public override bool Intersect(Ray r, Intersection isect)
{
Transform w2p;
WorldToPrimitive.Interpolate(r.time, out w2p);
Ray ray = w2p.Apply(r);
if (!primitive.Intersect(ray, isect))
return false;
r.maxt = ray.maxt;
isect.primitiveId = primitiveId;
if (!w2p.IsIdentity())
{
// Compute world-to-object transformation for instance
isect.WorldToObject = isect.WorldToObject * w2p;
isect.ObjectToWorld = Transform.Inverse isect.WorldToObject.Inverse(
// Transform instance's differential geometry to world space
Transform PrimitiveToWorld = Inverse(w2p);
isect->dg.p = PrimitiveToWorld(isect->dg.p);
isect->dg.nn = Normalize(PrimitiveToWorld(isect->dg.nn));
isect->dg.dpdu = PrimitiveToWorld(isect->dg.dpdu);
isect->dg.dpdv = PrimitiveToWorld(isect->dg.dpdv);
isect->dg.dndu = PrimitiveToWorld(isect->dg.dndu);
isect->dg.dndv = PrimitiveToWorld(isect->dg.dndv);
}
return true;
}
public Ray(Point origin, Vector direction, Ray parent, double start, double end = double.PositiveInfinity)
{
this.o = origin;
this.d = direction;
this.mint = start;
this.maxt = end;
this.time = parent.time;
this.depth = parent.depth + 1;
}
public Ray Copy()
{
Ray _r = new Ray();
_r.o = this.o;
_r.d = this.d;
_r.mint = this.mint;
_r.maxt = this.maxt;
_r.time = this.time;
_r.depth = this.depth;
return _r;
}
public override bool Intersect(Ray r, out double tHit, out double rayEpsilon, out DifferentialGeometry dg)
{
tHit = Double.NaN;
rayEpsilon = Double.NaN;
dg = null;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute plane intersection for disk
if (Math.Abs(ray.d.z) < 1e-7) return false;
double thit = (height - ray.o.z) / ray.d.z;
if (thit < ray.mint || thit > ray.maxt)
return false;
// See if hit point is inside disk radii and $\phimax$
Point phit = ray.GetPointAt(thit);
double dist2 = phit.x * phit.x + phit.y * phit.y;
if (dist2 > radius * radius || dist2 < innerRadius * innerRadius)
return false;
// Test disk $\phi$ value against $\phimax$
double phi = Math.Atan2(phit.y, phit.x);
if (phi < 0) phi += 2.0d * Math.PI;
if (phi > phiMax)
return false;
// Find parametric representation of disk hit
double u = phi / phiMax;
double oneMinusV = ((Math.Sqrt(dist2) - innerRadius) / (radius - innerRadius));
double invOneMinusV = (oneMinusV > 0.0d) ? (1.0d / oneMinusV) : 0.0d;
double v = 1.0d - oneMinusV;
Vector dpdu = new Vector(-phiMax * phit.y, phiMax * phit.x, 0.0d);
Vector dpdv = new Vector(-phit.x * invOneMinusV, -phit.y * invOneMinusV, 0.0d);
dpdu *= phiMax * Constants.INV_TWOPI;
dpdv *= (radius - innerRadius) / radius;
Normal dndu = new Normal(0, 0, 0);
Normal dndv = new Normal(0, 0, 0);
// Initialize _DifferentialGeometry_ from parametric information
Transform o2w = ObjectToWorld;
dg = new DifferentialGeometry(o2w.Apply(phit), o2w.Apply(dpdu), o2w.Apply(dpdv), o2w.Apply(dndu), o2w.Apply(dndv), u, v, this);
// Update _tHit_ for quadric intersection
tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
rayEpsilon = 5e-4d * tHit;
return true;
}
public override bool Intersect(Ray r, Intersection isect)
{
double thit, rayEpsilon;
if (!shape.Intersect(r, out thit, out rayEpsilon, out isect.dg))
return false;
isect.primitive = this;
isect.WorldToObject = shape.WorldToObject;
