我需要帮助将此 2D 天空着色器转换为 3D
I need help converting this 2D sky shader to 3D
我在 github 上找到了这个着色器函数，并设法让它在我当前选择的编程套件 GameMaker Studio 2 中运行。然而，这是一个 2D 效果，没有考虑相机向上矢量，也没有考虑 fov。无论如何可以添加到这个？在着色器方面，我的技能水平只是中等水平，所以我不确定到底该走哪条路，或者在这一点上它是否值得，或者我是否应该从一个不同的例子开始。
uniform vec3 u_sunPosition;
varying vec2 v_vTexcoord;
varying vec4 v_vColour;
varying vec3 v_vPosition;
#define PI 3.141592
#define iSteps 16
#define jSteps 8
vec2 rsi(vec3 r0, vec3 rd, float sr) {
// ray-sphere intersection that assumes
// the sphere is centered at the origin.
// No intersection when result.x > result.y
float a = dot(rd, rd);
float b = 2.0 * dot(rd, r0);
float c = dot(r0, r0) - (sr * sr);
float d = (b*b) - 4.0*a*c;
if (d < 0.0) return vec2(1e5,-1e5);
return vec2(
(-b - sqrt(d))/(2.0*a),
(-b + sqrt(d))/(2.0*a)
);
}
vec3 atmosphere(vec3 r, vec3 r0, vec3 pSun, float iSun, float rPlanet, float rAtmos, vec3 kRlh, float kMie, float shRlh, float shMie, float g) {
// Normalize the sun and view directions.
pSun = normalize(pSun);
r = normalize(r);
// Calculate the step size of the primary ray.
vec2 p = rsi(r0, r, rAtmos);
if (p.x > p.y) return vec3(0,0,0);
p.y = min(p.y, rsi(r0, r, rPlanet).x);
float iStepSize = (p.y - p.x) / float(iSteps);
// Initialize the primary ray time.
float iTime = 0.0;
// Initialize accumulators for Rayleigh and Mie scattering.
vec3 totalRlh = vec3(0,0,0);
vec3 totalMie = vec3(0,0,0);
// Initialize optical depth accumulators for the primary ray.
float iOdRlh = 0.0;
float iOdMie = 0.0;
// Calculate the Rayleigh and Mie phases.
float mu = dot(r, pSun);
float mumu = mu * mu;
float gg = g * g;
float pRlh = 3.0 / (16.0 * PI) * (1.0 + mumu);
float pp = 1.0 + gg - 2.0 * mu * g;
float pMie = 3.0 / (8.0 * PI) * ((1.0 - gg) * (mumu + 1.0)) / (sign(pp)*pow(abs(pp), 1.5) * (2.0 + gg));
// Sample the primary ray.
for (int i = 0; i < iSteps; i++) {
// Calculate the primary ray sample position.
vec3 iPos = r0 + r * (iTime + iStepSize * 0.5);
// Calculate the height of the sample.
float iHeight = length(iPos) - rPlanet;
// Calculate the optical depth of the Rayleigh and Mie scattering for this step.
float odStepRlh = exp(-iHeight / shRlh) * iStepSize;
float odStepMie = exp(-iHeight / shMie) * iStepSize;
// Accumulate optical depth.
iOdRlh += odStepRlh;
iOdMie += odStepMie;
// Calculate the step size of the secondary ray.
float jStepSize = rsi(iPos, pSun, rAtmos).y / float(jSteps);
// Initialize the secondary ray time.
float jTime = 0.0;
// Initialize optical depth accumulators for the secondary ray.
float jOdRlh = 0.0;
float jOdMie = 0.0;
// Sample the secondary ray.
for (int j = 0; j < jSteps; j++) {
// Calculate the secondary ray sample position.
vec3 jPos = iPos + pSun * (jTime + jStepSize * 0.5);
// Calculate the height of the sample.
float jHeight = length(jPos) - rPlanet;
// Accumulate the optical depth.
