Vector2 Sphere::Intersect(StraightLine line, Vector2 center, double r,char sign) {
//cout << "LINE " << line.a << sign <<endl;
double *x = Quadratic((1 + line.a*line.a), 2 * line.a*(line.b - center.y) -
2 * center.x, (line.b - center.y)*(line.b - center.y) - r*r + center.x*center.x);
if (x == NULL) {
cout << "!!!" << endl;
exit(1);
}
double* y = new double[2];
y[0] = line.a*x[0] + line.b;
y[1] = line.a*x[1] + line.b;
/* cout << x[0] << " " << y[0] << endl;
cout << x[1] << " " << y[1] << endl;*/
Vector2 points[] =
{
Vector2(x[0],y[0]),
Vector2(x[1],y[1]),
};
if (sign == '-')
{
if ((points[0].x) <= (points[1].x))
return points[0];
else
return points[1];
}
if (sign == '+')
{
// cout << x[1] << " " << y[1] << endl;
if ((points[0].x) >= (points[1].x))
return points[0];
else
return points[1];
}
}
bool Cone::Intersect(const Ray &r, float *tHit, float *rayEpsilon,
DifferentialGeometry *dg) const {
float phi;
pbrt::Point phit;
// Transform _Ray_ to object space
Ray ray;
(*WorldToObject)(r, &ray);
// Compute quadratic cone coefficients
float k = radius / height;
k = k*k;
float A = ray.d.x * ray.d.x + ray.d.y * ray.d.y -
k * ray.d.z * ray.d.z;
float B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y -
k * ray.d.z * (ray.o.z-height) );
float C = ray.o.x * ray.o.x + ray.o.y * ray.o.y -
k * (ray.o.z -height) * (ray.o.z-height);
// Solve quadratic equation for _t_ values
float t0, t1;
if (!Quadratic(A, B, C, &t0, &t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
float thit = t0;
if (t0 < ray.mint) {
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute cone inverse mapping
phit = ray(thit);
phi = atan2f(phit.y, phit.x);
if (phi < 0.) phi += 2.f*M_PI;
// Test cone intersection against clipping parameters
if (phit.z < 0 || phit.z > height || phi > phiMax) {
if (thit == t1) return false;
thit = t1;
if (t1 > ray.maxt) return false;
// Compute cone inverse mapping
phit = ray(thit);
phi = atan2f(phit.y, phit.x);
if (phi < 0.) phi += 2.f*M_PI;
if (phit.z < 0 || phit.z > height || phi > phiMax)
return false;
}
// Find parametric representation of cone hit
float u = phi / phiMax;
float v = phit.z / height;
// Compute cone $\dpdu$ and $\dpdv$
Vector dpdu(-phiMax * phit.y, phiMax * phit.x, 0);
Vector dpdv(-phit.x / (1.f - v),
-phit.y / (1.f - v), height);
// Compute cone $\dndu$ and $\dndv$
Vector d2Pduu = -phiMax * phiMax *
Vector(phit.x, phit.y, 0.);
Vector d2Pduv = phiMax / (1.f - v) *
Vector(phit.y, -phit.x, 0.);
Vector d2Pdvv(0, 0, 0);
// Compute coefficients for fundamental forms
float E = Dot(dpdu, dpdu);
float F = Dot(dpdu, dpdv);
float G = Dot(dpdv, dpdv);
Vector N = Normalize(Cross(dpdu, dpdv));
float e = Dot(N, d2Pduu);
float f = Dot(N, d2Pduv);
float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
float invEGF2 = 1.f / (E*G - F*F);
Normal dndu = Normal((f*F - e*G) * invEGF2 * dpdu +
(e*F - f*E) * invEGF2 * dpdv);
Normal dndv = Normal((g*F - f*G) * invEGF2 * dpdu +
(f*F - g*E) * invEGF2 * dpdv);
// Initialize _DifferentialGeometry_ from parametric information
const Transform &o2w = *ObjectToWorld;
*dg = DifferentialGeometry(o2w(phit), o2w(dpdu), o2w(dpdv),
o2w(dndu), o2w(dndv), u, v, this);
// Update _tHit_ for quadric intersection
*tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
*rayEpsilon = 5e-4f * *tHit;
return true;
}
int main(int, char **argv) {
const double myT = water_prop.kT; // room temperature in Hartree
const double R = 2.7;
Functional x(Identity());
Grid n(gd);
n = 0.001*VectorXd::Ones(gd.NxNyNz) + 0.001*(-10*r2(gd)).cwise().exp();
compare_functionals(Sum(), x + kT, myT, n, 2e-13);
compare_functionals(Quadratic(), sqr(x + kT) - x + 2*kT, myT, n, 2e-12);
compare_functionals(Sqrt(), sqrt(x), myT, n, 1e-12);
compare_functionals(SqrtAndMore(), sqrt(x) - x + 2*kT, myT, n, 1e-12);
compare_functionals(Log(), log(x), myT, n, 3e-14);
compare_functionals(LogAndSqr(), log(x) + sqr(x), myT, n, 3e-14);
compare_functionals(LogAndSqrAndInverse(), log(x) + (sqr(x)-Pow(3)) + Functional(1)/x, myT, n, 3e-10);
compare_functionals(LogOneMinusX(), log(1-x), myT, n, 1e-12);
compare_functionals(LogOneMinusNbar(R), log(1-StepConvolve(R)), myT, n, 1e-13);
compare_functionals(SquareXshell(R), sqr(xShellConvolve(R)), myT, n);
Functional n2 = ShellConvolve(R);
Functional n3 = StepConvolve(R);
compare_functionals(n2_and_n3(R), sqr(n2) + sqr(n3), myT, n, 1e-14);
const double four_pi_r2 = 4*M_PI*R*R;
Functional one_minus_n3 = 1 - n3;
Functional phi1 = (-1/four_pi_r2)*n2*log(one_minus_n3);
compare_functionals(Phi1(R), phi1, myT, n, 1e-13);
const double four_pi_r = 4*M_PI*R;
Functional n2x = xShellConvolve(R);
Functional n2y = yShellConvolve(R);
Functional n2z = zShellConvolve(R);
Functional phi2 = (sqr(n2) - sqr(n2x) - sqr(n2y) - sqr(n2z))/(four_pi_r*one_minus_n3);
