*=2.0;
    c=(p0.x*p0.x*r.x)
     +(p0.y*p0.y*r.y)
     +(p0.z*p0.z*r.z)-1.0;
    d=((b*b)-(2.0*a*c));
    if (d<0.0) return false;
    d=sqrt(d);
    l0=(-b+d)/a;
    l1=(-b-d)/a;
    if (abs(l0)>abs(l1)) { a=l0; l0=l1; l1=a; }
    if (l0<0.0)          { a=l0; l0=l1; l1=a; }
    if (l0<0.0) return false;
    view_depth_l0=l0;
    view_depth_l1=l1;
    return true;
    }
// determine if ray (p0,dp) hits a sphere ((0,0,0),r)
// where r is (sphere radius)^-2
bool _star_colide(vec3 p0,vec3 dp,float r)
    {
    float a,b,c,d,l0,l1;
    a=(dp.x*dp.x*r)
     +(dp.y*dp.y*r)
     +(dp.z*dp.z*r); a*=2.0;
    b=(p0.x*dp.x*r)
     +(p0.y*dp.y*r)
     +(p0.z*dp.z*r); b*=2.0;
    c=(p0.x*p0.x*r)
     +(p0.y*p0.y*r)
     +(p0.z*p0.z*r)-1.0;
    d=((b*b)-(2.0*a*c));
    if (d<0.0) return false;
    d=sqrt(d);
    l0=(-b+d)/a;
    l1=(-b-d)/a;
    if (abs(l0)>abs(l1)) { a=l0; l0=l1; l1=a; }
    if (l0<0.0)          { a=l0; l0=l1; l1=a; }
    if (l0<0.0) return false;
    return true;
    }

// compute atmosphere color between ellipsoids (planet_pos,planet_r) and (planet_pos,planet_R) for ray(pixel_pos,pixel_nor)
vec3 atmosphere()
    {
    const int n=8;
    const float _n=1.0/float(n);
    int i;
    bool b0,b1;
    vec3 p0,p1,dp,p,c,b;
    // c - color of pixel from start to end

    float l0,l1,l2,h,dl;
    c=vec3(0.0,0.0,0.0);
    b0=_view_depth(pixel_pos.xyz,pixel_nor,planet_r);
    if ((b0)&&(view_depth_l0>0.0)&&(view_depth_l1<0.0)) return c;
    l0=view_depth_l0;
    b1=_view_depth(pixel_pos.xyz,pixel_nor,planet_R);
    l1=view_depth_l0;
    l2=view_depth_l1;

    dp=pixel_nor;
    p0=pixel_pos.xyz;

    if (!b0)
        {                                       // outside surface
        if (!b1) return c;                      // completly outside planet
        if (l2<=0.0)                            // inside atmosphere to its boundary
            {
            l0=l1;
            }
        else{                                   // throu atmosphere from boundary to boundary
            p0=p0+(l1*dp);
            l0=l2-l1;
            }
        // if a light source is in visible path then start color is light source color
        for (i=0;i<_lights;i++)
        if (light_posr[i].a<=1.0)
        if (_star_colide(p0-light_posr[i].xyz,dp,light_posr[i].a))
        c+=light_col[i];
        }
    else{                                       // into surface
        if (l0<l1) b1=false;                    // atmosphere is behind surface
        if (!b1)                                // inside atmosphere to surface
            {
            l0=l0;
            }
        else{                                   // from atmosphere boundary to surface
            p0=p0+(l1*dp);
            l0=l0-l1;
            }
        }
    dp*=l0;
    p1=p0+dp;
    dp*=_n;
/*
    p=normalize(p1);
    h=0.0; l2=0.0;
    for (i=0;i<_lights;i++)
     if (light_posr[i].a<=1.0)
        {
        dl=dot(pixel_nor,light_dir[i]);         // cos(ang: light-eye)
        if (dl<0.0) dl=0.0;
        h+=dl;
        dl=dot(p,light_dir[i]);                 // normal shading
        if (dl<0.0) dl=0.0;
        l2+=dl;
        }
    if (h>1.0) h=1.0;
    if (l2>1.0) l2=1.0;
    h=0.5*(2.0+(h*h));
*/
    float qqq=dot(normalize(p1),light_dir[0]);


