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-rw-r--r--assets/shaders/geodesic.slang438
1 files changed, 438 insertions, 0 deletions
diff --git a/assets/shaders/geodesic.slang b/assets/shaders/geodesic.slang
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+struct VSInput { float2 position : POSITION; float2 texCoord : TEXCOORD0; };
+struct VSOutput { float4 position : SV_Position; float2 texCoord : TEXCOORD0; };
+
+[shader("vertex")]
+VSOutput vertexMain(VSInput input)
+{
+ VSOutput output;
+ output.position = float4(input.position, 0.0, 1.0);
+ output.texCoord = input.texCoord;
+ return output;
+}
+
+struct Camera
+{
+ float3 camPos; float _pad0;
+ float3 camRight; float _pad1;
+ float3 camUp; float _pad2;
+ float3 camForward; float _pad3;
+ float tanHalfFov;
+ float aspect;
+ bool moving;
+ int _pad4;
+};
+ConstantBuffer<Camera> cam;
+
+struct Disk
+{
+ float disk_r1; // inner edge (clamped to the ISCO, 3 r_s, below)
+ float disk_r2; // outer edge
+ float disk_num; // turbulence strength (0 = smooth physical disk)
+ float thickness; // slab half-height (anti-aliases the edge-on disk)
+ float disk_density; // disk brightness / exposure
+ float temperature; // Kelvin at the flux peak (disk colour)
+};
+ConstantBuffer<Disk> disk;
+
+struct Objects
+{
+ int numObjects;
+ float4 objPosRadius[16];
+ float4 objColor[16];
+ float mass[16];
+};
+ConstantBuffer<Objects> obj;
+
+struct Simulation
+{
+ int maxStepsMoving;
+ int maxStepsStatic;
+ float earlyExitDistance;
+ float time;
+};
+ConstantBuffer<Simulation> sim;
+
+SamplerCube u_HDRIEnvironment;
+
+// Schwarzschild radius of Sgr A* (metres). Geometric units with c = G = 1 are
+// used throughout the geodesic integration; the black-hole mass is M = r_s / 2.
+static const float SagA_rs = 1.269e10;
+static const float D_LAMBDA = 1e7;
+static const float ESCAPE_R = 1e30;
+
+static const float R_ISCO = 3.0 * SagA_rs; // innermost stable circular orbit (6M)
+static const float R_PHOTON = 1.5 * SagA_rs; // photon sphere (3M)
+static const float FLUX_PEAK = 0.0569; // peak of the r^-3(1-sqrt(r_in/r)) profile (at r/r_in ~ 1.36)
+
+static const int DEFAULT_MAX_STEPS_MOVING = 12000;
+static const int DEFAULT_MAX_STEPS_STATIC = 8000;
+static const float DEFAULT_EARLY_EXIT_DISTANCE = 2e12;
+
+static const float MIN_STEP_SIZE = 1e6;
+static const float MAX_STEP_SIZE = 2e10;
+
+// Display mapping for the (relative) Novikov-Thorne flux -> visible colour.
+// The RADIAL PROFILE is physical; the absolute temperature scale is a display
+// choice (a real Sgr A* disk is far cooler / redder than this).