compare_functionals(Phi2(R), phi2, myT, n, 1e-14);
Functional phi3rf = n2*(sqr(n2) - 3*(sqr(n2x) + sqr(n2y) + sqr(n2z)))/(24*M_PI*sqr(one_minus_n3));
compare_functionals(Phi3rf(R), phi3rf, myT, n, 1e-13);
compare_functionals(AlmostRF(R), myT*(phi1 + phi2 + phi3rf), myT, n, 2e-14);
Functional veff = EffectivePotentialToDensity();
compare_functionals(SquareVeff(R), sqr(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-12);
compare_functionals(AlmostRFnokT(R), phi1 + phi2 + phi3rf, myT, n, 3e-14);
compare_functionals(AlmostRF(R),
(myT*phi1).set_name("phi1") + (myT*phi2).set_name("phi2") + (myT*phi3rf).set_name("phi3"),
myT, n, 4e-14);
compare_functionals(Phi1Veff(R), phi1(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-13);
compare_functionals(Phi2Veff(R), phi2(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-14);
compare_functionals(Phi3rfVeff(R), phi3rf(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-13);
compare_functionals(IdealGasFast(), IdealGasOfVeff, myT, Grid(gd, -myT*n.cwise().log()),
1e-12);
double mu = -1;
compare_functionals(Phi1plus(R, mu),
phi1(veff) + IdealGasOfVeff + ChemicalPotential(mu)(veff),
myT, Grid(gd, -myT*n.cwise().log()), 1e-12);
if (errors == 0) printf("\n%s passes!\n", argv[0]);
else printf("\n%s fails %d tests!\n", argv[0], errors);
return errors;
}
Painter& Painter::Path(CParser& p)
{
Pointf current(0, 0);
while(!p.IsEof()) {
int c = p.GetChar();
p.Spaces();
bool rel = IsLower(c);
Pointf t, t1, t2;
switch(ToUpper(c)) {
case 'M':
current = ReadPoint(p, current, rel);
Move(current);
case 'L':
while(p.IsDouble2()) {
current = ReadPoint(p, current, rel);
Line(current);
}
break;
case 'Z':
Close();
break;
case 'H':
while(p.IsDouble2()) {
current.x = p.ReadDouble() + rel * current.x;
Line(current);
}
break;
case 'V':
while(p.IsDouble2()) {
current.y = p.ReadDouble() + rel * current.y;
Line(current);
}
break;
case 'C':
while(p.IsDouble2()) {
t1 = ReadPoint(p, current, rel);
t2 = ReadPoint(p, current, rel);
current = ReadPoint(p, current, rel);
Cubic(t1, t2, current);
}
break;
case 'S':
while(p.IsDouble2()) {
t2 = ReadPoint(p, current, rel);
current = ReadPoint(p, current, rel);
Cubic(t2, current);
}
break;
case 'Q':
while(p.IsDouble2()) {
t1 = ReadPoint(p, current, rel);
current = ReadPoint(p, current, rel);
Quadratic(t1, current);
}
break;
case 'T':
while(p.IsDouble2()) {
current = ReadPoint(p, current, rel);
Quadratic(current);
}
break;
case 'A':
while(p.IsDouble2()) {
t1 = ReadPoint(p, Pointf(0, 0), false);
double xangle = ReadDouble(p);
bool large = ReadBool(p);
bool sweep = ReadBool(p);
current = ReadPoint(p, current, rel);
SvgArc(t1, xangle * M_PI / 180.0, large, sweep, current);
}
break;
default:
return *this;
}
}
return *this;
}
bool Hyperboloid::Intersect(const Ray &r, float *tHit,
float *rayEpsilon, DifferentialGeometry *dg) const {
float phi, v;
Point phit;
// Transform _Ray_ to object space
Ray ray;
(*WorldToObject)(r, &ray);
// Compute quadratic hyperboloid coefficients
float A = a*ray.d.x*ray.d.x +
a*ray.d.y*ray.d.y -
c*ray.d.z*ray.d.z;
float B = 2.f * (a*ray.d.x*ray.o.x +
a*ray.d.y*ray.o.y -
c*ray.d.z*ray.o.z);
float 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
float t0, t1;
if (!Quadratic(A, B, C, &t0, &t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
float thit = t0;
if (t0 < ray.mint) {
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute hyperboloid inverse mapping
phit = ray(thit);
v = (phit.z - p1.z)/(p2.z - p1.z);
Point pr = (1.f-v) * p1 + v * p2;
phi = atan2f(pr.x*phit.y - phit.x*pr.y,
phit.x*pr.x + phit.y*pr.y);
if (phi < 0)
phi += 2*M_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(thit);
v = (phit.z - p1.z)/(p2.z - p1.z);
Point pr = (1.f-v) * p1 + v * p2;
phi = atan2f(pr.x*phit.y - phit.x*pr.y,
phit.x*pr.x + phit.y*pr.y);
if (phi < 0)
phi += 2*M_PI;
if (phit.z < zmin || phit.z > zmax || phi > phiMax)
return false;
}
// Compute parametric representation of hyperboloid hit
float u = phi / phiMax;
// Compute hyperboloid $\dpdu$ and $\dpdv$
float cosphi = cosf(phi), sinphi = sinf(phi);
Vector dpdu(-phiMax * phit.y, phiMax * phit.x, 0.);
Vector dpdv((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 *
Vector(phit.x, phit.y, 0);
Vector d2Pduv = phiMax *
Vector(-dpdv.y, dpdv.x, 0.);
Vector d2Pdvv(0, 0, 0);
// Compute coefficients for fundamental forms
float E = Dot(dpdu, dpdu);
float F = Dot(dpdu, dpdv);
float G = Dot(dpdv, dpdv);
Vector N = Normalize(Cross(dpdu, dpdv));
float e = Dot(N, d2Pduu);
float f = Dot(N, d2Pduv);
float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
float invEGF2 = 1.f / (E*G - F*F);
Normal dndu = Normal((f*F - e*G) * invEGF2 * dpdu +
(e*F - f*E) * invEGF2 * dpdv);
Normal dndv = Normal((g*F - f*G) * invEGF2 * dpdu +
(f*F - g*E) * invEGF2 * dpdv);