isect.ObjectToWorld = shape.ObjectToWorld;
isect.shapeId = shape.shapeId;
isect.primitiveId = primitiveId;
isect.rayEpsilon = rayEpsilon;
r.maxt = thit;
return true;
}
public virtual double Pdf(Point p, Vector wi)
{
// Intersect sample ray with area light geometry
DifferentialGeometry dgLight;
Ray ray = new Ray(p, wi, 1e-3d);
ray.depth = -1; // temporary hack to ignore alpha mask
double thit, rayEpsilon;
if (!Intersect(ray, out thit, out rayEpsilon, out dgLight)) return 0.0d;
// Convert light sample weight to solid angle measure
double pdf = Geometry.DistanceSquared(p, ray.GetPointAt(thit)) / ( Geometry.AbsDot(dgLight.nn, -wi) * Area());
if (Double.IsInfinity(pdf)) pdf = 0.0d;
return pdf;
}
public override bool IntersectP(Ray r)
{
// Compute $\VEC{s}_1$
// Get triangle vertices in _p1_, _p2_, and _p3_
Point p1 = mesh.p[v[0]];
Point p2 = mesh.p[v[1]];
Point p3 = mesh.p[v[2]];
Vector e1 = p2 - p1;
Vector e2 = p3 - p1;
Vector s1 = Geometry.Cross(r.d, e2);
double divisor = Geometry.Dot(s1, e1);
if (divisor == 0.0d)
return false;
double invDivisor = 1.0d / divisor;
// Compute first barycentric coordinate
Vector d = r.o - p1;
double b1 = Geometry.Dot(d, s1) * invDivisor;
if (b1 < 0.0d || b1 > 1.0d)
return false;
// Compute second barycentric coordinate
Vector s2 = Geometry.Cross(d, e1);
double b2 = Geometry.Dot(r.d, s2) * invDivisor;
if (b2 < 0.0d || b1 + b2 > 1.0d)
return false;
// Compute _t_ to intersection point
double t = Geometry.Dot(e2, s2) * invDivisor;
if (t < r.mint || t > r.maxt)
return false;
// Test shadow r intersection against alpha texture, if present
if (r.depth != -1 && mesh.alphaTexture != null)
{
// Compute triangle partial derivatives
Vector dpdu, dpdv;
double[,] uvs = new double[3, 2];
GetUVs(uvs);
// Compute deltas for triangle partial derivatives
double du1 = uvs[0, 0] - uvs[2, 0];
double du2 = uvs[1, 0] - uvs[2, 0];
double dv1 = uvs[0, 1] - uvs[2, 1];
double dv2 = uvs[1, 1] - uvs[2, 1];
Vector dp1 = p1 - p3, dp2 = p2 - p3;
double determinant = du1 * dv2 - dv1 * du2;
if (determinant == 0.0d)
{
// Handle zero determinant for triangle partial derivative matrix
Geometry.CoordinateSystem(Geometry.Normalize(Geometry.Cross(e2, e1)), out dpdu, out dpdv);
}
else
{
double invdet = 1.0d / determinant;
dpdu = (dv2 * dp1 - dv1 * dp2) * invdet;
dpdv = (-du2 * dp1 + du1 * dp2) * invdet;
}
// Interpolate $(u,v)$ triangle parametric coordinates
double b0 = 1 - b1 - b2;
double tu = b0 * uvs[0, 0] + b1 * uvs[1, 0] + b2 * uvs[2, 0];
double tv = b0 * uvs[0, 1] + b1 * uvs[1, 1] + b2 * uvs[2, 1];
DifferentialGeometry dgLocal = new DifferentialGeometry(r.GetPointAt(t), dpdu, dpdv, new Normal(0, 0, 0), new Normal(0, 0, 0), tu, tv, this);
if (mesh.alphaTexture.Evaluate(dgLocal) == 0.0d)
return false;
}
return true;
}
public override bool IntersectP(Ray r)
{
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute plane intersection for disk
if (Math.Abs(ray.d.z) < 1e-7) return false;
double thit = (height - ray.o.z) / ray.d.z;
if (thit < ray.mint || thit > ray.maxt)
return false;
// See if hit point is inside disk radii and $\phimax$
Point phit = ray.GetPointAt(thit);
double dist2 = phit.x * phit.x + phit.y * phit.y;
