bool Triangle::IntersectP(const Ray &ray, bool testAlphaTexture) const {
ProfilePhase p(Prof::TriIntersectP);
++nTests;
// Get triangle vertices in _p0_, _p1_, and _p2_
const Point3f &p0 = mesh->p[v[0]];
const Point3f &p1 = mesh->p[v[1]];
const Point3f &p2 = mesh->p[v[2]];
// Perform ray--triangle intersection test
// Transform triangle vertices to ray coordinate space
// Translate vertices based on ray origin
Point3f p0t = p0 - Vector3f(ray.o);
Point3f p1t = p1 - Vector3f(ray.o);
Point3f p2t = p2 - Vector3f(ray.o);
// Permute components of triangle vertices and ray direction
int kz = MaxDimension(Abs(ray.d));
int kx = kz + 1;
if (kx == 3) kx = 0;
int ky = kx + 1;
if (ky == 3) ky = 0;
Vector3f d = Permute(ray.d, kx, ky, kz);
p0t = Permute(p0t, kx, ky, kz);
p1t = Permute(p1t, kx, ky, kz);
p2t = Permute(p2t, kx, ky, kz);
// Apply shear transformation to translated vertex positions
Float Sx = -d.x / d.z;
Float Sy = -d.y / d.z;
Float Sz = 1.f / d.z;
p0t.x += Sx * p0t.z;
p0t.y += Sy * p0t.z;
p1t.x += Sx * p1t.z;
p1t.y += Sy * p1t.z;
p2t.x += Sx * p2t.z;
p2t.y += Sy * p2t.z;
// Compute edge function coefficients _e0_, _e1_, and _e2_
Float e0 = p1t.x * p2t.y - p1t.y * p2t.x;
Float e1 = p2t.x * p0t.y - p2t.y * p0t.x;
Float e2 = p0t.x * p1t.y - p0t.y * p1t.x;
// Fall back to double precision test at triangle edges
if (sizeof(Float) == sizeof(float) &&
(e0 == 0.0f || e1 == 0.0f || e2 == 0.0f)) {
double p2txp1ty = (double)p2t.x * (double)p1t.y;
double p2typ1tx = (double)p2t.y * (double)p1t.x;
e0 = (float)(p2typ1tx - p2txp1ty);
double p0txp2ty = (double)p0t.x * (double)p2t.y;
double p0typ2tx = (double)p0t.y * (double)p2t.x;
e1 = (float)(p0typ2tx - p0txp2ty);
double p1txp0ty = (double)p1t.x * (double)p0t.y;
double p1typ0tx = (double)p1t.y * (double)p0t.x;
e2 = (float)(p1typ0tx - p1txp0ty);
}
// Perform triangle edge and determinant tests
if ((e0 < 0 || e1 < 0 || e2 < 0) && (e0 > 0 || e1 > 0 || e2 > 0))
return false;
Float det = e0 + e1 + e2;
if (det == 0) return false;
// Compute scaled hit distance to triangle and test against ray $t$ range
p0t.z *= Sz;
p1t.z *= Sz;
p2t.z *= Sz;
Float tScaled = e0 * p0t.z + e1 * p1t.z + e2 * p2t.z;
if (det < 0 && (tScaled >= 0 || tScaled < ray.tMax * det))
return false;
else if (det > 0 && (tScaled <= 0 || tScaled > ray.tMax * det))
return false;
// Compute barycentric coordinates and $t$ value for triangle intersection
Float invDet = 1 / det;
Float b0 = e0 * invDet;
Float b1 = e1 * invDet;
Float b2 = e2 * invDet;
Float t = tScaled * invDet;
// Ensure that computed triangle $t$ is conservatively greater than zero
// Compute $\delta_z$ term for triangle $t$ error bounds
Float maxZt = MaxComponent(Abs(Vector3f(p0t.z, p1t.z, p2t.z)));
Float deltaZ = gamma(3) * maxZt;
// Compute $\delta_x$ and $\delta_y$ terms for triangle $t$ error bounds
Float maxXt = MaxComponent(Abs(Vector3f(p0t.x, p1t.x, p2t.x)));
Float maxYt = MaxComponent(Abs(Vector3f(p0t.y, p1t.y, p2t.y)));