// Initialize _DifferentialGeometry_ from parametric information
const Transform &o2w = *ObjectToWorld;
*dg = DifferentialGeometry(o2w(phit), o2w(dpdu), o2w(dpdv),
o2w(dndu), o2w(dndv), u, v, this);
// Update _tHit_ for quadric intersection
*tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
*rayEpsilon = 5e-4f * *tHit;
return true;
}
bool Cylinder::Intersect(const Ray &r, Float *tHit, SurfaceInteraction *isect,
bool testAlphaTexture) const {
Float phi;
Point3f pHit;
// Transform _Ray_ to object space
Vector3f oErr, dErr;
Ray ray = (*WorldToObject)(r, &oErr, &dErr);
// Compute quadratic cylinder coefficients
// Initialize _EFloat_ ray coordinate values
EFloat ox(ray.o.x, oErr.x), oy(ray.o.y, oErr.y), oz(ray.o.z, oErr.z);
EFloat dx(ray.d.x, dErr.x), dy(ray.d.y, dErr.y), dz(ray.d.z, dErr.z);
EFloat a = dx * dx + dy * dy;
EFloat b = 2 * (dx * ox + dy * oy);
EFloat c = ox * ox + oy * oy - EFloat(radius) * EFloat(radius);
// Solve quadratic equation for _t_ values
EFloat t0, t1;
if (!Quadratic(a, b, c, &t0, &t1)) return false;
// Check quadric shape _t0_ and _t1_ for nearest intersection
if (t0.UpperBound() > ray.tMax || t1.LowerBound() <= 0) return false;
EFloat tShapeHit = t0;
if (tShapeHit.LowerBound() <= 0) {
tShapeHit = t1;
if (tShapeHit.UpperBound() > ray.tMax) return false;
}
// Compute cylinder hit point and $\phi$
pHit = ray((Float)tShapeHit);
// Refine cylinder intersection point
Float hitRad = std::sqrt(pHit.x * pHit.x + pHit.y * pHit.y);
pHit.x *= radius / hitRad;
pHit.y *= radius / hitRad;
phi = std::atan2(pHit.y, pHit.x);
if (phi < 0) phi += 2 * Pi;
// Test cylinder intersection against clipping parameters
if (pHit.z < zMin || pHit.z > zMax || phi > phiMax) {
if (tShapeHit == t1) return false;
tShapeHit = t1;
if (t1.UpperBound() > ray.tMax) return false;
// Compute cylinder hit point and $\phi$
pHit = ray((Float)tShapeHit);
// Refine cylinder intersection point
Float hitRad = std::sqrt(pHit.x * pHit.x + pHit.y * pHit.y);
pHit.x *= radius / hitRad;
pHit.y *= radius / hitRad;
phi = std::atan2(pHit.y, pHit.x);
if (phi < 0) phi += 2 * Pi;
if (pHit.z < zMin || pHit.z > zMax || phi > phiMax) return false;
}
// Find parametric representation of cylinder hit
Float u = phi / phiMax;
Float v = (pHit.z - zMin) / (zMax - zMin);
// Compute cylinder $\dpdu$ and $\dpdv$
Vector3f dpdu(-phiMax * pHit.y, phiMax * pHit.x, 0);
Vector3f dpdv(0, 0, zMax - zMin);
// Compute cylinder $\dndu$ and $\dndv$
Vector3f d2Pduu = -phiMax * phiMax * Vector3f(pHit.x, pHit.y, 0);
Vector3f d2Pduv(0, 0, 0), d2Pdvv(0, 0, 0);
// Compute coefficients for fundamental forms
Float E = Dot(dpdu, dpdu);
Float F = Dot(dpdu, dpdv);
Float G = Dot(dpdv, dpdv);
Vector3f N = Normalize(Cross(dpdu, dpdv));
Float e = Dot(N, d2Pduu);
Float f = Dot(N, d2Pduv);
Float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
Float invEGF2 = 1 / (E * G - F * F);
Normal3f dndu = Normal3f((f * F - e * G) * invEGF2 * dpdu +
(e * F - f * E) * invEGF2 * dpdv);
Normal3f dndv = Normal3f((g * F - f * G) * invEGF2 * dpdu +
(f * F - g * E) * invEGF2 * dpdv);
// Compute error bounds for cylinder intersection
Vector3f pError = gamma(3) * Abs(Vector3f(pHit.x, pHit.y, 0));
// Initialize _SurfaceInteraction_ from parametric information
*isect = (*ObjectToWorld)(SurfaceInteraction(pHit, pError, Point2f(u, v),
-ray.d, dpdu, dpdv, dndu, dndv,
ray.time, this));
// Update _tHit_ for quadric intersection
*tHit = (Float)tShapeHit;
return true;
}
Painter& Painter::RelQuadratic(double x, double y)
{
return Quadratic(x, y, true);
}
bool NaiadFoamParticle::Intersect(const Ray &rayInc, float *tHit, float *rayEpsilon,
DifferentialGeometry *dg) const {
/*const float X0 = ray.o.x;
const float Y0 = ray.o.y;
const float Z0 = ray.o.z;
const float Xd = ray.d.x;
const float Yd = ray.d.y;
const float Zd = ray.d.z;
const float Xc = pos.x;
const float Yc = pos.y;
const float Zc = pos.z;
const float B = 2.0f * (Xd * (X0 - Xc) + Yd * (Y0 - Yc) + Zd * (Z0 - Zc));
const float C = (X0-Xc)*(X0-Xc) + (Y0-Yc)*(Y0-Yc) + (Z0-Zc)*(Z0-Zc) - r*r;
const float discriminant = B*B - 4*C;
if (discriminant < 0.0f)
return false;
const float t0 = (- B - sqrt(discriminant)) / 2.0f;
const float t1 = (- B + sqrt(discriminant)) / 2.0f;
if (t0 < 0 || t0 != t0) {
return true;
}*/
Matrix4x4 w2o_m;
w2o_m.m[0][3] = -pos.x;
w2o_m.m[1][3] = -pos.y;
w2o_m.m[2][3] = -pos.z;
Transform w2o = Transform(w2o_m);
const float thetaMin = -M_PI;
const float thetaMax = 0;
const float phiMax = 2.f*M_PI;
float phi;
Point phit;
// Transform _Ray_ to object space
Ray ray;
w2o(rayInc, &ray);
// Compute quadratic sphere coefficients
float A = ray.d.x*ray.d.x + ray.d.y*ray.d.y + ray.d.z*ray.d.z;
float B = 2 * (ray.d.x*ray.o.x + ray.d.y*ray.o.y + ray.d.z*ray.o.z);
float C = ray.o.x*ray.o.x + ray.o.y*ray.o.y +