if (dist2 > radius * radius || dist2 < innerRadius * innerRadius)
return false;
// Test disk $\phi$ value against $\phimax$
double phi = Math.Atan2(phit.y, phit.x);
if (phi < 0) phi += 2.0d * Math.PI;
if (phi > phiMax)
return false;
return true;
}
public bool IntersectP(Ray ray, out double hitt0, out double hitt1)
{
hitt0 = hitt1 = double.PositiveInfinity;
double t0 = ray.mint, t1 = ray.maxt;
for (int i = 0; i < 3; ++i)
{
// Update interval for _i_th bounding box slab
double invRayDir = 1.0d / ray.d[i];
double tNear = (pMin[i] - ray.o[i]) * invRayDir;
double tFar = (pMax[i] - ray.o[i]) * invRayDir;
// Update parametric interval from slab intersection $t$s
if (tNear > tFar) Utility.Swap<double>(ref tNear, ref tFar);
t0 = tNear > t0 ? tNear : t0;
t1 = tFar < t1 ? tFar : t1;
if (t0 > t1) return false;
}
hitt0 = t0;
hitt1 = t1;
return true;
}
public abstract bool IntersectP(Ray r);
public override bool Intersect(Ray r, out double tHit, out double rayEpsilon, out DifferentialGeometry dg)
{
double phi, v;
Point phit;
tHit = Double.NaN;
rayEpsilon = Double.NaN;
dg = null;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute quadratic hyperboloid coefficients
double A = a * ray.d.x * ray.d.x + a * ray.d.y * ray.d.y - c * ray.d.z * ray.d.z;
double B = 2.0d * (a * ray.d.x * ray.o.x + a * ray.d.y * ray.o.y - c * ray.d.z * ray.o.z);
double C = a * ray.o.x * ray.o.x +
a * ray.o.y * ray.o.y -
c * ray.o.z * ray.o.z - 1;
// Solve quadratic equation for _t_ values
double t0, t1;
if (!Utility.Quadratic(A, B, C, out t0, out t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
double thit = t0;
if (t0 < ray.mint)
{
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute hyperboloid inverse mapping
phit = ray.GetPointAt(thit);
v = (phit.z - p1.z) / (p2.z - p1.z);
Point pr = (1.0d - v) * p1 + v * p2;
phi = Math.Atan2(pr.x * phit.y - phit.x * pr.y,
phit.x * pr.x + phit.y * pr.y);
if (phi < 0)
phi += 2 * Math.PI;
// Test hyperboloid intersection against clipping parameters
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
{
if (thit == t1) return false;
thit = t1;
if (t1 > ray.maxt) return false;
// Compute hyperboloid inverse mapping
phit = ray.GetPointAt(thit);
v = (phit.z - p1.z) / (p2.z - p1.z);
pr = (1.0d - v) * p1 + v * p2;
phi = Math.Atan2(pr.x * phit.y - phit.x * pr.y,
phit.x * pr.x + phit.y * pr.y);
if (phi < 0)
phi += 2 * Math.PI;
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
return false;
}
// Compute parametric representation of hyperboloid hit
double u = phi / phiMax;
// Compute hyperboloid $\dpdu$ and $\dpdv$
double cosphi = Math.Cos(phi), sinphi = Math.Sin(phi);
Vector dpdu = new Vector(-phiMax * phit.y, phiMax * phit.x, 0.0d);
Vector dpdv = new Vector((p2.x - p1.x) * cosphi - (p2.y - p1.y) * sinphi, (p2.x - p1.x) * sinphi + (p2.y - p1.y) * cosphi, p2.z - p1.z);
// Compute hyperboloid $\dndu$ and $\dndv$
Vector d2Pduu = -phiMax * phiMax * new Vector(phit.x, phit.y, 0);
Vector d2Pduv = phiMax * new Vector(-dpdv.y, dpdv.x, 0.0d);
Vector d2Pdvv = new Vector(0, 0, 0);
// Compute coefficients for fundamental forms
double E = Geometry.Dot(dpdu, dpdu);
double F = Geometry.Dot(dpdu, dpdv);
double G = Geometry.Dot(dpdv, dpdv);
Vector N = Geometry.Normalize(Geometry.Cross(dpdu, dpdv));