    dl=l0*_n/view_depth;
    for (p=p1,i=0;i<n;p-=dp,i++)                // p1->p0 path throu atmosphere from ground
        {
        _view_depth(p,normalize(p),planet_R);   // view_depth_l0=depth above atmosphere top [m]
        h=exp(view_depth_l0/planet_h)/2.78;

        b=B0.rgb*h*dl;
        c.r*=1.0-b.r;
        c.g*=1.0-b.g;
        c.b*=1.0-b.b;
        c+=b*qqq;
        }
    if (c.r<0.0) c.r=0.0;
    if (c.g<0.0) c.g=0.0;
    if (c.b<0.0) c.b=0.0;
    h=0.0;
    if (h<c.r) h=c.r;
    if (h<c.g) h=c.g;
    if (h<c.b) h=c.b;
    if (h>1.0)
        {
        h=1.0/h;
        c.r*=h;
        c.g*=h;
        c.b*=h;
        }
    return c;
    }

void main(void)
    {
    gl_FragColor.rgb=atmosphere();
    }

抱歉，但它是我的一个非常古老的来源......应该可以转换为核心配置文件

[编辑 1] 抱歉忘记添加我输入的地球大气散射常数

    double view_depth=1000000.0;    // [m] ... longer path is saturated atmosphere color
    double ha=40000.0;              // [m] ... usable atmosphere height (higher is too low pressure)

//  this is how B0 should be computed (for real atmospheric scattering with nested volume integration)
//  const float lambdar=650.0*0.000000001; // wavelengths for R,G,B rays
//  const float lambdag=525.0*0.000000001;
//  const float lambdab=450.0*0.000000001;
//  double r=1.0/(lambdar*lambdar*lambdar*lambdar); // B0 coefficients
//  double g=1.0/(lambdag*lambdag*lambdag*lambdag);
//  double b=1.0/(lambdab*lambdab*lambdab*lambdab);

//  and these are my empirical coefficients for earth like 
//  blue atmosphere with my simplified integration style
//  images above are rendered with this:
    float r=0.198141888310295;
    float g=0.465578010163675;
    float b=0.862540960504986;
    float B0=2.50000E-25;
    i=glGetUniformLocation(ShaderProgram,"planet_h");   glUniform1f(i,ha);
    i=glGetUniformLocation(ShaderProgram,"view_depth"); glUniform1f(i,view_depth);
    i=glGetUniformLocation(ShaderProgram,"B0");     glUniform4f(i,r,g,b,B0);
//  all other atributes are based on position and size of planet and are 
//  pretty straightforward so here is just the earth size i use ...
    double r_equator=6378141.2; // [m]
    double r_poles=6356754.8;   // [m]

[edit2] 3.9.2014 新源码

我最近花了一些时间对我的引擎实现缩放，并发现原始源代码从 0.002 AU 以上的距离来看不是很精确。没有缩放它只是几个像素，所以什么都看不到，但是缩放所有变化所以我试图尽可能地提高准确性。

• 在这里ray and ellipsoid intersection accuracy improvement是与此相关的问题

经过一些更多的调整后，我让它可以在高达 25.0 AU 的范围内使用，并且在高达 50.0-100.0 AU 的范围内可以使用插值伪影。这是当前硬件的限制，因为我不能通过非 flat fp64从顶点到片段的插值器。一种解决方法是将坐标系变换移动到片段，但尚未尝试过。这里有一些变化:

• 新源代码使用 64 位 float
• 并添加uniform int lights这是已用灯的数量
• B0 的意义也有一些变化(它们不再是波长相关常数而是颜色)所以你需要稍微改变统一值填充到 CPU 代码中。
• 添加了一些性能改进

[顶点]