ray.o.z*ray.o.z - r*r;
// Solve quadratic equation for _t_ values
float t0, t1;
if (!Quadratic(A, B, C, &t0, &t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
float thit = t0;
if (t0 < ray.mint) {
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute sphere hit position and $\phi$
phit = ray(thit);
rayInc.hitFoam = true;
PerspectiveCamera * cam = PerspectiveCamera::cur_cam;
Transform c2w;
cam->CameraToWorld.Interpolate(0.f, &c2w);
Transform w2c = Inverse(c2w);
Transform c2s = cam->CameraToScreen;
Transform s2r = cam->ScreenToRaster;
Point cPos = w2c(phit);
Point rPos = s2r(c2s(cPos));
int x = (int)(rPos.x + 0.5);
int y = (int)(rPos.y + 0.5);
int w = cam->film->xResolution;
int h = cam->film->yResolution;
if (x > 0 && y > 0 && x < w && y < h) {
rayInc.hitFoam = true;
/*printf("%i %i %i %i\n", x, y, w ,h);
std::cout << parent << std::endl;
std::cout << parent->parent << std::endl;
std::cout << parent->parent->foamPlane[0] << std::endl;
std::cout << parent->parent->foamPlane.size() << std::endl;
std::cout << x + y*w << std::endl;*/
//std::cout << NaiadFoam::cur->FoamPlane().size() << std::endl;
rayInc.alphaFoam = NaiadFoam::cur->FoamPlane()[x + y*w];
}
/*if (phit.x == 0.f && phit.y == 0.f) phit.x = 1e-5f * r;
phi = atan2f(phit.y, phit.x);
if (phi < 0.) phi += 2.f*M_PI;
// Find parametric representation of sphere hit
float u = phi / phiMax;
float theta = acosf(Clamp(phit.z / r, -1.f, 1.f));
float v = (theta - thetaMin) / (thetaMax - thetaMin);
// Compute sphere $\dpdu$ and $\dpdv$
float zradius = sqrtf(phit.x*phit.x + phit.y*phit.y);
float invzradius = 1.f / zradius;
float cosphi = phit.x * invzradius;
float sinphi = phit.y * invzradius;
Vector dpdu(-phiMax * phit.y, phiMax * phit.x, 0);
Vector dpdv = (thetaMax-thetaMin) *
Vector(phit.z * cosphi, phit.z * sinphi,
-r * sinf(theta));
// Compute sphere $\dndu$ and $\dndv$
Vector d2Pduu = -phiMax * phiMax * Vector(phit.x, phit.y, 0);
Vector d2Pduv = (thetaMax - thetaMin) * phit.z * phiMax *
Vector(-sinphi, cosphi, 0.);
Vector d2Pdvv = -(thetaMax - thetaMin) * (thetaMax - thetaMin) *
Vector(phit.x, phit.y, phit.z);
// Compute coefficients for fundamental forms
float E = Dot(dpdu, dpdu);
float F = Dot(dpdu, dpdv);
float G = Dot(dpdv, dpdv);
Vector N = Normalize(Cross(dpdu, dpdv));
float e = Dot(N, d2Pduu);
float f = Dot(N, d2Pduv);
float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
float invEGF2 = 1.f / (E*G - F*F);
Normal dndu = Normal((f*F - e*G) * invEGF2 * dpdu +
(e*F - f*E) * invEGF2 * dpdv);
Normal dndv = Normal((g*F - f*G) * invEGF2 * dpdu +
(f*F - g*E) * invEGF2 * dpdv);
//std::cout << "Got here?" << std::endl;
Matrix4x4 o2w_m;
o2w_m.m[0][3] = pos.x;
o2w_m.m[1][3] = pos.y;
o2w_m.m[2][3] = pos.z;
Transform o2w = Transform(o2w_m);
// Initialize _DifferentialGeometry_ from parametric information
*dg = DifferentialGeometry(o2w(phit), o2w(dpdu), o2w(dpdv),
o2w(dndu), o2w(dndv), u, v, parent);
dg->mult = 1.f;*/
// Update _tHit_ for quadric intersection
//*tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
//*rayEpsilon = 5e-4f * *tHit;
return true;
}
void
OGL_Light::BindIntoShader(OGL_Shader* _shader, unsigned int _index)
{
std::string typeName = "";
std::string index = std::to_string(_index);
switch (m_Type)
{
case DIRECTIONAL:
typeName = "Directional";
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Direction"), 1, m_Direction.ToStdVec().data());
break;
case POINT:
typeName = "Point";
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Position"), 1, m_Position.ToStdVec().data());
// These values describe a light with a range of 20 units
glUniform1f(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Constant"), Constant());
glUniform1f(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Linear"), Linear());
glUniform1f(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Quadratic"), Quadratic());
break;
case SPOT:
typeName = "Spot";
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Position"), 1, m_Position.ToStdVec().data());
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Direction"), 1, m_Direction.ToStdVec().data());
glUniform1f(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].OuterCutoff"), Cutoff());
glUniform1f(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].InnerCutoff"), InnerCutoff());
break;
default:
return;
}
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Ia"), 1, m_Ia.ToStdVec().data());
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Id"), 1, m_Id.ToStdVec().data());
glUniform3fv(_shader->GetUniform("u_" + typeName + "Lights[" + index + "].Is"), 1, m_Is.ToStdVec().data());
}
Painter& Painter::Quadratic(double x, double y)
{
Quadratic(x, y, false);
return *this;
}
Painter& Painter::RelQuadratic(double x, double y)
{
