public bool HasScale()
{
float la2 = new Vector(1, 0, 0).SquaredMagnitude;
float lb2 = new Vector(0, 1, 0).SquaredMagnitude;
float lc2 = new Vector(0, 0, 1).SquaredMagnitude;
return ((la2 < 0.999f || la2 > 1.001f) || (lb2 < 0.999f || lb2 > 1.001f) || (lc2 < 0.999f || lc2 > 1.001f));
}
public static Vector UniformSampleCone(float u1, float u2, float costhetamax, Vector x, Vector y, Vector z)
{
float costheta = MathHelper.Lerp(u1, costhetamax, 1.0f);
float sintheta = MathHelper.Sqrt(1.0f - costheta * costheta);
float phi = u2 * 2.0f * MathHelper.PI;
return MathHelper.Cos(phi) * sintheta * x + MathHelper.Sin(phi) * sintheta * y + costheta * z;
}
public override bool Intersect(Ray r, Pointer<float> tHit, Pointer<float> rayEpsilon, Pointer<DifferentialGeometry> dg)
{
Ray ray = (WorldToObject)[r];
if (MathHelper.Abs(ray.Direction.Z) < 1e-7) return false;
float thit = (Height - ray.Origin.Z) / ray.Direction.Z;
if (thit < ray.MinT || thit > ray.MaxT)
return false;
Point phit = ray[thit];
float dist2 = phit.X * phit.X + phit.Y * phit.Y;
if (dist2 > Radius * Radius || dist2 < InnerRadius * InnerRadius)
return false;
float phi = MathHelper.Atan2(phit.Y, phit.X);
if (phi < 0) phi += 2.0f * MathHelper.PI;
if (phi > PhiMax)
return false;
float u = phi / PhiMax;
float oneMinusV = ((MathHelper.Sqrt(dist2) - InnerRadius) /
(Radius - InnerRadius));
float invOneMinusV = (oneMinusV > 0.0f) ? (1.0f / oneMinusV) : 0.0f;
float v = 1.0f - oneMinusV;
Vector dpdu = new Vector(-PhiMax * phit.Y, PhiMax * phit.X, 0);
Vector dpdv = new Vector(-phit.X * invOneMinusV, -phit.Y * invOneMinusV, 0);
dpdu *= PhiMax * MathHelper.InvTwoPI;
dpdv *= (Radius - InnerRadius) / Radius;
Normal dndu = new Normal(0, 0, 0), dndv = new Normal(0, 0, 0);
Transform o2w = ObjectToWorld;
dg[0] = new DifferentialGeometry(o2w[phit], o2w[dpdu], o2w[dpdv],
o2w[dndu], o2w[dndv], u, v, this);
tHit[0] = thit;
rayEpsilon[0] = 5e-4f * ~tHit;
return true;
}
public void ScaleDifferentials(float s)
{
RXOrigin = Origin + (RXOrigin - Origin) * s;
RYOrigin = Origin + (RYOrigin - Origin) * s;
RXDirection = Direction + (Vector)(RXDirection - Origin) * s;
RYDirection = Direction + (Vector)(RYDirection - Origin) * s;
}
public TriangleMesh(Transform o2w, Transform w2o, bool ro, int nt,
int nv, int[] vi, Point[] P, Normal[] N,
Vector[] S, float[] uv, Texture<float> atex)
: base(o2w, w2o, ro)
{
alphaTexture = atex;
ntris = nt;
nverts = nv;
MathHelper.Copy<int>(ref vertexIndex, ref vi);
if (uv != null)
{
MathHelper.Copy<float>(ref uvs, ref uv);
}
else
uvs = null;
if (N != null)
{
MathHelper.Copy<Normal>(ref n, ref N);
}
else n = null;
if (S != null)
{
MathHelper.Copy<Vector>(ref s, ref S);
}
else s = null;
for (int i = 0; i < nverts; ++i)
p[i] = (ObjectToWorld)[P[i]];
}
public Ray(Point orig, Vector dir, float start, float end = float.MaxValue, float t = 0, int d = 0)
{
Origin = orig;
Direction = dir;
MinT = start;
MaxT = end;
Time = t;
Depth = d;
}
public Ray(Point orig, Vector dir, Ray parent, float start, float end = float.MaxValue)
{
Origin = orig;
Direction = dir;