/* SSH GLSL Atmospheric Ray light scattering ver 3.1

    glEnable(GL_BLEND);
    glBlendFunc(GL_ONE,GL_ONE_MINUS_SRC_ALPHA);
    use with single quad covering whole screen

    no Modelview/Projection/Texture matrixes used

    gl_Normal   is camera direction in ellipsoid space
    gl_Vertex   is pixel in ellipsoid space
    gl_Color    is pixel pos in screen space <-1,+1>

    const int _lights=3;
    uniform int  lights;                 // actual number of lights
    uniform vec3 light_dir[_lights];     // direction to local star in ellipsoid space
    uniform vec3 light_col[_lights];     // local star color * visual intensity
    uniform vec4 light_posr[_lights];    // local star position and radius^-2 in ellipsoid space
    uniform vec4 B0;                     // atmosphere scattering coefficient (affects color) (r,g,b,-)

    [ToDo:]
    add light map texture for light source instead of uniform star colide parameters
    - all stars and distant planets as dots
    - near planets ??? maybe too slow for reading pixels
    aspect ratio correction
*/

varying vec3 pixel_nor;       // camera direction in ellipsoid space
varying vec4 pixel_pos;       // pixel in ellipsoid space
varying vec4 pixel_scr;       // pixel in screen space <-1,+1>

varying vec3 p_r;               // rx,ry,rz
uniform vec3 planet_r;          // rx^-2,ry^-2,rz^-2 - surface

void main(void)
    {
    p_r.x=1.0/sqrt(planet_r.x);
    p_r.y=1.0/sqrt(planet_r.y);
    p_r.z=1.0/sqrt(planet_r.z);
    pixel_nor=gl_Normal;
    pixel_pos=gl_Vertex;
    pixel_scr=gl_Color;
    gl_Position=gl_Color;
    }

[片段]

#extension GL_ARB_gpu_shader_fp64 : enable
double abs(double x) { if (x<0.0) x=-x; return x; }

varying vec3 pixel_nor;              // camera direction in ellipsoid space
varying vec4 pixel_pos;              // pixel in ellipsoid space
varying vec4 pixel_scr;              // pixel in screen space
varying vec3 p_r;                    // rx,ry,rz                        

uniform vec3 planet_r;               // rx^-2,ry^-2,rz^-2 - surface
uniform vec3 planet_R;               // Rx^-2,Ry^-2,Rz^-2 - atmosphere
uniform float planet_h;              // atmoshere height [m]
uniform float view_depth;            // max. optical path length [m] ... saturation

// lights are only for local stars-atmosphere ray colision to set start color to star color
const int _lights=3;
uniform int  lights;                 // actual number of lights
uniform vec3 light_dir[_lights];     // direction to local star in ellipsoid space
uniform vec3 light_col[_lights];     // local star color * visual intensity
uniform vec4 light_posr[_lights];    // local star position and radius^-2 in ellipsoid space
uniform vec4 B0;                     // atmosphere scattering color coefficients (r,g,b,ambient)

// compute length of ray(p0,dp) to intersection with ellipsoid((0,0,0),r) -> view_depth_l0,1
// where r.x is elipsoid rx^-2, r.y = ry^-2 and r.z=rz^-2
const double view_depth_max=100000000.0; // > max view depth
double view_depth_l0=-1.0, // view_depth_l0 first hit
       view_depth_l1=-1.0; // view_depth_l1 second hit
bool  _view_depth_l0=false;
bool  _view_depth_l1=false;
bool _view_depth(vec3 _p0,vec3 _dp,vec3 _r)
    {
    dvec3 p0,dp,r;
    double a,b,c,d,l0,l1;
    view_depth_l0=-1.0; _view_depth_l0=false;
    view_depth_l1=-1.0; _view_depth_l1=false;
    // conversion to double
    p0=dvec3(_p0);
    dp=dvec3(_dp);
    r =dvec3(_r );
    // quadratic equation a.l.l+b.l+c=0; l0,l1=?;
    a=(dp.x*dp.x*r.x)
     +(dp.y*dp.y*r.y)
     +(dp.z*dp.z*r.z);
    b=(p0.x*dp.x*r.x)
     +(p0.y*dp.y*r.y)
     +(p0.z*dp.z*r.z); b*=2.0;
    c=(p0.x*p0.x*r.x)
     +(p0.y*p0.y*r.y)
     +(p0.z*p0.z*r.z)-1.0;
    // discriminant d=sqrt(b.b-4.a.c)
    d=((b*b)-(4.0*a*c));
    if (d<0.0) return false;
    d=sqrt(d);
    // standard solution l0,l1=(-b +/- d)/2.a
    a*=2.0;
    l0=(-b+d)/a;
    l1=(-b-d)/a;
    // alternative solution q=-0.5*(b+sign(b).d) l0=q/a; l1=c/q; (should be more accurate sometimes)
//  if (b<0.0) d=-d; d=-0.5*(b+d);
//  l0=d/a;
//  l1=c/d;
    // sort l0,l1 asc
    if ((l0<0.0)||((l1<l0)&&(l1>=0.0))) { a=l0; l0=l1; l1=a; }
    // exit
    if (l1>=0.0) { view_depth_l1=l1; _view_depth_l1=true; }
    if (l0>=0.0) { view_depth_l0=l0; _view_depth_l0=true; return true; }
    return false;
    }