Quadratic(x, y, true);
return *this;
}
bool Paraboloid::Intersect(const Ray &r, Float *tHit,
SurfaceInteraction *isect) const {
Float phi;
Point3f pHit;
// Transform _Ray_ to object space
Vector3f oErr, dErr;
Ray ray = (*WorldToObject)(r, &oErr, &dErr);
// Compute quadratic paraboloid coefficients
// Initialize _EFloat_ ray coordinate values
EFloat ox(ray.o.x, oErr.x), oy(ray.o.y, oErr.y), oz(ray.o.z, oErr.z);
EFloat dx(ray.d.x, dErr.x), dy(ray.d.y, dErr.y), dz(ray.d.z, dErr.z);
EFloat k = EFloat(zMax) / (EFloat(radius) * EFloat(radius));
EFloat a = k * (dx * dx + dy * dy);
EFloat b = 2.f * k * (dx * ox + dy * oy) - dz;
EFloat c = k * (ox * ox + oy * oy) - oz;
// Solve quadratic equation for _t_ values
EFloat t0, t1;
if (!Quadratic(a, b, c, &t0, &t1)) return false;
// Check quadric shape _t0_ and _t1_ for nearest intersection
if (t0.UpperBound() > ray.tMax || t1.LowerBound() <= 0) return false;
EFloat tShapeHit = t0;
if (tShapeHit.LowerBound() <= 0) {
tShapeHit = t1;
if (tShapeHit.UpperBound() > ray.tMax) return false;
}
// Compute paraboloid inverse mapping
pHit = ray((Float)tShapeHit);
phi = std::atan2(pHit.y, pHit.x);
if (phi < 0.) phi += 2 * Pi;
// Test paraboloid intersection against clipping parameters
if (pHit.z < zMin || pHit.z > zMax || phi > phiMax) {
if (tShapeHit == t1) return false;
tShapeHit = t1;
if (t1.UpperBound() > ray.tMax) return false;
// Compute paraboloid inverse mapping
pHit = ray((Float)tShapeHit);
phi = std::atan2(pHit.y, pHit.x);
if (phi < 0.) phi += 2 * Pi;
if (pHit.z < zMin || pHit.z > zMax || phi > phiMax) return false;
}
// Find parametric representation of paraboloid hit
Float u = phi / phiMax;
Float v = (pHit.z - zMin) / (zMax - zMin);
// Compute paraboloid $\dpdu$ and $\dpdv$
Vector3f dpdu(-phiMax * pHit.y, phiMax * pHit.x, 0.);
Vector3f dpdv = (zMax - zMin) *
Vector3f(pHit.x / (2 * pHit.z), pHit.y / (2 * pHit.z), 1.);
// Compute paraboloid $\dndu$ and $\dndv$
Vector3f d2Pduu = -phiMax * phiMax * Vector3f(pHit.x, pHit.y, 0);
Vector3f d2Pduv =
(zMax - zMin) * phiMax *
Vector3f(-pHit.y / (2 * pHit.z), pHit.x / (2 * pHit.z), 0);
Vector3f d2Pdvv = -(zMax - zMin) * (zMax - zMin) *
Vector3f(pHit.x / (4 * pHit.z * pHit.z),
pHit.y / (4 * pHit.z * pHit.z), 0.);
// Compute coefficients for fundamental forms
Float E = Dot(dpdu, dpdu);
Float F = Dot(dpdu, dpdv);
Float G = Dot(dpdv, dpdv);
Vector3f N = Normalize(Cross(dpdu, dpdv));
Float e = Dot(N, d2Pduu);
Float f = Dot(N, d2Pduv);
Float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
Float invEGF2 = 1 / (E * G - F * F);
Normal3f dndu = Normal3f((f * F - e * G) * invEGF2 * dpdu +
(e * F - f * E) * invEGF2 * dpdv);
Normal3f dndv = Normal3f((g * F - f * G) * invEGF2 * dpdu +
(f * F - g * E) * invEGF2 * dpdv);
// Compute error bounds for paraboloid intersection
// Compute error bounds for intersection computed with ray equation
EFloat px = ox + tShapeHit * dx;
EFloat py = oy + tShapeHit * dy;
EFloat pz = oz + tShapeHit * dz;
Vector3f pError = Vector3f(px.GetAbsoluteError(), py.GetAbsoluteError(),
pz.GetAbsoluteError());
// Initialize _SurfaceInteraction_ from parametric information
*isect = (*ObjectToWorld)(SurfaceInteraction(pHit, pError, Point2f(u, v),
-ray.d, dpdu, dpdv, dndu, dndv,
ray.time, this));
*tHit = (Float)tShapeHit;
return true;
}
bool Sphere::Intersect(const Ray &r, Float *tHit, SurfaceInteraction *isect,
bool testAlphaTexture) const {
Float phi;
Point3f pHit;
// Transform _Ray_ to object space
Vector3f oErr, dErr;
Ray ray = (*WorldToObject)(r, &oErr, &dErr);
// Compute quadratic sphere coefficients
// Initialize _EFloat_ ray coordinate values
EFloat ox(ray.o.x, oErr.x), oy(ray.o.y, oErr.y), oz(ray.o.z, oErr.z);
EFloat dx(ray.d.x, dErr.x), dy(ray.d.y, dErr.y), dz(ray.d.z, dErr.z);
EFloat a = dx * dx + dy * dy + dz * dz;
EFloat b = 2 * (dx * ox + dy * oy + dz * oz);
EFloat c = ox * ox + oy * oy + oz * oz - EFloat(radius) * EFloat(radius);
// Solve quadratic equation for _t_ values
EFloat t0, t1;
if (!Quadratic(a, b, c, &t0, &t1)) return false;
// Check quadric shape _t0_ and _t1_ for nearest intersection
if (t0.UpperBound() > ray.tMax || t1.LowerBound() <= 0) return false;
EFloat tShapeHit = t0;
if (tShapeHit.LowerBound() <= 0) {
tShapeHit = t1;
if (tShapeHit.UpperBound() > ray.tMax) return false;
}
// Compute sphere hit position and $\phi$
pHit = ray((Float)tShapeHit);
// Refine sphere intersection point
pHit *= radius / Distance(pHit, Point3f(0, 0, 0));
if (pHit.x == 0 && pHit.y == 0) pHit.x = 1e-5f * radius;
phi = std::atan2(pHit.y, pHit.x);
if (phi < 0) phi += 2 * Pi;
// Test sphere intersection against clipping parameters
if ((zMin > -radius && pHit.z < zMin) || (zMax < radius && pHit.z > zMax) ||
phi > phiMax) {
if (tShapeHit == t1) return false;
if (t1.UpperBound() > ray.tMax) return false;