MinT = start;
MaxT = end;
Time = parent.Time;
Depth = parent.Depth + 1;
}
public override bool Intersect(Ray r, Pointer<float> tHit, Pointer<float> rayEpsilon, Pointer<DifferentialGeometry> dg)
{
float phi;
Point phit;
Ray ray = (WorldToObject)[r];
float A = ray.Direction.X * ray.Direction.X + ray.Direction.Y * ray.Direction.Y;
float B = 2 * (ray.Direction.X * ray.Origin.X + ray.Direction.Y * ray.Origin.Y);
float C = ray.Origin.X * ray.Origin.X + ray.Origin.Y * ray.Origin.Y - Radius * Radius;
float t0 = 0, t1 = 0;
if (!MathHelper.Quadratic(A, B, C, ref t0, ref t1))
return false;
if (t0 > ray.MaxT || t1 < ray.MinT)
return false;
float thit = t0;
if (t0 < ray.MinT)
{
thit = t1;
if (thit > ray.MaxT) return false;
}
phit = ray[thit];
phi = MathHelper.Atan2(phit.Y, phit.X);
if (phi < 0) phi += 2.0f * MathHelper.PI;
if (phit.Z < ZMin || phit.Z > ZMax || phi > PhiMax)
{
if (thit == t1) return false;
thit = t1;
if (t1 > ray.MaxT) return false;
phit = ray[thit];
phi = MathHelper.Atan2(phit.Y, phit.X);
if (phi < 0) phi += 2.0f * MathHelper.PI;
if (phit.Z < ZMin || phit.Z > ZMax || phi > PhiMax)
return false;
}
float u = phi / PhiMax;
float v = (phit.Z - ZMin) / (ZMax - ZMin);
Vector dpdu = new Vector(-PhiMax * phit.Y, PhiMax * phit.X, 0);
Vector dpdv = new Vector(0, 0, ZMax - ZMin);
Vector d2Pduu = -PhiMax * PhiMax * new Vector(phit.X, phit.Y, 0);
Vector d2Pduv = new Vector(0, 0, 0), d2Pdvv = new Vector(0, 0, 0);
float E = Vector.Dot(dpdu, dpdu);
float F = Vector.Dot(dpdu, dpdv);
float G = Vector.Dot(dpdv, dpdv);
Vector N = Vector.Normalize(Vector.Cross(dpdu, dpdv));
float e = Vector.Dot(N, d2Pduu);
float f = Vector.Dot(N, d2Pduv);
float g = Vector.Dot(N, d2Pdvv);
float invEGF2 = 1.0f / (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);
Transform o2w = ObjectToWorld;
dg[0] = new DifferentialGeometry(o2w[phit], o2w[dpdu], o2w[dpdv],
o2w[dndu], o2w[dndv], u, v, this);
tHit[0] = thit;
rayEpsilon[0] = 5e-4f * ~tHit;
return true;
}
public virtual float Pdf(Point p, Vector wi)
{
Pointer<DifferentialGeometry> dgLight = new Pointer<DifferentialGeometry>(new DifferentialGeometry());
Ray ray = new Ray(p, wi, 1e-3f);
ray.Depth = -1;
Pointer<float> thit = (Pointer<float>)0, rayEpsilon = (Pointer<float>)0;
if (!Intersect(ray, thit, rayEpsilon, dgLight)) return 0.0f;
float pdf = (Point.DistanceSquared(p, ray[thit])) / (Vector.AbsDot((Vector)(~dgLight).nn, -1.0f * wi) * Area);
if (float.IsInfinity(pdf)) pdf = 0.0f;
return pdf;
}
public static void CoordinateSystem(Vector v1, out Vector v2, out Vector v3)
{
if (MathHelper.Abs(v1.X) > MathHelper.Abs(v1.Y))
{
float invLen = 1.0f / MathHelper.Sqrt(v1.X * v1.X + v1.Z * v1.Z);
v2 = new Vector(-v1.Z * invLen, 0.0f, v1.X * invLen);
}
else
{
float invLen = 1.0f / MathHelper.Sqrt(v1.Y * v1.Y + v1.Z * v1.Z);
v2 = new Vector(0.0f, v1.Z * invLen, -v1.Y * invLen);
}
v3 = Vector.Cross(v1, v2);
}
public static Transform Translate(Vector delta)
{
Matrix4x4 m = new Matrix4x4(new float[4, 4]{
{1,0,0,delta.X},
{0,1,0,delta.Y},
{0,0,1,delta.Z},
{0,0,0,1}});
Matrix4x4 minv = new Matrix4x4(new float[4, 4]{