// determine if ray (p0,dp) hits a sphere ((0,0,0),r)
// where r is (sphere radius)^-2
bool _star_colide(vec3 _p0,vec3 _dp,float _r)
    {
    dvec3 p0,dp,r;
    double a,b,c,d,l0,l1;
    // conversion to double
    p0=dvec3(_p0);
    dp=dvec3(_dp);
    r =dvec3(_r );
    // quadratic equation a.l.l+b.l+c=0; l0,l1=?;
    a=(dp.x*dp.x*r)
     +(dp.y*dp.y*r)
     +(dp.z*dp.z*r);
    b=(p0.x*dp.x*r)
     +(p0.y*dp.y*r)
     +(p0.z*dp.z*r); b*=2.0;
    c=(p0.x*p0.x*r)
     +(p0.y*p0.y*r)
     +(p0.z*p0.z*r)-1.0;
    // discriminant d=sqrt(b.b-4.a.c)
    d=((b*b)-(4.0*a*c));
    if (d<0.0) return false;
    d=sqrt(d);
    // standard solution l0,l1=(-b +/- d)/2.a
    a*=2.0;
    l0=(-b+d)/a;
    l1=(-b-d)/a;
    // alternative solution q=-0.5*(b+sign(b).d) l0=q/a; l1=c/q; (should be more accurate sometimes)
//  if (b<0.0) d=-d; d=-0.5*(b+d);
//  l0=d/a;
//  l1=c/d;
    // sort l0,l1 asc
    if (abs(l0)>abs(l1)) { a=l0; l0=l1; l1=a; }
    if (l0<0.0)          { a=l0; l0=l1; l1=a; }
    if (l0<0.0) return false;
    return true;
    }

// compute atmosphere color between ellipsoids (planet_pos,planet_r) and (planet_pos,planet_R) for ray(pixel_pos,pixel_nor)
vec4 atmosphere()
    {
    const int n=8;
    const float _n=1.0/float(n);
    int i;
    bool b0,b1;
    vec3 p0,p1,dp,p,b;
    vec4 c;     // c - color of pixel from start to end