Float deltaX = gamma(5) * (maxXt + maxZt);
Float deltaY = gamma(5) * (maxYt + maxZt);
// Compute $\delta_e$ term for triangle $t$ error bounds
Float deltaE =
2 * (gamma(2) * maxXt * maxYt + deltaY * maxXt + deltaX * maxYt);
// Compute $\delta_t$ term for triangle $t$ error bounds and check _t_
Float maxE = MaxComponent(Abs(Vector3f(e0, e1, e2)));
Float deltaT = 3 *
(gamma(3) * maxE * maxZt + deltaE * maxZt + deltaZ * maxE) *
std::abs(invDet);
if (t <= deltaT) return false;
// Test shadow ray intersection against alpha texture, if present
if (testAlphaTexture && (mesh->alphaMask || mesh->shadowAlphaMask)) {
// Compute triangle partial derivatives
Vector3f dpdu, dpdv;
Point2f uv[3];
GetUVs(uv);
// Compute deltas for triangle partial derivatives
Vector2f duv02 = uv[0] - uv[2], duv12 = uv[1] - uv[2];
Vector3f dp02 = p0 - p2, dp12 = p1 - p2;
Float determinant = duv02[0] * duv12[1] - duv02[1] * duv12[0];
if (determinant == 0) {
// Handle zero determinant for triangle partial derivative matrix
CoordinateSystem(Normalize(Cross(p2 - p0, p1 - p0)), &dpdu, &dpdv);
} else {
Float invdet = 1 / determinant;
dpdu = (duv12[1] * dp02 - duv02[1] * dp12) * invdet;
dpdv = (-duv12[0] * dp02 + duv02[0] * dp12) * invdet;
}
// Interpolate $(u,v)$ parametric coordinates and hit point
Point3f pHit = b0 * p0 + b1 * p1 + b2 * p2;
Point2f uvHit = b0 * uv[0] + b1 * uv[1] + b2 * uv[2];
SurfaceInteraction isectLocal(pHit, Vector3f(0, 0, 0), uvHit, -ray.d,
dpdu, dpdv, Normal3f(0, 0, 0),
Normal3f(0, 0, 0), ray.time, this);
if (mesh->alphaMask && mesh->alphaMask->Evaluate(isectLocal) == 0)
return false;
if (mesh->shadowAlphaMask &&
mesh->shadowAlphaMask->Evaluate(isectLocal) == 0)
return false;
}
++nHits;
return true;
}
void finalP(char *D, char *E) {
Permute( E, D, FinalPermuteMap, 8 );
}
bool Triangle::Intersect(const Ray &ray, Float *tHit, SurfaceInteraction *isect,
bool testAlphaTexture) const {
ProfilePhase p(Prof::TriIntersect);
++nTests;
// Get triangle vertices in _p0_, _p1_, and _p2_
const Point3f &p0 = mesh->p[v[0]];
const Point3f &p1 = mesh->p[v[1]];
const Point3f &p2 = mesh->p[v[2]];
// Perform ray--triangle intersection test
// Transform triangle vertices to ray coordinate space
// Translate vertices based on ray origin
Point3f p0t = p0 - Vector3f(ray.o);
Point3f p1t = p1 - Vector3f(ray.o);
Point3f p2t = p2 - Vector3f(ray.o);
// Permute components of triangle vertices and ray direction
int kz = MaxDimension(Abs(ray.d));
int kx = kz + 1;
if (kx == 3) kx = 0;
int ky = kx + 1;
if (ky == 3) ky = 0;
Vector3f d = Permute(ray.d, kx, ky, kz);
p0t = Permute(p0t, kx, ky, kz);
p1t = Permute(p1t, kx, ky, kz);
p2t = Permute(p2t, kx, ky, kz);
// Apply shear transformation to translated vertex positions
Float Sx = -d.x / d.z;
Float Sy = -d.y / d.z;
Float Sz = 1.f / d.z;
p0t.x += Sx * p0t.z;
p0t.y += Sy * p0t.z;
p1t.x += Sx * p1t.z;
p1t.y += Sy * p1t.z;
p2t.x += Sx * p2t.z;
p2t.y += Sy * p2t.z;