{1,0,0,-delta.X},
{0,1,0,-delta.Y},
{0,0,1,-delta.Z},
{0,0,0,1}});
return new Transform(m, minv);
}
public static float Dot(Vector vector1, Vector vector2)
{
return vector1.Dot(vector2);
}
public override bool Intersect(Ray r, Pointer<float> tHit, Pointer<float> rayEpsilon, Pointer<DifferentialGeometry> dg)
{
float phi, v;
Point phit;
Ray ray = (WorldToObject)[r];
float A = a * ray.Direction.X * ray.Direction.X +
a * ray.Direction.Y * ray.Direction.Y -
c * ray.Direction.Z * ray.Direction.Z;
float B = 2.0f * (a * ray.Direction.X * ray.Origin.X +
a * ray.Direction.Y * ray.Origin.Y -
c * ray.Direction.Z * ray.Origin.Z);
float C = a * ray.Origin.X * ray.Origin.X +
a * ray.Origin.Y * ray.Origin.Y -
c * ray.Origin.Z * ray.Origin.Z - 1;
float t0 = 0, t1 = 0;
if (!MathHelper.Quadratic(A, B, C, ref t0, ref t1))
return false;
if (t0 > ray.MaxT || t1 < ray.MinT)
return false;
float thit = t0;
if (t0 < ray.MinT)
{
thit = t1;
if (thit > ray.MaxT) return false;
}
phit = ray[thit];
v = (phit.Z - p1.Z) / (p2.Z - p1.Z);
Point pr = (1.0f - v) * p1 + v * p2;
phi = MathHelper.Atan2(pr.X * phit.Y - phit.X * pr.Y,
phit.X * pr.X + phit.Y * pr.Y);
if (phi < 0)
phi += 2 * MathHelper.PI;
if (phit.Z < zmin || phit.Z > zmax || phi > phiMax)
{
if (thit == t1) return false;
thit = t1;
if (t1 > ray.MaxT) return false;
phit = ray[thit];
v = (phit.Z - p1.Z) / (p2.Z - p1.Z);
Point pr2 = (1.0f - v) * p1 + v * p2;
phi = MathHelper.Atan2(pr2.X * phit.Y - phit.X * pr2.Y,
phit.X * pr2.X + phit.Y * pr2.Y);
if (phi < 0)
phi += 2 * MathHelper.PI;
if (phit.Z < zmin || phit.Z > zmax || phi > phiMax)
return false;
}
float u = phi / phiMax;
float cosphi = MathHelper.Cos(phi), sinphi = MathHelper.Sin(phi);
Vector dpdu = new Vector(-phiMax * phit.Y, phiMax * phit.X, 0);
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);
Vector d2Pduu = -phiMax * phiMax *
new Vector(phit.X, phit.Y, 0);
Vector d2Pduv = phiMax *
new Vector(-dpdv.Y, dpdv.X, 0);
Vector d2Pdvv = new Vector(0, 0, 0);
float E = Vector.Dot(dpdu, dpdu);
float F = Vector.Dot(dpdu, dpdv);
float G = Vector.Dot(dpdv, dpdv);
Vector N = Vector.Normalize(Vector.Cross(dpdu, dpdv));
float e = Vector.Dot(N, d2Pduu);
float f = Vector.Dot(N, d2Pduv);
float g = Vector.Dot(N, d2Pdvv);
float invEGF2 = 1.0f / (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);
Transform o2w = ObjectToWorld;
dg[0] = new DifferentialGeometry(o2w[phit], o2w[dpdu], o2w[dpdv],
o2w[dndu], o2w[dndv], u, v, this);
tHit[0] = thit;
rayEpsilon[0] = 5e-4f * tHit;
return true;
}
public static float Distance(Vector v1, Vector v2)
{
return (v2 - v1).Magnitude;
}
public RayDifferential(Point orig, Vector dir, Ray parent, float start, float end = float.MaxValue)
: base(orig, dir, start, end, parent.Time, parent.Depth + 1)
{
HasDifferentials = false;
}
public RayDifferential(Point orig, Vector dir, float start, float end = float.MaxValue, float t = 0.0f, int d = 0)
: base(orig, dir, start, end, t, d)
{
HasDifferentials = false;
}
public static float DistanceSquared(Vector v1, Vector v2)
{
