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<h1>paraboloid.cpp</h1><a href="paraboloid_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001
<a name="l00002"></a>00002 <span class="comment">/*</span>
<a name="l00003"></a>00003 <span class="comment"> pbrt source code Copyright(c) 1998-2007 Matt Pharr and Greg Humphreys.</span>
<a name="l00004"></a>00004 <span class="comment"></span>
<a name="l00005"></a>00005 <span class="comment"> This file is part of pbrt.</span>
<a name="l00006"></a>00006 <span class="comment"></span>
<a name="l00007"></a>00007 <span class="comment"> pbrt is free software; you can redistribute it and/or modify</span>
<a name="l00008"></a>00008 <span class="comment"> it under the terms of the GNU General Public License as published by</span>
<a name="l00009"></a>00009 <span class="comment"> the Free Software Foundation; either version 2 of the License, or</span>
<a name="l00010"></a>00010 <span class="comment"> (at your option) any later version. Note that the text contents of</span>
<a name="l00011"></a>00011 <span class="comment"> the book "Physically Based Rendering" are *not* licensed under the</span>
<a name="l00012"></a>00012 <span class="comment"> GNU GPL.</span>
<a name="l00013"></a>00013 <span class="comment"></span>
<a name="l00014"></a>00014 <span class="comment"> pbrt is distributed in the hope that it will be useful,</span>
<a name="l00015"></a>00015 <span class="comment"> but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<a name="l00016"></a>00016 <span class="comment"> MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
<a name="l00017"></a>00017 <span class="comment"> GNU General Public License for more details.</span>
<a name="l00018"></a>00018 <span class="comment"></span>
<a name="l00019"></a>00019 <span class="comment"> You should have received a copy of the GNU General Public License</span>
<a name="l00020"></a>00020 <span class="comment"> along with this program. If not, see <http://www.gnu.org/licenses/>.</span>
<a name="l00021"></a>00021 <span class="comment"></span>
<a name="l00022"></a>00022 <span class="comment"> */</span>
<a name="l00023"></a>00023
<a name="l00024"></a>00024 <span class="comment">// paraboloid.cpp*</span>
<a name="l00025"></a>00025 <span class="preprocessor">#include "<a class="code" href="shape_8h.html">shape.h</a>"</span>
<a name="l00026"></a>00026 <span class="comment">// Paraboloid Declarations</span>
<a name="l00027"></a><a class="code" href="classParaboloid.html">00027</a> <span class="keyword">class </span><a class="code" href="classParaboloid.html">Paraboloid</a>: <span class="keyword">public</span> <a class="code" href="classShape.html">Shape</a> {
<a name="l00028"></a>00028 <span class="keyword">public</span>:
<a name="l00029"></a>00029 <span class="comment">// Paraboloid Public Methods</span>
<a name="l00030"></a>00030 <a class="code" href="classParaboloid.html#76adacc8588508839bb117158369936a">Paraboloid</a>(<span class="keyword">const</span> <a class="code" href="classTransform.html">Transform</a> &o2w, <span class="keywordtype">bool</span> ro, <span class="keywordtype">float</span> rad,
<a name="l00031"></a>00031 <span class="keywordtype">float</span> z0, <span class="keywordtype">float</span> z1, <span class="keywordtype">float</span> tm );
<a name="l00032"></a>00032 <a class="code" href="classBBox.html">BBox</a> <a class="code" href="classParaboloid.html#459e0369531af65813c55ae32d8ba1f5">ObjectBound</a>() <span class="keyword">const</span>;
<a name="l00033"></a>00033 <span class="keywordtype">bool</span> <a class="code" href="classParaboloid.html#2be1e19cc38ad66c9e0ce86c145d65f6">Intersect</a>(<span class="keyword">const</span> <a class="code" href="classRay.html">Ray</a> &ray, <span class="keywordtype">float</span> *tHit,
<a name="l00034"></a>00034 <a class="code" href="structDifferentialGeometry.html">DifferentialGeometry</a> *dg) <span class="keyword">const</span>;
<a name="l00035"></a>00035 <span class="keywordtype">bool</span> <a class="code" href="classParaboloid.html#daa2f7b37d435552d09ab7456cdf6b82">IntersectP</a>(<span class="keyword">const</span> <a class="code" href="classRay.html">Ray</a> &ray) <span class="keyword">const</span>;
<a name="l00036"></a>00036 <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#dfca2ff655627c3063325899dfdaba9f">Area</a>() <span class="keyword">const</span>;
<a name="l00037"></a>00037 <span class="keyword">protected</span>:
<a name="l00038"></a>00038 <span class="comment">// Paraboloid Data</span>
<a name="l00039"></a><a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">00039</a> <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>;
<a name="l00040"></a><a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">00040</a> <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>, <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a>;
<a name="l00041"></a><a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">00041</a> <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>;
<a name="l00042"></a>00042 };
<a name="l00043"></a>00043 <span class="comment">// Paraboloid Method Definitions</span>
<a name="l00044"></a><a class="code" href="classParaboloid.html#76adacc8588508839bb117158369936a">00044</a> <a class="code" href="classParaboloid.html#76adacc8588508839bb117158369936a">Paraboloid::Paraboloid</a>(<span class="keyword">const</span> <a class="code" href="classTransform.html">Transform</a> &o2w, <span class="keywordtype">bool</span> ro,
<a name="l00045"></a>00045 <span class="keywordtype">float</span> rad, <span class="keywordtype">float</span> z0, <span class="keywordtype">float</span> z1,