double e = Geometry.Dot(N, d2Pduu);
double f = Geometry.Dot(N, d2Pduv);
double g = Geometry.Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
double invEGF2 = 1.0d / (E * G - F * F);
Normal dndu = new Normal((f * F - e * G) * invEGF2 * dpdu + (e * F - f * E) * invEGF2 * dpdv);
Normal dndv = new Normal((g * F - f * G) * invEGF2 * dpdu + (f * F - g * E) * invEGF2 * dpdv);
// Initialize _DifferentialGeometry_ from parametric information
Transform o2w = ObjectToWorld;
dg = new DifferentialGeometry(o2w.Apply(phit), o2w.Apply(dpdu), o2w.Apply(dpdv), o2w.Apply(dndu), o2w.Apply(dndv), u, v, this);
// Update _tHit_ for quadric intersection
tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
rayEpsilon = 5e-4d * tHit;
return true;
}
public override bool IntersectP(Ray r)
{
double phi;
Point phit;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute quadratic paraboloid coefficients
double k = zmax / (radius * radius);
double A = k * (ray.d.x * ray.d.x + ray.d.y * ray.d.y);
double B = 2 * k * (ray.d.x * ray.o.x + ray.d.y * ray.o.y) - ray.d.z;
double C = k * (ray.o.x * ray.o.x + ray.o.y * ray.o.y) - ray.o.z;
// Solve quadratic equation for _t_ values
double t0, t1;
if (!Utility.Quadratic(A, B, C, out t0, out t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
double thit = t0;
if (t0 < ray.mint)
{
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute paraboloid inverse mapping
phit = ray.GetPointAt(thit);
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
// Test paraboloid intersection against clipping parameters
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
{
if (thit == t1) return false;
thit = t1;
if (t1 > ray.maxt) return false;
// Compute paraboloid inverse mapping
phit = ray.GetPointAt(thit);
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
return false;
}
return true;
}
public RayDifferential(Point org, Vector dir, Ray parent, double start, double end = double.PositiveInfinity)
: base(org, dir, start, end, parent.time, parent.depth + 1)
{
this.hasDifferentials = false;
}
public Ray Apply(Ray r)
{
Ray ret = r.Copy();
ret.o = Apply(r.o);
ret.d = Apply(r.d);
return ret;
}
public abstract bool Intersect(Ray r, out double tHit, out double rayEpsilon, out DifferentialGeometry dg);
public override bool Intersect(Ray r, out double tHit, out double rayEpsilon, out DifferentialGeometry dg)
{
double phi;
Point phit;
tHit = Double.NaN;
rayEpsilon = Double.NaN;
dg = null;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute quadratic sphere coefficients
double A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z;
double B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z);
double C = ray.o.x * ray.o.x + ray.o.y * ray.o.y + ray.o.z * ray.o.z - radius * radius;
// Solve quadratic equation for _t_ values
double t0, t1;
if (!Utility.Quadratic(A, B, C, out t0, out t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
double thit = t0;
if (t0 < ray.mint)
{
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute sphere hit position and $\phi$
phit = ray.GetPointAt(thit);
if (phit.x == 0.0d && phit.y == 0.0d) phit.x = 1e-5d * radius;
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