+
+struct Hit
+{
+ float4 objectColor;
+ float3 hitCenter;
+ float hitRadius;
+};
+
+float hash(float3 p)
+{
+ p = frac(p * float3(0.1031, 0.1030, 0.0973));
+ p += dot(p, p.yxz + 33.33);
+ return frac((p.x + p.y) * p.z);
+}
+
+float noise(float3 x)
+{
+ float3 i = floor(x);
+ float3 fr = frac(x);
+ float3 u = fr * fr * (3.0 - 2.0 * fr);
+
+ float a = hash(i);
+ float b = hash(i + float3(1.0, 0.0, 0.0));
+ float c = hash(i + float3(0.0, 1.0, 0.0));
+ float d = hash(i + float3(1.0, 1.0, 0.0));
+ float e = hash(i + float3(0.0, 0.0, 1.0));
+ float f = hash(i + float3(1.0, 0.0, 1.0));
+ float g = hash(i + float3(0.0, 1.0, 1.0));
+ float h = hash(i + float3(1.0, 1.0, 1.0));
+
+ return lerp(lerp(lerp(a, b, u.x), lerp(c, d, u.x), u.y),
+ lerp(lerp(e, f, u.x), lerp(g, h, u.x), u.y), u.z);
+}
+
+float fbm(float3 x, int octaves)
+{
+ float v = 0.0;
+ float a = 0.5;
+ float3 shift = float3(100, 200, 300);
+ for (int i = 0; i < octaves; ++i)
+ {
+ v += a * noise(x);
+ x = x * 2.0 + shift;
+ a *= 0.5;
+ }
+ return v;
+}
+
+// Planckian-locus blackbody colour (Tanner Helland approximation), T in Kelvin.
+// Returns an sRGB-ish chromaticity normalised so the brightest channel ~ 1.
+float3 Blackbody(float T)
+{
+ T = clamp(T, 1000.0, 40000.0);
+ float t = T / 100.0;
+ float3 c;
+
+ c.r = (t <= 66.0) ? 1.0
+ : clamp(1.292936186 * pow(t - 60.0, -0.1332047592), 0.0, 1.0);
+
+ c.g = (t <= 66.0) ? clamp(0.3900815788 * log(t) - 0.6318414438, 0.0, 1.0)
+ : clamp(1.1298908609 * pow(t - 60.0, -0.0755148492), 0.0, 1.0);
+
+ c.b = (t >= 66.0) ? 1.0
+ : (t <= 19.0) ? 0.0
+ : clamp(0.5432067891 * log(t - 10.0) - 1.1962540891, 0.0, 1.0);
+ return c;
+}
+
+// Emission from the thin accretion disk at an equatorial crossing point P, seen
+// along the (backward-traced) ray direction rayDir. Combines a Novikov-Thorne
+// temperature profile with the full gravitational + Doppler redshift.
+// g = sqrt(1 - 3M/r) / (1 - beta . nhat) (verified: g -> sqrt(1/2) at ISCO)
+// Brightness follows relativistic beaming (I_obs = g^4 I_emit); colour follows
+// the redshifted blackbody at T_obs = g * T_emit.
+float3 DiskEmission(float3 P, float3 rayDir)
+{
+ float rc = length(float2(P.x, P.z)); // cylindrical radius (disk axis = +Y)
+ float rin = max(disk.disk_r1, R_ISCO);
+ float rout = disk.disk_r2;
+ if (rc < rin || rc > rout)
+ return float3(0.0);
+
+ // Novikov-Thorne-style radial flux: F(r) ~ r^-3 (1 - sqrt(r_in/r)), zero at
+ // the inner edge, peaking just outside it, then declining. T ~ F^(1/4).
+ float xr = rc / rin;
+ float flux = max((1.0 - sqrt(1.0 / xr)) / (xr * xr * xr), 0.0);
+ float Tn = pow(flux / FLUX_PEAK, 0.25); // normalised temperature, peak ~ 1
+ float Temit = disk.temperature * Tn;
+
+ // Keplerian orbit (prograde about +Y). Locally-measured orbital speed for a
+ // Schwarzschild circular geodesic: v = sqrt( M / (r - 2M) ) = 0.5 c at ISCO.
+ float3 rhat = normalize(float3(P.x, 0.0, P.z));
+ float3 phiHat = normalize(cross(float3(0.0, 1.0, 0.0), rhat));
+ float v = sqrt((SagA_rs * 0.5) / max(rc - SagA_rs, 1.0));
+ float3 beta = v * phiHat;
+ float3 nhat = -normalize(rayDir); // photon direction toward the observer
+
+ float g = sqrt(max(1.0 - 1.5 * SagA_rs / rc, 0.0)) / max(1.0 - dot(beta, nhat), 1e-3);
+
+ float Tobs = g * Temit;
+ float3 colour = Blackbody(Tobs);
+ // Physical bolometric intensity is ~ T_emit^4 * g^4, an enormous dynamic
+ // range. The g^4 relativistic beaming (the physical asymmetry) is kept; the
+ // radial falloff is display-compressed (Tn^2) so the colour gradient across
+ // the disk stays visible instead of collapsing to a thin saturated ring.