tShapeHit = t1;
// Compute sphere hit position and $\phi$
pHit = ray((Float)tShapeHit);
// Refine sphere intersection point
pHit *= radius / Distance(pHit, Point3f(0, 0, 0));
if (pHit.x == 0 && pHit.y == 0) pHit.x = 1e-5f * radius;
phi = std::atan2(pHit.y, pHit.x);
if (phi < 0) phi += 2 * Pi;
if ((zMin > -radius && pHit.z < zMin) ||
(zMax < radius && pHit.z > zMax) || phi > phiMax)
return false;
}
// Find parametric representation of sphere hit
Float u = phi / phiMax;
Float theta = std::acos(Clamp(pHit.z / radius, -1, 1));
Float v = (theta - thetaMin) / (thetaMax - thetaMin);
// Compute sphere $\dpdu$ and $\dpdv$
Float zRadius = std::sqrt(pHit.x * pHit.x + pHit.y * pHit.y);
Float invZRadius = 1 / zRadius;
Float cosPhi = pHit.x * invZRadius;
Float sinPhi = pHit.y * invZRadius;
Vector3f dpdu(-phiMax * pHit.y, phiMax * pHit.x, 0);
Vector3f dpdv =
(thetaMax - thetaMin) *
Vector3f(pHit.z * cosPhi, pHit.z * sinPhi, -radius * std::sin(theta));
// Compute sphere $\dndu$ and $\dndv$
Vector3f d2Pduu = -phiMax * phiMax * Vector3f(pHit.x, pHit.y, 0);
Vector3f d2Pduv =
(thetaMax - thetaMin) * pHit.z * phiMax * Vector3f(-sinPhi, cosPhi, 0.);
Vector3f d2Pdvv = -(thetaMax - thetaMin) * (thetaMax - thetaMin) *
Vector3f(pHit.x, pHit.y, pHit.z);
// Compute coefficients for fundamental forms
Float E = Dot(dpdu, dpdu);
Float F = Dot(dpdu, dpdv);
Float G = Dot(dpdv, dpdv);
Vector3f N = Normalize(Cross(dpdu, dpdv));
Float e = Dot(N, d2Pduu);
Float f = Dot(N, d2Pduv);
Float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
Float invEGF2 = 1 / (E * G - F * F);
Normal3f dndu = Normal3f((f * F - e * G) * invEGF2 * dpdu +
(e * F - f * E) * invEGF2 * dpdv);
Normal3f dndv = Normal3f((g * F - f * G) * invEGF2 * dpdu +
(f * F - g * E) * invEGF2 * dpdv);
// Compute error bounds for sphere intersection
Vector3f pError = gamma(5) * Abs((Vector3f)pHit);
// Initialize _SurfaceInteraction_ from parametric information
*isect = (*ObjectToWorld)(SurfaceInteraction(pHit, pError, Point2f(u, v),
-ray.d, dpdu, dpdv, dndu, dndv,
ray.time, this));
// Update _tHit_ for quadric intersection
*tHit = (Float)tShapeHit;
return true;
}
void BoundsPainter::QuadraticOp(const Pointf& p1, const Pointf& p, bool)
{
sw.Quadratic(p1, p);
Quadratic(p1, p);
}
// 1. -- intersection or not.
// 2. -- fill differentialGeometry
bool Sphere::Intersect(const Ray &r, float *tHit, float *rayEpsilon,
DifferentialGeometry *dg) const {
float phi;
Point phit;
// Transform _Ray_ to object space
Ray ray;
(*WorldToObject)(r, &ray);
// 1. -- intersection or not.
// Compute quadratic sphere coefficients
float A = ray.d.x*ray.d.x + ray.d.y*ray.d.y + ray.d.z*ray.d.z;
float B = 2 * (ray.d.x*ray.o.x + ray.d.y*ray.o.y + ray.d.z*ray.o.z);
float 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
float t0, t1;
if (!Quadratic(A, B, C, &t0, &t1)) // in pbrt.h: Find quadratic discriminant
return false;
// Compute intersection distance along ray
if (t0 > ray.maxt || t1 < ray.mint)
return false;
float thit = t0;
if (t0 < ray.mint) {
thit = t1;
if (thit > ray.maxt) return false;
}
// Compute sphere hit position and $\phi$
phit = ray(thit);
if (phit.x == 0.f && phit.y == 0.f) phit.x = 1e-5f * radius;
phi = atan2f(phit.y, phit.x);
if (phi < 0.) phi += 2.f*M_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(thit);
if (phit.x == 0.f && phit.y == 0.f) phit.x = 1e-5f * radius;
phi = atan2f(phit.y, phit.x);
if (phi < 0.) phi += 2.f*M_PI;
if ((zmin > -radius && phit.z < zmin) ||
(zmax < radius && phit.z > zmax) || phi > phiMax)
return false;
}
// 2. -- fill differentialGeometry
// Find parametric representation of sphere hit
float u = phi / phiMax;
float theta = acosf(Clamp(phit.z / radius, -1.f, 1.f));
float v = (theta - thetaMin) / (thetaMax - thetaMin);
// Compute sphere $\dpdu$ and $\dpdv$
float zradius = sqrtf(phit.x*phit.x + phit.y*phit.y);
float invzradius = 1.f / zradius;
float cosphi = phit.x * invzradius;
float sinphi = phit.y * invzradius;
Vector dpdu(-phiMax * phit.y, phiMax * phit.x, 0);
Vector dpdv = (thetaMax-thetaMin) *
Vector(phit.z * cosphi, phit.z * sinphi,
-radius * sinf(theta));
// Compute sphere $\dndu$ and $\dndv$
Vector d2Pduu = -phiMax * phiMax * Vector(phit.x, phit.y, 0);
Vector d2Pduv = (thetaMax - thetaMin) * phit.z * phiMax *
Vector(-sinphi, cosphi, 0.);
Vector d2Pdvv = -(thetaMax - thetaMin) * (thetaMax - thetaMin) *
Vector(phit.x, phit.y, phit.z);
// Compute coefficients for fundamental forms
float E = Dot(dpdu, dpdu);
float F = Dot(dpdu, dpdv);
float G = Dot(dpdv, dpdv);
Vector N = Normalize(Cross(dpdu, dpdv));
float e = Dot(N, d2Pduu);
float f = Dot(N, d2Pduv);
float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
float invEGF2 = 1.f / (E*G - F*F);
Normal dndu = Normal((f*F - e*G) * invEGF2 * dpdu +