jOdRlh += exp(-jHeight / shRlh) * jStepSize;
jOdMie += exp(-jHeight / shMie) * jStepSize;
// Increment the secondary ray time.
jTime += jStepSize;
}
// Calculate attenuation.
vec3 attn = exp(-(kMie * (iOdMie + jOdMie) + kRlh * (iOdRlh + jOdRlh)));
// Accumulate scattering.
totalRlh += odStepRlh * attn;
totalMie += odStepMie * attn;
// Increment the primary ray time.
iTime += iStepSize;
}
// Calculate and return the final color.
return iSun * (pRlh * kRlh * totalRlh + pMie * kMie * totalMie);
}
vec3 ACESFilm( vec3 x )
{
float tA = 2.51;
float tB = 0.03;
float tC = 2.43;
float tD = 0.59;
float tE = 0.14;
return clamp((x*(tA*x+tB))/(x*(tC*x+tD)+tE),0.0,1.0);
}
void main() {
vec3 color = atmosphere(
normalize( v_vPosition ), // normalized ray direction
vec3(0,6372e3,0), // ray origin
u_sunPosition, // position of the sun
22.0, // intensity of the sun
6371e3, // radius of the planet in meters
6471e3, // radius of the atmosphere in meters
vec3(5.5e-6, 13.0e-6, 22.4e-6), // Rayleigh scattering coefficient
21e-6, // Mie scattering coefficient
8e3, // Rayleigh scale height
1.2e3, // Mie scale height
0.758 // Mie preferred scattering direction
);
// Apply exposure.
color = ACESFilm( color );
gl_FragColor = vec4(color, 1.0);
}
However this is a 2D effect that doesn't take into account the camera up vector, nor fov.
如果要绘制3D 天空，则必须在归一化设备的背板上绘制space。归一化设备space是一个立方体，左下靠近(-1, -1, -1)，右上远为(1, 1, 1)。
背板是方形的：
bottom left: -1, -1, 1
bottom right: 1, -1, 1
top right: -1, -1, 1
top left: -1, -1, 1
渲染这个四边形。请注意，顶点坐标不必由任何矩阵转换，因为它们是标准化的设备 space 坐标。但是你必须转换用于天空的光线（传递给 atmosphere 的方向）。
这条光线必须是世界 space 中的一个方向，从相机位置到天空。通过四边形的顶点坐标，您可以获得归一化设备 space 中的射线。您必须将此射线转换为世界 space。逆投影矩阵 (MATRIX_PROJECTION) transforms from normalized devices space to view space and the inverse view matrix (MATRIX_VIEW) 将视图 space 转换为世界 space。在顶点着色器中使用这个矩阵：
attribute vec3 in_Position;
varying vec3 v_world_ray;
void main()
{
gl_Position = vec4(inPos, 1.0);
vec3 proj_ray = vec3(inverse(gm_Matrices[MATRIX_PROJECTION]) * vec4(inPos.xyz, 1.0));
v_world_ray = vec3(inverse(gm_Matrices[MATRIX_VIEW]) * vec4(proj_ray.xyz, 0.0));
}
在片段着色器中，您必须将光线绕 x 轴旋转 90°，但这只是由函数解释光线的方式造成的 atmosphere:
varying vec3 v_world_ray;
// [...]
void main() {
vec3 world_ray = vec3(v_world_ray.x, v_world_ray.z, -v_world_ray.y);
vec3 color = atmosphere(
normalize( world_ray.xyz ), // normalized ray direction
vec3(0,6372e3,0), // ray origin
u_sunPosition, // position of the sun
22.0, // intensity of the sun
6371e3, // radius of the planet in meters
6471e3, // radius of the atmosphere in meters
vec3(5.5e-6, 13.0e-6, 22.4e-6), // Rayleigh scattering coefficient
21e-6, // Mie scattering coefficient
8e3, // Rayleigh scale height
1.2e3, // Mie scale height
0.758 // Mie preferred scattering direction
);
// Apply exposure.