+ float bright = pow(Tn, 2.0) * pow(g, 4.0);
+
+ // Soft inner/outer edges (disks have no hard rim); also tames rim aliasing.
+ float edge = smoothstep(rin, rin * 1.12, rc) * (1.0 - smoothstep(rout * 0.88, rout, rc));
+ bright *= edge;
+
+ // Optional turbulence overlay (disk.disk_num = strength; 0 = smooth).
+ if (disk.disk_num > 0.0)
+ {
+ float ang = sim.time * 0.3 / sqrt(xr);
+ float3 rp = float3(P.x * cos(ang) - P.z * sin(ang),
+ 0.0,
+ P.x * sin(ang) + P.z * cos(ang)) * 1e-10;
+ float turb = 1.0 + disk.disk_num * (fbm(rp * 3.0, 3) - 0.5);
+ bright *= max(turb, 0.0);
+ }
+
+ return colour * bright * max(disk.disk_density, 0.0);
+}
+
+struct Ray
+{
+ float x, y, z;
+ float r, theta, phi;
+ float dr, dtheta, dphi;
+ float E, L;
+};
+
+Ray InitRay(float3 pos, float3 dir)
+{
+ Ray ray;
+ ray.x = pos.x;
+ ray.y = pos.y;
+ ray.z = pos.z;
+ ray.r = length(pos);
+ ray.theta = acos(pos.z / ray.r);
+ ray.phi = atan2(pos.y, pos.x);
+
+ float dx = dir.x, dy = dir.y, dz = dir.z;
+
+ ray.dr = 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.r;
+ ray.dphi = (-sin(ray.phi)*dx + cos(ray.phi)*dy) /
+ (ray.r * sin(ray.theta));
+
+ ray.L = ray.r * ray.r * sin(ray.theta) * ray.dphi;
+ float f = 1.0 - SagA_rs / ray.r;
+ float dt_dL = sqrt((ray.dr*ray.dr)/f +
+ ray.r*ray.r*(ray.dtheta*ray.dtheta +
+ sin(ray.theta)*sin(ray.theta)*ray.dphi*ray.dphi));
+ ray.E = f * dt_dL;
+ return ray;
+}
+
+bool Intercept(Ray ray, float rs) { return ray.r <= rs; }
+
+bool InterceptObject(Ray ray, inout Hit hit)
+{
+ float3 P = float3(ray.x, ray.y, ray.z);
+ for (int i = 0; i < obj.numObjects; ++i)
+ {
+ float3 center = obj.objPosRadius[i].xyz;
+ float radius = obj.objPosRadius[i].w;
+ float distSq = dot(P - center, P - center);
+ if (distSq > radius * radius * 4.0) continue;
+ if (distSq <= radius * radius)
+ {
+ hit.objectColor = obj.objColor[i];
+ hit.hitCenter = center;
+ hit.hitRadius = radius;
+ return true;
+ }
+ }
+ return false;
+}
+
+void GeodesicRHS(Ray ray, out float3 d1, out float3 d2)
+{
+ float r = ray.r;
+ float theta = ray.theta;
+ float dr = ray.dr;
+ float dtheta = ray.dtheta;
+ float dphi = ray.dphi;
+ float f = 1.0 - SagA_rs / r;
+ float dt_dL = ray.E / f;
+
+ d1 = float3(dr, dtheta, dphi);
+ d2.x = - (SagA_rs / (2.0 * r*r)) * f * dt_dL * dt_dL
+ + (SagA_rs / (2.0 * r*r * f)) * dr * dr
+ + r * (dtheta*dtheta + sin(theta)*sin(theta)*dphi*dphi);
+ d2.y = -2.0*dr*dtheta/r + sin(theta)*cos(theta)*dphi*dphi;
+ d2.z = -2.0*dr*dphi/r - 2.0*cos(theta)/(sin(theta)) * dtheta * dphi;
+}
+
+void RK4Step(inout Ray ray, float dL)
+{
+ float3 k1a, k1b;
+ GeodesicRHS(ray, k1a, k1b);