(e*F - f*E) * invEGF2 * dpdv);
Normal dndv = Normal((g*F - f*G) * invEGF2 * dpdu +
(f*F - g*E) * invEGF2 * dpdv);
// Initialize _DifferentialGeometry_ from parametric information
const Transform &o2w = *ObjectToWorld;
*dg = DifferentialGeometry(o2w(phit), o2w(dpdu), o2w(dpdv),
o2w(dndu), o2w(dndv), u, v, this);
// Update _tHit_ for quadric intersection
*tHit = thit;
// Compute _rayEpsilon_ for quadric intersection
*rayEpsilon = 5e-4f * *tHit;
return true;
}
float Cubic(float a,float b,float c,float d,float t)
{
return Linear(Quadratic(a,b,c,t),Quadratic(b,c,d,t),t);
}
bool Hyperboloid::Intersect(const Ray &r, Float *tHit,
SurfaceInteraction *isect) const {
Float phi, v;
Point3f pHit;
// Transform _Ray_ to object space
Vector3f oErr, dErr;
Ray ray = (*WorldToObject)(r, &oErr, &dErr);
// Compute quadratic hyperboloid coefficients
// Initialize _EFloat_ ray coordinate values
EFloat ox(ray.o.x, oErr.x), oy(ray.o.y, oErr.y), oz(ray.o.z, oErr.z);
EFloat dx(ray.d.x, dErr.x), dy(ray.d.y, dErr.y), dz(ray.d.z, dErr.z);
EFloat a = ah * dx * dx + ah * dy * dy - ch * dz * dz;
EFloat b = 2.f * (ah * dx * ox + ah * dy * oy - ch * dz * oz);
EFloat c = ah * ox * ox + ah * oy * oy - ch * oz * oz - 1.f;
// Solve quadratic equation for _t_ values
EFloat t0, t1;
if (!Quadratic(a, b, c, &t0, &t1)) return false;
// Check quadric shape _t0_ and _t1_ for nearest intersection
if (t0.UpperBound() > ray.tMax || t1.LowerBound() <= 0) return false;
EFloat tShapeHit = t0;
if (t0.LowerBound() <= 0) {
tShapeHit = t1;
if (tShapeHit.UpperBound() > ray.tMax) return false;
}
// Compute hyperboloid inverse mapping
pHit = ray((Float)tShapeHit);
v = (pHit.z - p1.z) / (p2.z - p1.z);
Point3f pr = (1 - v) * p1 + v * p2;
phi = std::atan2(pr.x * pHit.y - pHit.x * pr.y,
pHit.x * pr.x + pHit.y * pr.y);
if (phi < 0) phi += 2 * Pi;
// Test hyperboloid intersection against clipping parameters
if (pHit.z < zMin || pHit.z > zMax || phi > phiMax) {
if (tShapeHit == t1) return false;
tShapeHit = t1;
if (t1.UpperBound() > ray.tMax) return false;
// Compute hyperboloid inverse mapping
pHit = ray((Float)tShapeHit);
v = (pHit.z - p1.z) / (p2.z - p1.z);
Point3f pr = (1 - v) * p1 + v * p2;
phi = std::atan2(pr.x * pHit.y - pHit.x * pr.y,
pHit.x * pr.x + pHit.y * pr.y);
if (phi < 0) phi += 2 * Pi;
if (pHit.z < zMin || pHit.z > zMax || phi > phiMax) return false;
}
// Compute parametric representation of hyperboloid hit
Float u = phi / phiMax;
// Compute hyperboloid $\dpdu$ and $\dpdv$
Float cosPhi = std::cos(phi), sinPhi = std::sin(phi);
Vector3f dpdu(-phiMax * pHit.y, phiMax * pHit.x, 0.);
Vector3f dpdv((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 $\dndv$
Vector3f d2Pduu = -phiMax * phiMax * Vector3f(pHit.x, pHit.y, 0);
Vector3f d2Pduv = phiMax * Vector3f(-dpdv.y, dpdv.x, 0.);
Vector3f d2Pdvv(0, 0, 0);
// Compute coefficients for fundamental forms
Float E = Dot(dpdu, dpdu);
Float F = Dot(dpdu, dpdv);
Float G = Dot(dpdv, dpdv);
Vector3f N = Normalize(Cross(dpdu, dpdv));
Float e = Dot(N, d2Pduu);
Float f = Dot(N, d2Pduv);
Float g = Dot(N, d2Pdvv);
// Compute $\dndu$ and $\dndv$ from fundamental form coefficients
Float invEGF2 = 1 / (E * G - F * F);
Normal3f dndu = Normal3f((f * F - e * G) * invEGF2 * dpdu +
(e * F - f * E) * invEGF2 * dpdv);
Normal3f dndv = Normal3f((g * F - f * G) * invEGF2 * dpdu +
(f * F - g * E) * invEGF2 * dpdv);
// Compute error bounds for hyperboloid intersection
// Compute error bounds for intersection computed with ray equation
EFloat px = ox + tShapeHit * dx;
EFloat py = oy + tShapeHit * dy;
EFloat pz = oz + tShapeHit * dz;
Vector3f pError = Vector3f(px.GetAbsoluteError(), py.GetAbsoluteError(),
pz.GetAbsoluteError());
// Initialize _SurfaceInteraction_ from parametric information
*isect = (*ObjectToWorld)(SurfaceInteraction(pHit, pError, Point2f(u, v),
-ray.d, dpdu, dpdv, dndu, dndv,
ray.time, this));
*tHit = (Float)tShapeHit;
return true;
}
Real OneDimSolve::Solve(Real Y, Real X, Real Dev, int Lim)
{
enum Loop { start, captured1, captured2, binary, finish };
Tracer et("OneDimSolve::Solve");
lim=Lim; Captured = false;
if (Dev==0.0) Throw(SolutionException("Dev is zero"));
L=0; C=1; U=2; vpol=1; hpol=1; y[C]=0.0; y[U]=0.0;
if (Dev<0.0) { hpol=-1; Dev = -Dev; }
YY=Y; // target value
x[L] = X; // initial trial value
if (!function.IsValid(X))
Throw(SolutionException("Starting value is invalid"));
Loop TheLoop = start;
for (;;)
{
switch (TheLoop)
{
case start:
LookAt(L); if (Finish) { TheLoop = finish; break; }
if (y[L]>0.0) VFlip(); // so Y[L] < 0
x[U] = X + Dev * hpol;
if (!function.maxXinf && x[U] > function.maxX)
x[U] = (function.maxX + X) / 2.0;
if (!function.minXinf && x[U] < function.minX)
x[U] = (function.minX + X) / 2.0;
LookAt(U); if (Finish) { TheLoop = finish; break; }