// Test sphere intersection against clipping parameters
if ((zmin > -radius && phit.z < zmin) ||
(zmax < radius && phit.z > zmax) || phi > phiMax)
{
if (thit == t1) return false;
if (t1 > ray.maxt) return false;
thit = t1;
// Compute sphere hit position and $\phi$
phit = ray.GetPointAt(thit);
if (phit.x == 0.0d && phit.y == 0.0d) phit.x = 1e-5d * radius;
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
if ((zmin > -radius && phit.z < zmin) ||
(zmax < radius && phit.z > zmax) || phi > phiMax)
return false;
}
// Find parametric representation of sphere hit
double u = phi / phiMax;
double theta = Math.Acos(Utility.Clamp(phit.z / radius, -1.0d, 1.0d));
double v = (theta - thetaMin) / (thetaMax - thetaMin);
// Compute sphere $\dpdu$ and $\dpdv$
double zradius = Math.Sqrt(phit.x * phit.x + phit.y * phit.y);
double invzradius = 1.0d / zradius;
double cosphi = phit.x * invzradius;
double sinphi = phit.y * invzradius;
Vector dpdu = new Vector(-phiMax * phit.y, phiMax * phit.x, 0);
Vector dpdv = (thetaMax - thetaMin) * new Vector(phit.z * cosphi, phit.z * sinphi, -radius * Math.Sin(theta));
// Compute sphere $\dndu$ and $\dndv$
Vector d2Pduu = -phiMax * phiMax * new Vector(phit.x, phit.y, 0);
Vector d2Pduv = (thetaMax - thetaMin) * phit.z * phiMax * new Vector(-sinphi, cosphi, 0.0d);
Vector d2Pdvv = -(thetaMax - thetaMin) * (thetaMax - thetaMin) * new Vector(phit.x, phit.y, phit.z);
// Compute coefficients for fundamental forms
double E = Geometry.Dot(dpdu, dpdu);
double F = Geometry.Dot(dpdu, dpdv);
double G = Geometry.Dot(dpdv, dpdv);
Vector N = Geometry.Normalize(Geometry.Cross(dpdu, dpdv));
double e = Geometry.Dot(N, d2Pduu);
double f = Geometry.Dot(N, d2Pduv);
double g = Geometry.Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
double invEGF2 = 1.0d / (E * G - F * F);
Normal dndu = new Normal((f * F - e * G) * invEGF2 * dpdu + (e * F - f * E) * invEGF2 * dpdv);
Normal dndv = new Normal((g * F - f * G) * invEGF2 * dpdu + (f * F - g * E) * invEGF2 * dpdv);
// Initialize _DifferentialGeometry_ from parametric information
Transform o2w = ObjectToWorld;
dg = new DifferentialGeometry(o2w.Apply(phit), o2w.Apply(dpdu), o2w.Apply(dpdv),
o2w.Apply(dndu), o2w.Apply(dndv), u, v, this);
// Update _tHit_ for quadric intersection
tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
rayEpsilon = 5e-4d * tHit;
return true;
}
public override Point Sample(Point p, double u1, double u2, ref Normal ns)
{
// Compute coordinate system for sphere sampling
Point Pcenter = ObjectToWorld.Apply(new Point(0, 0, 0));
Vector wc = Geometry.Normalize(Pcenter - p);
Vector wcX, wcY;
Geometry.CoordinateSystem(wc, out wcX, out wcY);
// Sample uniformly on sphere if $\pt{}$ is inside it
if (Geometry.DistanceSquared(p, Pcenter) - radius * radius < 1e-4f)
return Sample(u1, u2, ref ns);
// Sample sphere uniformly inside subtended cone
double sinThetaMax2 = radius * radius / Geometry.DistanceSquared(p, Pcenter);
double cosThetaMax = Math.Sqrt(Math.Max(0.0d, 1.0d - sinThetaMax2));
DifferentialGeometry dgSphere;
double thit, rayEpsilon;
Point ps;
Ray r = new Ray(p, MonteCarlo.UniformSampleCone(u1, u2, cosThetaMax, wcX, wcY, wc), 1e-3d);
if (!Intersect(r, out thit, out rayEpsilon, out dgSphere))