+ ray.r += dL * k1a.x;
+ ray.theta += dL * k1a.y;
+ ray.phi += dL * k1a.z;
+ ray.dr += dL * k1b.x;
+ ray.dtheta += dL * k1b.y;
+ ray.dphi += dL * k1b.z;
+
+ ray.x = ray.r * sin(ray.theta) * cos(ray.phi);
+ ray.y = ray.r * sin(ray.theta) * sin(ray.phi);
+ ray.z = ray.r * cos(ray.theta);
+}
+
+float CalculateAdaptiveStepSize(Ray ray, float baseStepSize)
+{
+ // Step proportional to the distance from the photon sphere: near-flat space
+ // far from the hole is crossed in a few huge steps, while the sharply curved
+ // region near the photon sphere is resolved with tiny ones. This keeps the
+ // integration accurate near the hole regardless of how far the camera is.
+ float step = 0.02 * max(ray.r - R_PHOTON, 0.0);
+
+ // Slow down when near the disk plane (within its radial extent) so the thin
+ // slab is never stepped over -- otherwise grazing rays leak through it.
+ float rc = length(float2(ray.x, ray.z));
+ if (rc < disk.disk_r2 * 3.0 && abs(ray.y) < disk.thickness * 8.0)
+ step = min(step, disk.thickness);
+
+ return clamp(step, MIN_STEP_SIZE, MAX_STEP_SIZE);
+}
+
+float3 ACESFilm(float3 x)
+{
+ return clamp((x * (2.51 * x + 0.03)) / (x * (2.43 * x + 0.59) + 0.14), 0.0, 1.0);
+}
+
+// Trace one primary ray for the given image UV and return its linear,
+// pre-tone-map radiance. Called once per sub-sample by fragmentMain.
+float3 TracePixel(float2 texCoord)
+{
+ float u = (2.0 * texCoord.x - 1.0) * cam.aspect * cam.tanHalfFov;
+ float v = (1.0 - 2.0 * texCoord.y) * cam.tanHalfFov;
+ float3 dir = normalize(u * cam.camRight - v * cam.camUp + cam.camForward);
+ Ray ray = InitRay(cam.camPos, dir);
+
+ bool hitBlackHole = false;
+ bool hitObject = false;
+ Hit hit;
+ hit.objectColor = float4(0.0);
+ hit.hitCenter = float3(0.0);
+ hit.hitRadius = 0.0;
+
+ bool hitDisk = false;
+ float3 diskColor = float3(0.0); // emission of the first (opaque) disk surface hit
+
+ int maxSteps = cam.moving ? sim.maxStepsMoving : sim.maxStepsStatic;
+ if (maxSteps <= 0)
+ maxSteps = cam.moving ? DEFAULT_MAX_STEPS_MOVING : DEFAULT_MAX_STEPS_STATIC;
+
+ float exitDistance = sim.earlyExitDistance > 0.0 ? sim.earlyExitDistance : DEFAULT_EARLY_EXIT_DISTANCE;
+ int objectCheckInterval = 5;
+
+ for (int i = 0; i < maxSteps; ++i)
+ {
+ if (Intercept(ray, SagA_rs)) { hitBlackHole = true; break; }
+ if (ray.r > exitDistance || ray.r > ESCAPE_R) break;
+
+ float3 prevPos = float3(ray.x, ray.y, ray.z);
+ float stepSize = CalculateAdaptiveStepSize(ray, D_LAMBDA);
+ RK4Step(ray, stepSize);
+ float3 newPos = float3(ray.x, ray.y, ray.z);
+
+ // Opaque disk of small half-thickness H (a slab about the midplane y=0).