// Compute edge function coefficients _e0_, _e1_, and _e2_
Float e0 = p1t.x * p2t.y - p1t.y * p2t.x;
Float e1 = p2t.x * p0t.y - p2t.y * p0t.x;
Float e2 = p0t.x * p1t.y - p0t.y * p1t.x;
// Fall back to double precision test at triangle edges
if (sizeof(Float) == sizeof(float) &&
(e0 == 0.0f || e1 == 0.0f || e2 == 0.0f)) {
double p2txp1ty = (double)p2t.x * (double)p1t.y;
double p2typ1tx = (double)p2t.y * (double)p1t.x;
e0 = (float)(p2typ1tx - p2txp1ty);
double p0txp2ty = (double)p0t.x * (double)p2t.y;
double p0typ2tx = (double)p0t.y * (double)p2t.x;
e1 = (float)(p0typ2tx - p0txp2ty);
double p1txp0ty = (double)p1t.x * (double)p0t.y;
double p1typ0tx = (double)p1t.y * (double)p0t.x;
e2 = (float)(p1typ0tx - p1txp0ty);
}
// Perform triangle edge and determinant tests
if ((e0 < 0 || e1 < 0 || e2 < 0) && (e0 > 0 || e1 > 0 || e2 > 0))
return false;
Float det = e0 + e1 + e2;
if (det == 0) return false;
// Compute scaled hit distance to triangle and test against ray $t$ range
p0t.z *= Sz;
p1t.z *= Sz;
p2t.z *= Sz;
Float tScaled = e0 * p0t.z + e1 * p1t.z + e2 * p2t.z;
if (det < 0 && (tScaled >= 0 || tScaled < ray.tMax * det))
return false;
else if (det > 0 && (tScaled <= 0 || tScaled > ray.tMax * det))
return false;
// Compute barycentric coordinates and $t$ value for triangle intersection
Float invDet = 1 / det;
Float b0 = e0 * invDet;
Float b1 = e1 * invDet;
Float b2 = e2 * invDet;
Float t = tScaled * invDet;
// Ensure that computed triangle $t$ is conservatively greater than zero
// Compute $\delta_z$ term for triangle $t$ error bounds
Float maxZt = MaxComponent(Abs(Vector3f(p0t.z, p1t.z, p2t.z)));
Float deltaZ = gamma(3) * maxZt;
// Compute $\delta_x$ and $\delta_y$ terms for triangle $t$ error bounds
Float maxXt = MaxComponent(Abs(Vector3f(p0t.x, p1t.x, p2t.x)));
Float maxYt = MaxComponent(Abs(Vector3f(p0t.y, p1t.y, p2t.y)));
Float deltaX = gamma(5) * (maxXt + maxZt);
Float deltaY = gamma(5) * (maxYt + maxZt);
// Compute $\delta_e$ term for triangle $t$ error bounds
Float deltaE =
2 * (gamma(2) * maxXt * maxYt + deltaY * maxXt + deltaX * maxYt);
// Compute $\delta_t$ term for triangle $t$ error bounds and check _t_
Float maxE = MaxComponent(Abs(Vector3f(e0, e1, e2)));
Float deltaT = 3 *
(gamma(3) * maxE * maxZt + deltaE * maxZt + deltaZ * maxE) *
std::abs(invDet);
if (t <= deltaT) return false;
// Compute triangle partial derivatives
Vector3f dpdu, dpdv;
Point2f uv[3];
GetUVs(uv);
// Compute deltas for triangle partial derivatives
Vector2f duv02 = uv[0] - uv[2], duv12 = uv[1] - uv[2];
Vector3f dp02 = p0 - p2, dp12 = p1 - p2;
Float determinant = duv02[0] * duv12[1] - duv02[1] * duv12[0];
if (determinant == 0) {
// Handle zero determinant for triangle partial derivative matrix
CoordinateSystem(Normalize(Cross(p2 - p0, p1 - p0)), &dpdu, &dpdv);
} else {
Float invdet = 1 / determinant;
dpdu = (duv12[1] * dp02 - duv02[1] * dp12) * invdet;
dpdv = (-duv12[0] * dp02 + duv02[0] * dp12) * invdet;
}
