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00024 #include "hyperboloid.h"
00025 #include "paramset.h"
00026
00027 using namespace lux;
00028
00029
00030 Hyperboloid::Hyperboloid(const Transform &o2w, bool ro,
00031 const Point &point1, const Point &point2, float tm)
00032 : Shape(o2w, ro) {
00033 p1 = point1;
00034 p2 = point2;
00035 phiMax = Radians(Clamp(tm, 0.0f, 360.0f));
00036 float rad_1 = sqrtf(p1.x*p1.x + p1.y*p1.y);
00037 float rad_2 = sqrtf(p2.x*p2.x + p2.y*p2.y);
00038 rmax = max(rad_1,rad_2);
00039 zmin = min(p1.z,p2.z);
00040 zmax = max(p1.z,p2.z);
00041
00042 if (p2.z == 0.) swap(p1, p2);
00043 Point pp = p1;
00044 float xy1, xy2;
00045 do {
00046 pp += 2.f * (p2-p1);
00047 xy1 = pp.x*pp.x + pp.y*pp.y;
00048 xy2 = p2.x*p2.x + p2.y*p2.y;
00049 a = (1.f/xy1 - (pp.z*pp.z)/(xy1*p2.z*p2.z)) /
00050 (1 - (xy2*pp.z*pp.z)/(xy1*p2.z*p2.z));
00051 c = (a * xy2 - 1) / (p2.z*p2.z);
00052 } while (isinf(a) || isnan(a));
00053 }
00054 BBox Hyperboloid::ObjectBound() const {
00055 Point p1 = Point( -rmax, -rmax, zmin );
00056 Point p2 = Point( rmax, rmax, zmax );
00057 return BBox( p1, p2 );
00058 }
00059 bool Hyperboloid::Intersect(const Ray &r, float *tHit,
00060 DifferentialGeometry *dg) const {
00061 float phi, v;
00062 Point phit;
00063
00064 Ray ray;
00065 WorldToObject(r, &ray);
00066
00067 float A = a*ray.d.x*ray.d.x +
00068 a*ray.d.y*ray.d.y -
00069 c*ray.d.z*ray.d.z;
00070 float B = 2.f * (a*ray.d.x*ray.o.x +
00071 a*ray.d.y*ray.o.y -
00072 c*ray.d.z*ray.o.z);
00073 float C = a*ray.o.x*ray.o.x +
00074 a*ray.o.y*ray.o.y -
00075 c*ray.o.z*ray.o.z - 1;
00076
00077 float t0, t1;
00078 if (!Quadratic(A, B, C, &t0, &t1))
00079 return false;
00080
00081 if (t0 > ray.maxt || t1 < ray.mint)
00082 return false;
00083 float thit = t0;
00084 if (t0 < ray.mint) {
00085 thit = t1;
00086 if (thit > ray.maxt) return false;
00087 }
00088
00089 phit = ray(thit);
00090 v = (phit.z - p1.z)/(p2.z - p1.z);
00091 Point pr = (1.f-v) * p1 + v * p2;
00092 phi = atan2f(pr.x*phit.y - phit.x*pr.y,
00093 phit.x*pr.x + phit.y*pr.y);
00094 if (phi < 0)
00095 phi += 2*M_PI;
00096
00097 if (phit.z < zmin || phit.z > zmax || phi > phiMax) {
00098 if (thit == t1) return false;
00099 thit = t1;
00100 if (t1 > ray.maxt) return false;
00101
00102 phit = ray(thit);
00103 v = (phit.z - p1.z)/(p2.z - p1.z);
00104 Point pr = (1.f-v) * p1 + v * p2;
00105 phi = atan2f(pr.x*phit.y - phit.x*pr.y,
00106 phit.x*pr.x + phit.y*pr.y);
00107 if (phi < 0)
00108 phi += 2*M_PI;
00109 if (phit.z < zmin || phit.z > zmax || phi > phiMax)
00110 return false;
00111 }
00112
00113 float u = phi / phiMax;
00114
00115 float cosphi = cosf(phi), sinphi = sinf(phi);
00116 Vector dpdu(-phiMax * phit.y, phiMax * phit.x, 0.);
00117 Vector dpdv((p2.x-p1.x) * cosphi - (p2.y-p1.y) * sinphi,
00118 (p2.x-p1.x) * sinphi + (p2.y-p1.y) * cosphi,
00119 p2.z-p1.z);
00120
00121 Vector d2Pduu = -phiMax * phiMax *
00122 Vector(phit.x, phit.y, 0);
00123 Vector d2Pduv = phiMax *
00124 Vector(-dpdv.y, dpdv.x, 0.);
00125 Vector d2Pdvv(0, 0, 0);
00126
00127 float E = Dot(dpdu, dpdu);
00128 float F = Dot(dpdu, dpdv);
