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#version 430
layout(local_size_x = 16, local_size_y = 16) in;
layout(binding = 0, rgba8) writeonly uniform image2D outImage;
layout(std140, binding = 1) uniform Camera
{
vec3 camPos; float _pad0;
vec3 camRight; float _pad1;
vec3 camUp; float _pad2;
vec3 camForward; float _pad3;
float tanHalfFov;
float aspect;
bool moving;
int _pad4;
} cam;
layout(std140, binding = 2) uniform Disk
{
float disk_r1;
float disk_r2;
float disk_num;
float thickness;
};
layout(std140, binding = 3) uniform Objects
{
int numObjects;
vec4 objPosRadius[16];
vec4 objColor[16];
float mass[16];
};
const float SagA_rs = 1.269e10;
const float D_LAMBDA = 1e7;
const double ESCAPE_R = 1e30;
vec4 objectColor = vec4(0.0);
vec3 hitCenter = vec3(0.0);
float hitRadius = 0.0;
struct Ray
{
float x, y, z, radius, theta, phi;
float dRadius, dTheta, dPhi;
float energy, angularMomentum;
};
Ray InitRay(vec3 position, vec3 direction)
{
Ray ray;
ray.x = position.x;
ray.y = position.y;
ray.z = position.z;
ray.radius = length(position);
ray.theta = acos(position.z / ray.radius);
ray.phi = atan(position.y, position.x);
float dx = direction.x, dy = direction.y, dz = direction.z;
ray.dRadius = sin(ray.theta) * cos(ray.phi) * dx + sin(ray.theta) * sin(ray.phi) * dy + cos(ray.theta) * dz;
ray.dTheta = (cos(ray.theta) * cos(ray.phi) * dx + cos(ray.theta) * sin(ray.phi) * dy - sin(ray.theta) * dz) / ray.radius;
ray.dPhi = (-sin(ray.phi) * dx + cos(ray.phi) * dy) / (ray.radius * sin(ray.theta));
ray.angularMomentum = ray.radius * ray.radius * sin(ray.theta) * ray.dPhi;
float f = 1.0 - SagA_rs / ray.radius;
float dt_dL = sqrt((ray.dRadius * ray.dRadius) / f + ray.radius * ray.radius * (ray.dTheta * ray.dTheta + sin(ray.theta) * sin(ray.theta) * ray.dPhi * ray.dPhi));
ray.energy = f * dt_dL;
return ray;
}
bool Intercept(Ray ray, float schwarzschildRadius)
{
return ray.radius <= schwarzschildRadius;
}
bool InterceptObject(Ray ray)
{
vec3 position = vec3(ray.x, ray.y, ray.z);
for (int i = 0; i < numObjects; ++i)
{
vec3 center = objPosRadius[i].xyz;
float radius = objPosRadius[i].w;
if (distance(position, center) <= radius)
{
objectColor = objColor[i];
hitCenter = center;
hitRadius = radius;
return true;
}
}
return false;
}
void GeodesicRHS(Ray ray, out vec3 derivatives1, out vec3 derivatives2)
{
float radius = ray.radius, theta = ray.theta;
float dRadius = ray.dRadius, dTheta = ray.dTheta, dPhi = ray.dPhi;
float f = 1.0 - SagA_rs / radius;
float dt_dL = ray.energy / f;
derivatives1 = vec3(dRadius, dTheta, dPhi);
derivatives2.x = -(SagA_rs / (2.0 * radius * radius)) * f * dt_dL * dt_dL
+ (SagA_rs / (2.0 * radius * radius * f)) * dRadius * dRadius
+ radius * (dTheta * dTheta + sin(theta) * sin(theta) * dPhi * dPhi);
derivatives2.y = -2.0 * dRadius * dTheta / radius + sin(theta) * cos(theta) * dPhi * dPhi;
derivatives2.z = -2.0 * dRadius * dPhi / radius - 2.0 * cos(theta) / sin(theta) * dTheta * dPhi;
}
void RK4Step(inout Ray ray, float deltaLambda)
{
vec3 k1a, k1b;
GeodesicRHS(ray, k1a, k1b);
ray.radius += deltaLambda * k1a.x;
ray.theta += deltaLambda * k1a.y;
ray.phi += deltaLambda * k1a.z;
ray.dRadius += deltaLambda * k1b.x;
ray.dTheta += deltaLambda * k1b.y;
ray.dPhi += deltaLambda * k1b.z;
ray.x = ray.radius * sin(ray.theta) * cos(ray.phi);
ray.y = ray.radius * sin(ray.theta) * sin(ray.phi);
ray.z = ray.radius * cos(ray.theta);
}
bool CrossesEquatorialPlane(vec3 oldPosition, vec3 newPosition)
{
bool crossed = (oldPosition.y * newPosition.y < 0.0);
float radius = length(vec2(newPosition.x, newPosition.z));
return crossed && (radius >= disk_r1 && radius <= disk_r2);
}
void main()
{
ivec2 pixel = ivec2(gl_GlobalInvocationID.xy);
int width = imageSize(outImage).x;
int height = imageSize(outImage).y;
if (pixel.x >= width || pixel.y >= height)
return;
float u = (2.0 * (pixel.x + 0.5) / width - 1.0) * cam.aspect * cam.tanHalfFov;
float v = (1.0 - 2.0 * (pixel.y + 0.5) / height) * cam.tanHalfFov;
vec3 direction = normalize(u * cam.camRight - v * cam.camUp + cam.camForward);
Ray ray = InitRay(cam.camPos, direction);
vec4 color = vec4(0.0);
vec3 prevPosition = vec3(ray.x, ray.y, ray.z);
float lambda = 0.0;
bool hitBlackHole = false;
bool hitDisk = false;
bool hitObject = false;
int steps = cam.moving ? 60000 : 60000;
for (int i = 0; i < steps; ++i)
{
if (Intercept(ray, SagA_rs))
{
hitBlackHole = true;
break;
}
RK4Step(ray, D_LAMBDA);
lambda += D_LAMBDA;
vec3 newPosition = vec3(ray.x, ray.y, ray.z);
if (CrossesEquatorialPlane(prevPosition, newPosition))
{
hitDisk = true;
break;
}
if (InterceptObject(ray))
{
hitObject = true;
break;
}
prevPosition = newPosition;
if (ray.radius > ESCAPE_R)
break;
}
if (hitDisk)
{
double radius = length(vec3(ray.x, ray.y, ray.z)) / disk_r2;
vec3 diskColor = vec3(1.0, radius, 0.2);
color = vec4(diskColor, radius);
}
else if (hitBlackHole)
color = vec4(0.0, 0.0, 0.0, 1.0);
else if (hitObject)
{
vec3 position = vec3(ray.x, ray.y, ray.z);
vec3 normal = normalize(position - hitCenter);
vec3 viewDirection = normalize(cam.camPos - position);
float ambient = 0.1;
float diffuse = max(dot(normal, viewDirection), 0.0);
float intensity = ambient + (1.0 - ambient) * diffuse;
vec3 shaded = objectColor.rgb * intensity;
color = vec4(shaded, objectColor.a);
}
else
color = vec4(0.0);
imageStore(outImage, pixel, color);
}
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