// Compute error bounds for triangle intersection
Float xAbsSum =
(std::abs(b0 * p0.x) + std::abs(b1 * p1.x) + std::abs(b2 * p2.x));
Float yAbsSum =
(std::abs(b0 * p0.y) + std::abs(b1 * p1.y) + std::abs(b2 * p2.y));
Float zAbsSum =
(std::abs(b0 * p0.z) + std::abs(b1 * p1.z) + std::abs(b2 * p2.z));
Vector3f pError = gamma(7) * Vector3f(xAbsSum, yAbsSum, zAbsSum);
// Interpolate $(u,v)$ parametric coordinates and hit point
Point3f pHit = b0 * p0 + b1 * p1 + b2 * p2;
Point2f uvHit = b0 * uv[0] + b1 * uv[1] + b2 * uv[2];
// Test intersection against alpha texture, if present
if (testAlphaTexture && mesh->alphaMask) {
SurfaceInteraction isectLocal(pHit, Vector3f(0, 0, 0), uvHit, -ray.d,
dpdu, dpdv, Normal3f(0, 0, 0),
Normal3f(0, 0, 0), ray.time, this);
if (mesh->alphaMask->Evaluate(isectLocal) == 0) return false;
}
// Fill in _SurfaceInteraction_ from triangle hit
*isect = SurfaceInteraction(pHit, pError, uvHit, -ray.d, dpdu, dpdv,
Normal3f(0, 0, 0), Normal3f(0, 0, 0), ray.time,
this);
// Override surface normal in _isect_ for triangle
isect->n = isect->shading.n = Normal3f(Normalize(Cross(dp02, dp12)));
if (mesh->n || mesh->s) {
// Initialize _Triangle_ shading geometry
// Compute shading normal _ns_ for triangle
Normal3f ns;
if (mesh->n) {
ns = (b0 * mesh->n[v[0]] + b1 * mesh->n[v[1]] +
b2 * mesh->n[v[2]]);
if (ns.LengthSquared() > 0)
ns = Normalize(ns);
else
ns = isect->n;
} else
ns = isect->n;
// Compute shading tangent _ss_ for triangle
Vector3f ss;
if (mesh->s) {
ss = (b0 * mesh->s[v[0]] + b1 * mesh->s[v[1]] +
b2 * mesh->s[v[2]]);
if (ss.LengthSquared() > 0)
ss = Normalize(ss);
else
ss = Normalize(isect->dpdu);
}
else
ss = Normalize(isect->dpdu);
// Compute shading bitangent _ts_ for triangle and adjust _ss_
Vector3f ts = Cross(ss, ns);
if (ts.LengthSquared() > 0.f) {
ts = Normalize(ts);
ss = Cross(ts, ns);
} else
CoordinateSystem((Vector3f)ns, &ss, &ts);
// Compute $\dndu$ and $\dndv$ for triangle shading geometry
Normal3f dndu, dndv;
if (mesh->n) {
// Compute deltas for triangle partial derivatives of normal
Vector2f duv02 = uv[0] - uv[2];
Vector2f duv12 = uv[1] - uv[2];
Normal3f dn1 = mesh->n[v[0]] - mesh->n[v[2]];
Normal3f dn2 = mesh->n[v[1]] - mesh->n[v[2]];
Float determinant = duv02[0] * duv12[1] - duv02[1] * duv12[0];
if (determinant == 0)
dndu = dndv = Normal3f(0, 0, 0);
else {
Float invDet = 1 / determinant;
dndu = (duv12[1] * dn1 - duv02[1] * dn2) * invDet;
dndv = (-duv12[0] * dn1 + duv02[0] * dn2) * invDet;
}
} else
dndu = dndv = Normal3f(0, 0, 0);
isect->SetShadingGeometry(ss, ts, dndu, dndv, true);
}
// Ensure correct orientation of the geometric normal
if (mesh->n)
isect->n = Faceforward(isect->n, isect->shading.n);
else if (reverseOrientation ^ transformSwapsHandedness)
isect->n = isect->shading.n = -isect->n;
*tHit = t;
++nHits;
return true;
}
void initP(char *pt, char *key, char *D, char* K) {
Permute( K, key, KeyPermuteMap, 7 );
Permute( D, pt, InitialPermuteMap, 8 );
}