    float h,dl,ll;
    double l0,l1,l2;
    bool   e0,e1,e2;
    c=vec4(0.0,0.0,0.0,0.0);    // a=0.0 full background color, a=1.0 no background color (ignore star)
    b1=_view_depth(pixel_pos.xyz,pixel_nor,planet_R);
    if (!b1) return c;                          // completly outside atmosphere
    e1=_view_depth_l0; l1=view_depth_l0;        // first atmosphere hit
    e2=_view_depth_l1; l2=view_depth_l1;        // second atmosphere hit
    b0=_view_depth(pixel_pos.xyz,pixel_nor,planet_r);
    e0=_view_depth_l0; l0=view_depth_l0;        // first surface hit
    if ((b0)&&(view_depth_l1<0.0)) return c;    // under ground
    // set l0 to view depth and p0 to start point
    dp=pixel_nor;
    p0=pixel_pos.xyz;
    if (!b0)                                    // outside surface
        {
        if (!e2)                                // inside atmosphere to its boundary
            {
            l0=l1;
            }
        else{                                   // throu atmosphere from boundary to boundary
            p0=vec3(dvec3(p0)+(dvec3(dp)*l1));
            l0=l2-l1;
            }
        // if a light source is in visible path then start color is light source color
        for (i=0;i<lights;i++)
         if (_star_colide(p0.xyz-light_posr[i].xyz,dp.xyz,light_posr[i].a*0.75)) // 0.75 is enlargment to hide star texture corona
            {
            c.rgb+=light_col[i];
            c.a=1.0; // ignore already drawed local star color
            }
        }
    else{                                       // into surface
        if (l1<l0)                              // from atmosphere boundary to surface
            {
            p0=vec3(dvec3(p0)+(dvec3(dp)*l1));
            l0=l0-l1;
            }
        else{                                   // inside atmosphere to surface
            l0=l0;
            }
        }
    // set p1 to end of view depth, dp to intergral step
    p1=vec3(dvec3(p0)+(dvec3(dp)*l0)); dp=p1-p0;
    dp*=_n;

    dl=float(l0)*_n/view_depth;
    ll=B0.a; for (i=0;i<lights;i++)             // compute normal shaded combined light sources into ll
     ll+=dot(normalize(p1),light_dir[0]);
    for (p=p1,i=0;i<n;p-=dp,i++)                // p1->p0 path throu atmosphere from ground
        {
//      _view_depth(p,normalize(p),planet_R);   // too slow... view_depth_l0=depth above atmosphere top [m]
//      h=exp(view_depth_l0/planet_h)/2.78;

        b=normalize(p)*p_r;                     // much much faster
        h=length(p-b);
        h=exp(h/planet_h)/2.78;

        b=B0.rgb*h*dl;
        c.r*=1.0-b.r;
        c.g*=1.0-b.g;
        c.b*=1.0-b.b;
        c.rgb+=b*ll;
        }
    if (c.r<0.0) c.r=0.0;
    if (c.g<0.0) c.g=0.0;
    if (c.b<0.0) c.b=0.0;
    h=0.0;
    if (h<c.r) h=c.r;
    if (h<c.g) h=c.g;
    if (h<c.b) h=c.b;
    if (h>1.0)
        {
        h=1.0/h;
        c.r*=h;
        c.g*=h;
        c.b*=h;
        }
    return c;
    }

void main(void)
    {
    gl_FragColor.rgba=atmosphere();
    }

[统一值]

// Earth
re=6378141.2         // equatoreal radius r.x,r.y
rp=6356754.79506139 // polar radius r.z
planet_h=60000      // atmosphere thickness R(r.x+planet_h,r.y+planet_h,r.z+planet_h)
view_depth=250000   // max view distance before 100% scattering occur 
B0.r=0.1981         // 100% scattered atmosphere color
B0.g=0.4656
B0.b=0.8625
B0.a=0.75           // overglow (sky is lighter before Sun actually rise) it is added to light dot product

// Mars
re=3397000
rp=3374919.5
ha=30000
view_depth=300000
B0.r=0.4314
B0.g=0.3216
B0.b=0.196
B0.a=0.5

有关更多信息(和较新的图像)，请参阅相关内容:

• Is it possible to make realistic n-body solar system simulation in matter of size and mass?