if (y[U] > 0.0) { TheLoop = captured1; Captured = true; break; }
if (y[U] == y[L])
Throw(SolutionException("Function is flat"));
if (y[U] < y[L]) HFlip(); // Change direction
State(L,U,C);
for (i=0; i<20; i++)
{
// cout << "Searching for crossing point\n";
// Have L C then crossing point, Y[L]<Y[C]<0
x[U] = x[C] + Dev * hpol;
if (!function.maxXinf && x[U] > function.maxX)
x[U] = (function.maxX + x[C]) / 2.0;
if (!function.minXinf && x[U] < function.minX)
x[U] = (function.minX + x[C]) / 2.0;
LookAt(U); if (Finish) { TheLoop = finish; break; }
if (y[U] > 0) { TheLoop = captured2; Captured = true; break; }
if (y[U] < y[C])
Throw(SolutionException("Function is not monotone"));
Dev *= 2.0;
State(C,U,L);
}
if (TheLoop != start ) break;
Throw(SolutionException("Can't locate a crossing point"));
case captured1:
// cout << "Captured - 1\n";
// We have 2 points L and U with crossing between them
Linear(L,C,U); // linear interpolation
// - result to C
LookAt(C); if (Finish) { TheLoop = finish; break; }
if (y[C] > 0.0) Flip(); // Want y[C] < 0
if (y[C] < 0.5*y[L]) { State(C,L,U); TheLoop = binary; break; }
case captured2:
// cout << "Captured - 2\n";
// We have L,C before crossing, U after crossing
Quadratic(L,C,U); // quad interpolation
// - result to L
State(C,L,U);
if ((x[C] - x[L])*hpol <= 0.0 || (x[C] - x[U])*hpol >= 0.0)
{ TheLoop = captured1; break; }
LookAt(C); if (Finish) { TheLoop = finish; break; }
// cout << "Through first stage\n";
if (y[C] > 0.0) Flip();
if (y[C] > 0.5*y[L]) { TheLoop = captured2; break; }
else { State(C,L,U); TheLoop = captured1; break; }
case binary:
// We have L, U around crossing - do binary search
// cout << "Binary\n";
for (i=3; i; i--)
{
x[C] = 0.5*(x[L]+x[U]);
LookAt(C); if (Finish) { TheLoop = finish; break; }
if (y[C]>0.0) State(L,U,C); else State(C,L,U);
}
if (TheLoop != binary) break;
TheLoop = captured1; break;
case finish:
return x[Last];
}
}
}
bool Sphere::Intersect(const Ray &r, Float *distance, Float *rayEpsilon,
DifferentialGeometry *dg) const {
Ray ray;
(*worldToLocal)(r, &ray);
// Compute quadratic sphere coefficients
Float A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z;
Float B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z);
Float C = ray.o.x * ray.o.x + ray.o.y * ray.o.y + ray.o.z * ray.o.z
- mRad * mRad;
Float t0, t1;
if (!Quadratic(A, B, C, &t0, &t1))
return false;
// Compute intersection distance along ray
if (t0 > ray.maxT || t1 < ray.minT)
return false;
Float thit = t0;
if (t0 < ray.minT) {
thit = t1;
if (thit > ray.maxT)
return false;
}
//这里开始计算参数化变量
//计算phi
Point phit;
Float phi;
phit = ray(thit);
if (phit.x == 0.f && phit.y == 0.f)
phit.x = 1e-5f * mRad; //排除除零的情况
phi = atan2f(phit.y, phit.x);
if (phi < 0.)
phi += 2.f * Pi; //保证phi在2PI之中
//判断是否在Z坐标之间的裁剪空间中
if ((mZMin > -mRad && phit.z < mZMin) || (mZMax < mRad && phit.z > mZMax)
|| phi > mPhiMax) {
if (thit == t1)
return false;
if (t1 > ray.maxT)
return false;
thit = t1;
phit = ray(thit);
if (phit.x == 0.f && phit.y == 0.f)
phit.x = 1e-5f * mRad;
phi = atan2f(phit.y, phit.x);
if (phi < 0.)
phi += 2.f * Pi;
if ((mZMin > -mRad && phit.z < mZMin)
|| (mZMax < mRad && phit.z > mZMax) || phi > mPhiMax)
return false;
}
// Find parametric representation of sphere hit
//寻找参数化的u和v
Float u = phi / mPhiMax;
Float theta = acosf(Clamp(phit.z / mRad, -1.f, 1.f));
Float v = (theta - mThetaMin) / (mThetaMax - mThetaMin);
// 计算偏导 偏导还不是很熟悉,所以这里照搬了PBRT的公式,详细公式可以查阅PBRT
Float zradius = sqrtf(phit.x * phit.x + phit.y * phit.y);
Float invzradius = 1.f / zradius;
Float cosphi = phit.x * invzradius;
Float sinphi = phit.y * invzradius;
Vector3f dpdu(-mPhiMax * phit.y, mPhiMax * phit.x, 0);
Vector3f dpdv = (mThetaMax - mThetaMin)
* Vector3f(phit.z * cosphi, phit.z * sinphi, -mRad * sinf(theta));
//计算法线的偏导
Vector3f d2Pduu = -mPhiMax * mPhiMax * Vector3f(phit.x, phit.y, 0);
Vector3f d2Pduv = (mThetaMax - mThetaMin) * phit.z * mPhiMax
* Vector3f(-sinphi, cosphi, 0.);
Vector3f d2Pdvv = -(mThetaMax - mThetaMin) * (mThetaMax - mThetaMin)
* Vector3f(phit.x, phit.y, phit.z);
Float E = Dot(dpdu, dpdu);
Float F = Dot(dpdu, dpdv);
Float G = Dot(dpdv, dpdv);
Vector3f N = Normalize(Cross(dpdu, dpdv));
Float e = Dot(N, d2Pduu);
Float f = Dot(N, d2Pduv);
Float g = Dot(N, d2Pdvv);
Float invEGF2 = 1.f / (E * G - F * F);
Normal dndu = Normal(
(f * F - e * G) * invEGF2 * dpdu
+ (e * F - f * E) * invEGF2 * dpdv);
Normal dndv = Normal(
(g * F - f * G) * invEGF2 * dpdu
+ (f * F - g * E) * invEGF2 * dpdv);
const Transform &o2w = *localToWorld;
*dg = DifferentialGeometry(o2w(phit), o2w(dpdu), o2w(dpdv), o2w(dndu),
o2w(dndv), u, v, this);
*distance = thit;
*rayEpsilon = 5e-4f * *distance; //交点处的Float误差
return true;
}
Painter& Painter::Quadratic(double x, double y)
{
return Quadratic(x, y, false);
}