00129 float G = Dot(dpdv, dpdv);
00130 Vector N = Normalize(Cross(dpdu, dpdv));
00131 float e = Dot(N, d2Pduu);
00132 float f = Dot(N, d2Pduv);
00133 float g = Dot(N, d2Pdvv);
00134
00135 float invEGF2 = 1.f / (E*G - F*F);
00136 Vector dndu = (f*F - e*G) * invEGF2 * dpdu +
00137 (e*F - f*E) * invEGF2 * dpdv;
00138 Vector dndv = (g*F - f*G) * invEGF2 * dpdu +
00139 (f*F - g*E) * invEGF2 * dpdv;
00140
00141 *dg = DifferentialGeometry(ObjectToWorld(phit),
00142 ObjectToWorld(dpdu),
00143 ObjectToWorld(dpdv),
00144 ObjectToWorld(dndu),
00145 ObjectToWorld(dndv),
00146 u, v, this);
00147
00148 *tHit = thit;
00149 return true;
00150 }
00151 bool Hyperboloid::IntersectP(const Ray &r) const {
00152 float phi, v;
00153 Point phit;
00154
00155 Ray ray;
00156 WorldToObject(r, &ray);
00157
00158 float A = a*ray.d.x*ray.d.x +
00159 a*ray.d.y*ray.d.y -
00160 c*ray.d.z*ray.d.z;
00161 float B = 2.f * (a*ray.d.x*ray.o.x +
00162 a*ray.d.y*ray.o.y -
00163 c*ray.d.z*ray.o.z);
00164 float C = a*ray.o.x*ray.o.x +
00165 a*ray.o.y*ray.o.y -
00166 c*ray.o.z*ray.o.z - 1;
00167
00168 float t0, t1;
00169 if (!Quadratic(A, B, C, &t0, &t1))
00170 return false;
00171
00172 if (t0 > ray.maxt || t1 < ray.mint)
00173 return false;
00174 float thit = t0;
00175 if (t0 < ray.mint) {
00176 thit = t1;
00177 if (thit > ray.maxt) return false;
00178 }
00179
00180 phit = ray(thit);
00181 v = (phit.z - p1.z)/(p2.z - p1.z);
00182 Point pr = (1.f-v) * p1 + v * p2;
00183 phi = atan2f(pr.x*phit.y - phit.x*pr.y,
00184 phit.x*pr.x + phit.y*pr.y);
00185 if (phi < 0)
00186 phi += 2*M_PI;
00187
00188 if (phit.z < zmin || phit.z > zmax || phi > phiMax) {
00189 if (thit == t1) return false;
00190 thit = t1;
00191 if (t1 > ray.maxt) return false;
00192
00193 phit = ray(thit);
00194 v = (phit.z - p1.z)/(p2.z - p1.z);
00195 Point pr = (1.f-v) * p1 + v * p2;
00196 phi = atan2f(pr.x*phit.y - phit.x*pr.y,
00197 phit.x*pr.x + phit.y*pr.y);
00198 if (phi < 0)
00199 phi += 2*M_PI;
00200 if (phit.z < zmin || phit.z > zmax || phi > phiMax)
00201 return false;
00202 }
00203 return true;
00204 }
00205 #define SQR(a) ((a)*(a))
00206 #define QUAD(a) ((SQR(a))*(SQR(a)))
00207 float Hyperboloid::Area() const {
00208 return phiMax/6.f *
00209 (2.f*QUAD(p1.x) - 2.f*p1.x*p1.x*p1.x*p2.x +
00210 2.f*QUAD(p2.x) +
00211 2.f*(p1.y*p1.y + p1.y*p2.y + p2.y*p2.y)*
00212 (SQR(p1.y - p2.y) + SQR(p1.z - p2.z)) +
00213 p2.x*p2.x*(5.f*p1.y*p1.y + 2.f*p1.y*p2.y -
00214 4.f*p2.y*p2.y + 2.f*SQR(p1.z - p2.z)) +
00215 p1.x*p1.x*(-4.f*p1.y*p1.y + 2.f*p1.y*p2.y +
00216 5.f*p2.y*p2.y + 2.f*SQR(p1.z - p2.z)) -
00217 2.f*p1.x*p2.x*(p2.x*p2.x - p1.y*p1.y +
00218 5.f*p1.y*p2.y - p2.y*p2.y - p1.z*p1.z +
00219 2.f*p1.z*p2.z - p2.z*p2.z));
00220 }
00221 #undef SQR
00222 #undef QUAD
00223 Shape* Hyperboloid::CreateShape(const Transform &o2w,
00224 bool reverseOrientation, const ParamSet ¶ms) {
00225 Point p1 = params.FindOnePoint( "p1", Point(0,0,0) );
00226 Point p2 = params.FindOnePoint( "p2", Point(1,1,1) );
00227 float phimax = params.FindOneFloat( "phimax", 360 );
00228 return new Hyperboloid(o2w, reverseOrientation, p1, p2, phimax);
00229 }