[编辑3]

这里是我在我的引擎中使用上面的着色器渲染气氛的小型 CPU 端代码:

if (sys->_enable_bodya) // has planet atmosphere?
 if (view_depth>=0.0)
    {
    glColor4f(1.0,1.0,1.0,1.0);
    double a,b,p[3],d[3];
    sys->shd_engine.unbind();
    sys->shd_scatter.bind(); // this is the atmospheric shader
    if (1) //*** GLSL_uniform_supported (leftover from old GL engine version)
        {
        int j;
        double *w;
        AnsiString s;
        a=re; b=rp; a=divide(1.0,a*a); b=divide(1.0,b*b); // radius of planet re equatoral and rp polar and ha is atmosphere thickness
        sys->shd_scatter.set3f("planet_r",a,a,b);
        a=re+ha; b=rp+ha;   a=divide(1.0,a*a); b=divide(1.0,b*b);
        sys->shd_scatter.set3f("planet_R"  ,a,a,b);
        sys->shd_scatter.set1f("planet_h"  ,ha);
        sys->shd_scatter.set1f("view_depth",view_depth); // visibility distance
        sys->shd_scatter.set4f("B0",B0[0],B0[1],B0[2],B0[3]); // saturated atmosphere color and overglow
        sys->shd_scatter.set1i("lights",sys->local_star.num); // local stars
        for (j=0;j<sys->local_star.num;j++)
            {
            a=sys->local_star[j].r;
            w=sys->local_star[j].p;
            s=AnsiString().sprintf("light_posr[%i]",j);
            sys->shd_scatter.set4f(s,w[0],w[1],w[2],divide(1.0,a*a));

            w=sys->local_star[j].d;
            s=AnsiString().sprintf("light_dir[%i]",j);
            sys->shd_scatter.set3f(s,w[0],w[1],w[2]);

            vector_mul(p,sys->local_star[j].col,10.0);
            s=AnsiString().sprintf("light_col[%i]",j);
            sys->shd_scatter.set3f(s,p[0],p[1],p[2]);
            }
        }
    glEnable(GL_BLEND);
    glBlendFunc(GL_ONE,GL_ONE_MINUS_SRC_ALPHA);
    a=1.0;
    b=-2.0*view.scr->views[view.scr->view].znear;
    // color  = pixel pos in screen space <-1,+1> ... no Projection/ModelView is used :)
    // vertex = pixel pos in elypsoid space
    // normal = eye-pixel direction in elypsoid space
    zsort.rep0.g2l_dir(d,zsort.obj_pos0);
    glDepthMask(0);
    glBegin(GL_QUADS);
    a=divide(1.0,view.zoom);
    glColor4d(-1.0,-1.0,0.0,1.0); vector_ld(p,-a,-a,b); view.scr->fromscr(p,p); view.eye0.l2g(q,p); zsort.rep0.g2l_dir(q,q); vector_sub(p,q,d); vector_one(q,q); glNormal3dv(q); glVertex3dv(p);
    glColor4d(+1.0,-1.0,0.0,1.0); vector_ld(p,+a,-a,b); view.scr->fromscr(p,p); view.eye0.l2g(q,p); zsort.rep0.g2l_dir(q,q); vector_sub(p,q,d); vector_one(q,q); glNormal3dv(q); glVertex3dv(p);
    glColor4d(+1.0,+1.0,0.0,1.0); vector_ld(p,+a,+a,b); view.scr->fromscr(p,p); view.eye0.l2g(q,p); zsort.rep0.g2l_dir(q,q); vector_sub(p,q,d); vector_one(q,q); glNormal3dv(q); glVertex3dv(p);
    glColor4d(-1.0,+1.0,0.0,1.0); vector_ld(p,-a,+a,b); view.scr->fromscr(p,p); view.eye0.l2g(q,p); zsort.rep0.g2l_dir(q,q); vector_sub(p,q,d); vector_one(q,q); glNormal3dv(q); glVertex3dv(p);
    glEnd();
    glDepthMask(1);
    glDisable(GL_BLEND);
    sys->shd_scatter.unbind();
    sys->shd_engine.bind();
    }

它是从我的引擎中提取出来的，所以它使用了很多你没有的东西，但你知道这些东西是如何使用的……顺便说一句l2g表示从局部坐标到全局坐标的变换，g2l恰恰相反。如果_dir像l2g_dir一样存在这意味着变换正在处理矢量而不是位置，因此没有翻译。 fromscr转换屏幕 <-1,+1>到 3D(本地相机)和 vector_one将向量归一化为单位一。希望我没有忘记解释一些事情......