color = ACESFilm( color );
fragColor = vec4(color.rgb, 1.0);
}
我在 github 上找到了这个着色器函数，并设法让它在我当前选择的编程套件 GameMaker Studio 2 中运行。然而，这是一个 2D 效果，没有考虑相机向上矢量，也没有考虑 fov。无论如何可以添加到这个？在着色器方面，我的技能水平只是中等水平，所以我不确定到底该走哪条路，或者在这一点上它是否值得，或者我是否应该从一个不同的例子开始。
uniform vec3 u_sunPosition;
varying vec2 v_vTexcoord;
varying vec4 v_vColour;
varying vec3 v_vPosition;
#define PI 3.141592
#define iSteps 16
#define jSteps 8
vec2 rsi(vec3 r0, vec3 rd, float sr) {
// ray-sphere intersection that assumes
// the sphere is centered at the origin.
// No intersection when result.x > result.y
float a = dot(rd, rd);
float b = 2.0 * dot(rd, r0);
float c = dot(r0, r0) - (sr * sr);
float d = (b*b) - 4.0*a*c;
if (d < 0.0) return vec2(1e5,-1e5);
return vec2(
(-b - sqrt(d))/(2.0*a),
(-b + sqrt(d))/(2.0*a)
);
}
vec3 atmosphere(vec3 r, vec3 r0, vec3 pSun, float iSun, float rPlanet, float rAtmos, vec3 kRlh, float kMie, float shRlh, float shMie, float g) {
// Normalize the sun and view directions.
pSun = normalize(pSun);
r = normalize(r);
// Calculate the step size of the primary ray.
vec2 p = rsi(r0, r, rAtmos);
if (p.x > p.y) return vec3(0,0,0);
p.y = min(p.y, rsi(r0, r, rPlanet).x);
float iStepSize = (p.y - p.x) / float(iSteps);
// Initialize the primary ray time.
float iTime = 0.0;
// Initialize accumulators for Rayleigh and Mie scattering.
vec3 totalRlh = vec3(0,0,0);
vec3 totalMie = vec3(0,0,0);
// Initialize optical depth accumulators for the primary ray.
float iOdRlh = 0.0;
float iOdMie = 0.0;
// Calculate the Rayleigh and Mie phases.
float mu = dot(r, pSun);
float mumu = mu * mu;
float gg = g * g;
float pRlh = 3.0 / (16.0 * PI) * (1.0 + mumu);
float pp = 1.0 + gg - 2.0 * mu * g;
float pMie = 3.0 / (8.0 * PI) * ((1.0 - gg) * (mumu + 1.0)) / (sign(pp)*pow(abs(pp), 1.5) * (2.0 + gg));
// Sample the primary ray.
for (int i = 0; i < iSteps; i++) {
// Calculate the primary ray sample position.
vec3 iPos = r0 + r * (iTime + iStepSize * 0.5);
// Calculate the height of the sample.
float iHeight = length(iPos) - rPlanet;
// Calculate the optical depth of the Rayleigh and Mie scattering for this step.
float odStepRlh = exp(-iHeight / shRlh) * iStepSize;
float odStepMie = exp(-iHeight / shMie) * iStepSize;
// Accumulate optical depth.
iOdRlh += odStepRlh;
iOdMie += odStepMie;
// Calculate the step size of the secondary ray.
float jStepSize = rsi(iPos, pSun, rAtmos).y / float(jSteps);
// Initialize the secondary ray time.
float jTime = 0.0;
// Initialize optical depth accumulators for the secondary ray.
float jOdRlh = 0.0;
float jOdMie = 0.0;
// Sample the secondary ray.
for (int j = 0; j < jSteps; j++) {
// Calculate the secondary ray sample position.
vec3 jPos = iPos + pSun * (jTime + jStepSize * 0.5);
// Calculate the height of the sample.
float jHeight = length(jPos) - rPlanet;
// Accumulate the optical depth.
jOdRlh += exp(-jHeight / shRlh) * jStepSize;
jOdMie += exp(-jHeight / shMie) * jStepSize;
// Increment the secondary ray time.