+ // The ray hits when it first crosses the midplane OR enters the slab
+ // while grazing along it. Real (nonzero) thickness stops the zero-height
+ // edge-on "razor" from aliasing into a beam streaking across the frame.
+ {
+ float H = disk.thickness;
+ bool crossed = prevPos.y * newPos.y < 0.0;
+ bool inSlab = abs(newPos.y) <= H;
+ if (crossed || inSlab)
+ {
+ float3 hitP = crossed
+ ? lerp(prevPos, newPos, prevPos.y / (prevPos.y - newPos.y))
+ : newPos;
+ float rc = length(float2(hitP.x, hitP.z));
+ if (rc >= max(disk.disk_r1, R_ISCO) && rc <= disk.disk_r2)
+ {
+ diskColor = DiskEmission(hitP, newPos - prevPos);
+ hitDisk = true;
+ break;
+ }
+ }
+ }
+
+ if (i % objectCheckInterval == 0 && InterceptObject(ray, hit)) { hitObject = true; break; }
+
+ // Principled escape: once outbound in near-flat spacetime (r >> r_s) the
+ // ray direction no longer changes, so stop and read the background.
+ if (ray.dr > 0.0 && ray.r > 50.0 * SagA_rs) break;
+ }
+
+ // Escape direction + environment mip LOD from the ray's angular divergence.
+ // Computed UNCONDITIONALLY (before the branch) so ddx/ddy are valid; strongly
+ // lensed background rays diverge fast, so they read a blurred cubemap mip and
+ // the starfield stops aliasing into a fan along the equatorial plane.
+ float3 rayDir = normalize(float3(ray.x, ray.y, ray.z) - cam.camPos);
+ float footprint = max(length(ddx(rayDir)), length(ddy(rayDir)));
+ float envLod = clamp(log2(max(footprint / 0.0015, 1.0)), 0.0, 10.0);
+
+ float3 shade;
+ if (hitDisk)
+ {
+ shade = diskColor; // opaque, self-luminous disk surface
+ }
+ else if (hitBlackHole)
+ {
+ shade = float3(0.0); // event-horizon shadow
+ }
+ else if (hitObject)
+ {
+ float3 P = float3(ray.x, ray.y, ray.z);
+ float3 N = normalize(P - hit.hitCenter);
+ float3 V = normalize(cam.camPos - P);
+ float intensity = 0.1 + 0.9 * max(dot(N, V), 0.0);
+ shade = hit.objectColor.rgb * intensity;
+ }
+ else
+ {
+ shade = u_HDRIEnvironment.SampleLevel(rayDir, envLod).rgb;
+ }
+
+ return shade;
+}
+
+[shader("fragment")]
+float4 fragmentMain(VSOutput input) : SV_Target
+{
+ // Moving frame: one sample for responsiveness. Settled frame: rotated-grid
+ // 4x supersampling (the 4-rook pattern gives 4 distinct sub-pixel positions
+ // on BOTH axes, far better on the near-horizontal lensed edges than an
+ // ordered grid). Radiance is averaged before tone-mapping; ddx/ddy give the
+ // resolution-correct per-pixel UV footprint.
+ if (cam.moving)
+ return float4(ACESFilm(TracePixel(input.texCoord)), 1.0);
+
+ float2 dUV = float2(ddx(input.texCoord.x), ddy(input.texCoord.y));
+ float2 offs[4] = {
+ float2( 0.125, 0.375), float2( 0.375, -0.125),
+ float2(-0.125, -0.375), float2(-0.375, 0.125),
+ };
+ float3 sum = float3(0.0);
+ for (int i = 0; i < 4; ++i)
+ sum += TracePixel(input.texCoord + offs[i] * dUV);
+
+ return float4(ACESFilm(sum * 0.25), 1.0);
+}