paraboloid.cpp

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/*
    pbrt source code Copyright(c) 1998-2010 Matt Pharr and Greg Humphreys.

    This file is part of pbrt.

    pbrt is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.  Note that the text contents of
    the book "Physically Based Rendering" are *not* licensed under the
    GNU GPL.

    pbrt is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.

 */


// shapes/paraboloid.cpp*
#include "stdafx.h"
#include "shapes/paraboloid.h"
#include "paramset.h"

// Paraboloid Method Definitions
Paraboloid::Paraboloid(const Transform *o2w, const Transform *w2o, bool ro,
                       float rad, float z0, float z1,
                       float tm)
    : Shape(o2w, w2o, ro) {
    radius = rad;
    zmin = min(z0,z1);
    zmax = max(z0,z1);
    phiMax = Radians(Clamp(tm, 0.0f, 360.0f));
}


BBox Paraboloid::ObjectBound() const {
    Point p1 = Point( -radius, -radius, zmin );
    Point p2 = Point(  radius,  radius, zmax );
    return BBox( p1, p2 );
}


bool Paraboloid::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);

    // Compute quadratic paraboloid coefficients
    float k = zmax/(radius*radius);
    float A =   k*(ray.d.x * ray.d.x + ray.d.y * ray.d.y);
    float B = 2*k*(ray.d.x * ray.o.x + ray.d.y * ray.o.y) -
                ray.d.z;
    float C =   k*(ray.o.x * ray.o.x + ray.o.y * ray.o.y) -
                ray.o.z;

    // 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 paraboloid inverse mapping
    phit = ray(thit);
    phi = atan2f(phit.y, phit.x);
    if (phi < 0.) phi += 2.f*M_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(thit);
        phi = atan2f(phit.y, phit.x);
        if (phi < 0.) phi += 2.f*M_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 parabaloid $\dpdu$ and $\dpdv$
    Vector dpdu(-phiMax * phit.y, phiMax * phit.x, 0.);
    Vector dpdv = (zmax - zmin) *
        Vector(phit.x / (2.f * phit.z), phit.y / (2.f * phit.z), 1.);

    // Compute parabaloid $\dndu$ and $\dndv$
    Vector d2Pduu = -phiMax * phiMax *
                    Vector(phit.x, phit.y, 0);
    Vector d2Pduv = (zmax - zmin) * phiMax *
                    Vector(-phit.y / (2.f * phit.z),
                           phit.x / (2.f * phit.z),
                           0);
    Vector d2Pdvv = -(zmax - zmin) * (zmax - zmin) *
                    Vector(phit.x / (4.f * phit.z * phit.z),
                           phit.y / (4.f * 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);
    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 Paraboloid::IntersectP(const Ray &r) const {
    float phi;
    Point phit;
    // Transform _Ray_ to object space
    Ray ray;
    (*WorldToObject)(r, &ray);

    // Compute quadratic paraboloid coefficients
    float k = zmax/(radius*radius);
    float A =   k*(ray.d.x * ray.d.x + ray.d.y * ray.d.y);
    float B = 2*k*(ray.d.x * ray.o.x + ray.d.y * ray.o.y) -
                ray.d.z;
    float C =   k*(ray.o.x * ray.o.x + ray.o.y * ray.o.y) -
                ray.o.z;

    // 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 paraboloid inverse mapping
    phit = ray(thit);
    phi = atan2f(phit.y, phit.x);
    if (phi < 0.) phi += 2.f*M_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(thit);
        phi = atan2f(phit.y, phit.x);
        if (phi < 0.) phi += 2.f*M_PI;
        if (phit.z < zmin || phit.z > zmax || phi > phiMax)
            return false;
    }
    return true;
}


float Paraboloid::Area() const {
    return phiMax/12.0f *
        (powf(1+4*zmin, 1.5f) - powf(1+4*zmax, 1.5f));
}


Paraboloid *CreateParaboloidShape(const Transform *o2w, const Transform *w2o,
        bool reverseOrientation, const ParamSet &params) {
    float radius = params.FindOneFloat("radius", 1);
    float zmin = params.FindOneFloat("zmin", 0);
    float zmax = params.FindOneFloat("zmax", 1);
    float phimax = params.FindOneFloat("phimax", 360);
    return new Paraboloid(o2w, w2o, reverseOrientation, radius, zmin, zmax, phimax);
}

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