thit = Geometry.Dot(Pcenter - p, Geometry.Normalize(r.d));
ps = r.GetPointAt(thit);
ns = new Normal(Geometry.Normalize(ps - Pcenter));
if (ReverseOrientation) ns *= -1.0d;
return ps;
}
public override bool IntersectP(Ray r)
{
double phi;
Point phit;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute quadratic sphere coefficients
double A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z;
double B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z);
double C = ray.o.x * ray.o.x + ray.o.y * ray.o.y + ray.o.z * ray.o.z - radius * radius;
// Solve quadratic equation for _t_ values
double t0, t1;
if (!Utility.Quadratic(A, B, C, out t0, out t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
double thit = t0;
if (t0 < ray.mint)
{
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute sphere hit position and $\phi$
phit = ray.GetPointAt(thit);
if (phit.x == 0.0d && phit.y == 0.0d) phit.x = 1e-5d * radius;
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
// Test sphere intersection against clipping parameters
if ((zmin > -radius && phit.z < zmin) ||
(zmax < radius && phit.z > zmax) || phi > phiMax)
{
if (thit == t1) return false;
if (t1 > ray.maxt) return false;
thit = t1;
// Compute sphere hit position and $\phi$
phit = ray.GetPointAt(thit);
if (phit.x == 0.0d && phit.y == 0.0d) phit.x = 1e-5d * radius;
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
if ((zmin > -radius && phit.z < zmin) ||
(zmax < radius && phit.z > zmax) || phi > phiMax)
return false;
}
return true;
}
public override bool IntersectP(Ray r)
{
return shape.IntersectP(r);
}
public override bool IntersectP(Ray r)
{
throw new NotImplementedException();
}
public abstract bool Intersect(Ray r, Intersection isect);
public override bool Intersect(Ray r, out double tHit, out double rayEpsilon, out DifferentialGeometry dg)
{
double phi;
Point phit;
tHit = Double.NaN;
rayEpsilon = Double.NaN;
dg = null;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute quadratic paraboloid coefficients
double k = zmax / (radius * radius);
double A = k * (ray.d.x * ray.d.x + ray.d.y * ray.d.y);
double B = 2 * k * (ray.d.x * ray.o.x + ray.d.y * ray.o.y) -
ray.d.z;
double C = k * (ray.o.x * ray.o.x + ray.o.y * ray.o.y) -
ray.o.z;
// Solve quadratic equation for _t_ values
double t0, t1;
if (!Utility.Quadratic(A, B, C, out t0, out t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
double thit = t0;
if (t0 < ray.mint)
{
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute paraboloid inverse mapping
phit = ray.GetPointAt(thit);
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
// Test paraboloid intersection against clipping parameters
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
{
if (thit == t1) return false;
thit = t1;
if (t1 > ray.maxt) return false;
// Compute paraboloid inverse mapping
phit = ray.GetPointAt(thit);
phi = Math.Atan2(phit.y, phit.x);
if (phi < 0.0d) phi += 2.0d * Math.PI;
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
return false;
}
// Find parametric representation of paraboloid hit
double u = phi / phiMax;
double v = (phit.z - zmin) / (zmax - zmin);
// Compute parabaloid $\dpdu$ and $\dpdv$