jTime += jStepSize;
}
// Calculate attenuation.
vec3 attn = exp(-(kMie * (iOdMie + jOdMie) + kRlh * (iOdRlh + jOdRlh)));
// Accumulate scattering.
totalRlh += odStepRlh * attn;
totalMie += odStepMie * attn;
// Increment the primary ray time.
iTime += iStepSize;
}
// Calculate and return the final color.
return iSun * (pRlh * kRlh * totalRlh + pMie * kMie * totalMie);
}
vec3 ACESFilm( vec3 x )
{
float tA = 2.51;
float tB = 0.03;
float tC = 2.43;
float tD = 0.59;
float tE = 0.14;
return clamp((x*(tA*x+tB))/(x*(tC*x+tD)+tE),0.0,1.0);
}
void main() {
vec3 color = atmosphere(
normalize( v_vPosition ), // normalized ray direction
vec3(0,6372e3,0), // ray origin
u_sunPosition, // position of the sun
22.0, // intensity of the sun
6371e3, // radius of the planet in meters
6471e3, // radius of the atmosphere in meters
vec3(5.5e-6, 13.0e-6, 22.4e-6), // Rayleigh scattering coefficient
21e-6, // Mie scattering coefficient
8e3, // Rayleigh scale height
1.2e3, // Mie scale height
0.758 // Mie preferred scattering direction
);
// Apply exposure.
color = ACESFilm( color );
gl_FragColor = vec4(color, 1.0);
}
However this is a 2D effect that doesn't take into account the camera up vector, nor fov.
如果要绘制3D 天空，则必须在归一化设备的背板上绘制space。归一化设备space是一个立方体，左下靠近(-1, -1, -1)，右上远为(1, 1, 1)。
背板是方形的：
bottom left: -1, -1, 1
bottom right: 1, -1, 1
top right: -1, -1, 1
top left: -1, -1, 1
渲染这个四边形。请注意，顶点坐标不必由任何矩阵转换，因为它们是标准化的设备 space 坐标。但是你必须转换用于天空的光线（传递给 atmosphere 的方向）。
这条光线必须是世界 space 中的一个方向，从相机位置到天空。通过四边形的顶点坐标，您可以获得归一化设备 space 中的射线。您必须将此射线转换为世界 space。逆投影矩阵 (MATRIX_PROJECTION) transforms from normalized devices space to view space and the inverse view matrix (MATRIX_VIEW) 将视图 space 转换为世界 space。在顶点着色器中使用这个矩阵：
attribute vec3 in_Position;
varying vec3 v_world_ray;
void main()
{
gl_Position = vec4(inPos, 1.0);
vec3 proj_ray = vec3(inverse(gm_Matrices[MATRIX_PROJECTION]) * vec4(inPos.xyz, 1.0));
v_world_ray = vec3(inverse(gm_Matrices[MATRIX_VIEW]) * vec4(proj_ray.xyz, 0.0));
}
在片段着色器中，您必须将光线绕 x 轴旋转 90°，但这只是由函数解释光线的方式造成的 atmosphere:
varying vec3 v_world_ray;
// [...]
void main() {
vec3 world_ray = vec3(v_world_ray.x, v_world_ray.z, -v_world_ray.y);
vec3 color = atmosphere(
normalize( world_ray.xyz ), // normalized ray direction
vec3(0,6372e3,0), // ray origin
u_sunPosition, // position of the sun
22.0, // intensity of the sun
6371e3, // radius of the planet in meters
6471e3, // radius of the atmosphere in meters
vec3(5.5e-6, 13.0e-6, 22.4e-6), // Rayleigh scattering coefficient
21e-6, // Mie scattering coefficient
8e3, // Rayleigh scale height
1.2e3, // Mie scale height
0.758 // Mie preferred scattering direction
);
// Apply exposure.
color = ACESFilm( color );
fragColor = vec4(color.rgb, 1.0);
}