return (v2 - v1).SquaredMagnitude;
}
public void Setdpdv(Vector dpdv)
{
this.dpdv = dpdv;
}
public void Setdpdy(Vector dpdv)
{
this.dpdy = dpdv;
}
public void ComputeDifferentials(RayDifferential ray)
{
if (ray.HasDifferentials)
{
float d = -Vector.Dot((Vector)nn, new Vector(p.X, p.Y, p.Z));
Vector rxv = new Vector(ray.RXOrigin.X, ray.RXOrigin.Y, ray.RXOrigin.Z);
float tx = -(Vector.Dot((Vector)nn, rxv) + d) / Vector.Dot((Vector)nn, ray.RXDirection);
if (float.IsNaN(tx))
{
dudx = dvdx = 0.0f;
dudy = dvdy = 0.0f;
dpdx = dpdy = new Vector(0, 0, 0);
goto end;
}
Point px = ray.RXOrigin + tx * ray.RXDirection;
Vector ryv = new Vector(ray.RYOrigin.X, ray.RYOrigin.Y, ray.RYOrigin.Z);
float ty = -(Vector.Dot((Vector)nn, ryv) + d) / Vector.Dot((Vector)nn, ray.RYDirection);
if (float.IsNaN(ty))
{
dudx = dvdx = 0.0f;
dudy = dvdy = 0.0f;
dpdx = dpdy = new Vector(0, 0, 0);
goto end;
}
Point py = ray.RYOrigin + ty * ray.RYDirection;
dpdx = px - p;
dpdy = py - p;
float[][] A = new float[2][];
float[] Bx = new float[2];
float[] By = new float[2];
int[] axes = new int[2];
if (MathHelper.Abs(nn.X) > MathHelper.Abs(nn.Y) && MathHelper.Abs(nn.X) > MathHelper.Abs(nn.Z))
{
axes[0] = 1; axes[1] = 2;
}
else if (MathHelper.Abs(nn.Y) > MathHelper.Abs(nn.Z))
{
axes[0] = 0; axes[1] = 2;
}
else
{
axes[0] = 0; axes[1] = 1;
}
A[0][0] = dpdu[axes[0]];
A[0][1] = dpdv[axes[0]];
A[1][0] = dpdu[axes[1]];
A[1][1] = dpdv[axes[1]];
Bx[0] = px[axes[0]] - p[axes[0]];
Bx[1] = px[axes[1]] - p[axes[1]];
By[0] = py[axes[0]] - p[axes[0]];
By[1] = py[axes[1]] - p[axes[1]];
float a = 0, b = 0, c = 0, f = 0;
if (!Transform.SolveLinearSystem2x2(A, Bx, ref a, ref b))
{
dudx = 0.0f;
dvdx = 0.0f;
}
else
{
dudx = a;
dvdx = b;
}
if (!Transform.SolveLinearSystem2x2(A, By, ref c, ref f))
{
dudy = 0.0f; dvdy = 0.0f;
}
else
{
dudy = c;
dvdy = f;
}
end:
float j = 0;
}
else
{
dudx = dvdx = 0.0f;
dudy = dvdy = 0.0f;
dpdx = dpdy = new Vector(0, 0, 0);
}
}
public Vector Cross(Vector vector)
{
return new Vector(Y * vector.Z - Z * vector.Y, Z * vector.X - X * vector.Z, X * vector.Y - Y * vector.X);
}
public static float AbsDot(Vector v1, Vector v2)
{
return MathHelper.Abs(Dot(v1, v2));
}
public float AbsDot(Vector v)
{
return MathHelper.Abs(Dot(v));
}
public float Dot(Vector v)
{
return X * v.X + Y * v.Y + Z * v.Z;
}
public void Setdpdu(Vector dpdu)
{
this.dpdu = dpdu;
}
public static Vector Cross(Vector v1, Normal v2)
{
return v2.Cross(v1);
}
public void Setdpdx(Vector dpdu)
{
this.dpdx = dpdu;
}
public static Vector Cross(Normal v1, Vector v2)
{
return v1.Cross(v2);
}
public DifferentialGeometry(Point P, Vector DPDU, Vector DPDV, Normal DNDU, Normal DNDV, float uu, float vv, Shape sh)
{
p = (P);
dpdu = (DPDU);
dpdv = (DPDV);
dndu = (DNDU);
dndv = (DNDV);
nn = new Normal(Vector.Normalize(Vector.Cross(dpdu, dpdv)));
u = uu;
v = vv;
shape = sh;
dudx = dvdx = dudy = dvdy = 0;
dpdx = dpdy = new Vector();
if (shape != null && (shape.ReverseOrientation ^ shape.TransformSwapsHandedness))
nn *= -1.0f;
}
public static Vector Invert(Vector vector)
{
vector.Invert();
return vector;
}