Vector dpdu = new Vector(-phiMax * phit.y, phiMax * phit.x, 0.0d);
Vector dpdv = (zmax - zmin) * new Vector(phit.x / (2.0d * phit.z), phit.y / (2.0d * phit.z), 1.0d);
// Compute parabaloid $\dndu$ and $\dndv$
Vector d2Pduu = -phiMax * phiMax * new Vector(phit.x, phit.y, 0);
Vector d2Pduv = (zmax - zmin) * phiMax * new Vector(-phit.y / (2.0d * phit.z), phit.x / (2.0d * phit.z), 0);
Vector d2Pdvv = -(zmax - zmin) * (zmax - zmin) * new Vector(phit.x / (4.0d * phit.z * phit.z), phit.y / (4.0d * phit.z * phit.z), 0.0d);
// Compute coefficients for fundamental forms
double E = Geometry.Dot(dpdu, dpdu);
double F = Geometry.Dot(dpdu, dpdv);
double G = Geometry.Dot(dpdv, dpdv);
Vector N = Geometry.Normalize(Geometry.Cross(dpdu, dpdv));
double e = Geometry.Dot(N, d2Pduu);
double f = Geometry.Dot(N, d2Pduv);
double g = Geometry.Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
double invEGF2 = 1.0d / (E * G - F * F);
Normal dndu = new Normal((f * F - e * G) * invEGF2 * dpdu + (e * F - f * E) * invEGF2 * dpdv);
Normal dndv = new Normal((g * F - f * G) * invEGF2 * dpdu + (f * F - g * E) * invEGF2 * dpdv);
// Initialize _DifferentialGeometry_ from parametric information
Transform o2w = ObjectToWorld;
dg = new DifferentialGeometry(o2w.Apply(phit), o2w.Apply(dpdu), o2w.Apply(dpdv), o2w.Apply(dndu), o2w.Apply(dndv), u, v, this);
// Update _tHit_ for quadric intersection
tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
rayEpsilon = 5e-4d * tHit;
return true;
}
public override bool IntersectP(Ray r)
{
double phi, v;
Point phit;
// Transform _Ray_ to object space
Ray ray = WorldToObject.Apply(r);
// Compute quadratic hyperboloid coefficients
double A = a * ray.d.x * ray.d.x + a * ray.d.y * ray.d.y - c * ray.d.z * ray.d.z;
double B = 2.0d * (a * ray.d.x * ray.o.x + a * ray.d.y * ray.o.y - c * ray.d.z * ray.o.z);
double C = a * ray.o.x * ray.o.x + a * ray.o.y * ray.o.y - c * ray.o.z * ray.o.z - 1;
// Solve quadratic equation for _t_ values
double t0, t1;
if (!Utility.Quadratic(A, B, C, out t0, out t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
double thit = t0;
if (t0 < ray.mint)
{
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute hyperboloid inverse mapping
phit = ray.GetPointAt(thit);
v = (phit.z - p1.z) / (p2.z - p1.z);
Point pr = (1.0d - v) * p1 + v * p2;
phi = Math.Atan2(pr.x * phit.y - phit.x * pr.y,
phit.x * pr.x + phit.y * pr.y);
if (phi < 0)
phi += 2 * Math.PI;
// Test hyperboloid intersection against clipping parameters
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
{
if (thit == t1) return false;
thit = t1;
if (t1 > ray.maxt) return false;
// Compute hyperboloid inverse mapping
phit = ray.GetPointAt(thit);
v = (phit.z - p1.z) / (p2.z - p1.z);
pr = (1.0d - v) * p1 + v * p2;
phi = Math.Atan2(pr.x * phit.y - phit.x * pr.y,
phit.x * pr.x + phit.y * pr.y);
if (phi < 0)
phi += 2 * Math.PI;
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
return false;
}
return true;
}
public RayDifferential(Ray ray)
: base(ray.o, ray.d, ray.mint, ray.maxt, ray.time, ray.depth)
{
this.hasDifferentials = false;
}
public override bool Intersect(Ray r, out double tHit, out double rayEpsilon, out DifferentialGeometry dg)
{
throw new NotImplementedException();
}