<a name="l00046"></a>00046 <span class="keywordtype">float</span> tm)
<a name="l00047"></a>00047 : <a class="code" href="classShape.html">Shape</a>(o2w, ro) {
<a name="l00048"></a>00048 <a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a> = rad;
<a name="l00049"></a>00049 <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> = min(z0,z1);
<a name="l00050"></a>00050 <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> = max(z0,z1);
<a name="l00051"></a>00051 <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a> = <a class="code" href="pbrt_8h.html#12544670622d3fbc783e1cb4d56b3a23">Radians</a>( <a class="code" href="pbrt_8h.html#036098e5cec04b73d8720de12e8e5cd1">Clamp</a>( tm, 0.0f, 360.0f ) );
<a name="l00052"></a>00052 }
<a name="l00053"></a><a class="code" href="classParaboloid.html#459e0369531af65813c55ae32d8ba1f5">00053</a> <a class="code" href="classBBox.html">BBox</a> <a class="code" href="classParaboloid.html#459e0369531af65813c55ae32d8ba1f5">Paraboloid::ObjectBound</a>()<span class="keyword"> const </span>{
<a name="l00054"></a>00054 <a class="code" href="classPoint.html">Point</a> p1 = <a class="code" href="classPoint.html">Point</a>( -<a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>, -<a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>, <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> );
<a name="l00055"></a>00055 <a class="code" href="classPoint.html">Point</a> p2 = <a class="code" href="classPoint.html">Point</a>( <a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>, <a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>, <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> );
<a name="l00056"></a>00056 <span class="keywordflow">return</span> <a class="code" href="classBBox.html">BBox</a>( p1, p2 );
<a name="l00057"></a>00057 }
<a name="l00058"></a><a class="code" href="classParaboloid.html#2be1e19cc38ad66c9e0ce86c145d65f6">00058</a> <span class="keywordtype">bool</span> <a class="code" href="classParaboloid.html#2be1e19cc38ad66c9e0ce86c145d65f6">Paraboloid::Intersect</a>(<span class="keyword">const</span> <a class="code" href="classRay.html">Ray</a> &r, <span class="keywordtype">float</span> *tHit,
<a name="l00059"></a>00059 <a class="code" href="structDifferentialGeometry.html">DifferentialGeometry</a> *dg)<span class="keyword"> const </span>{
<a name="l00060"></a>00060 <span class="keywordtype">float</span> phi;
<a name="l00061"></a>00061 <a class="code" href="classPoint.html">Point</a> phit;
<a name="l00062"></a>00062 <span class="comment">// Transform _Ray_ to object space</span>
<a name="l00063"></a>00063 <a class="code" href="classRay.html">Ray</a> ray;
<a name="l00064"></a>00064 <a class="code" href="classShape.html#72cf45b4c359fc22b3264a02e932324e">WorldToObject</a>(r, &ray);
<a name="l00065"></a>00065 <span class="comment">// Compute quadratic paraboloid coefficients</span>
<a name="l00066"></a>00066 <span class="keywordtype">float</span> k = <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a>/(<a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>*<a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>);
<a name="l00067"></a>00067 <span class="keywordtype">float</span> A = k*(ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#ca49165049a1e21ae47afcfc078819ed">x</a> * ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#ca49165049a1e21ae47afcfc078819ed">x</a> + ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#81be9102fca6d9beea3efef522c4c09d">y</a> * ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#81be9102fca6d9beea3efef522c4c09d">y</a>);
<a name="l00068"></a>00068 <span class="keywordtype">float</span> B = 2*k*(ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#ca49165049a1e21ae47afcfc078819ed">x</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> + ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#81be9102fca6d9beea3efef522c4c09d">y</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>) -
<a name="l00069"></a>00069 ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#0e84237d0830d5c459bfa5676b5fbfba">z</a>;
<a name="l00070"></a>00070 <span class="keywordtype">float</span> C = k*(ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> + ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>) -
<a name="l00071"></a>00071 ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>;
<a name="l00072"></a>00072 <span class="comment">// Solve quadratic equation for _t_ values</span>
<a name="l00073"></a>00073 <span class="keywordtype">float</span> t0, t1;
<a name="l00074"></a>00074 <span class="keywordflow">if</span> (!<a class="code" href="pbrt_8h.html#14bbcf80fc40915df82a84e6eb2dfb3b">Quadratic</a>(A, B, C, &t0, &t1))
<a name="l00075"></a>00075 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00076"></a>00076 <span class="comment">// Compute intersection distance along ray</span>
<a name="l00077"></a>00077 <span class="keywordflow">if</span> (t0 > ray.<a class="code" href="classRay.html#aa6c29ceae8edc5c9d37e879daa1557a">maxt</a> || t1 < ray.<a class="code" href="classRay.html#ded3b6e00c215611ebd61a6965560ba0">mint</a>)
<a name="l00078"></a>00078 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00079"></a>00079 <span class="keywordtype">float</span> thit = t0;
<a name="l00080"></a>00080 <span class="keywordflow">if</span> (t0 < ray.<a class="code" href="classRay.html#ded3b6e00c215611ebd61a6965560ba0">mint</a>) {
<a name="l00081"></a>00081 thit = t1;
<a name="l00082"></a>00082 <span class="keywordflow">if</span> (thit > ray.<a class="code" href="classRay.html#aa6c29ceae8edc5c9d37e879daa1557a">maxt</a>) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00083"></a>00083 }
<a name="l00084"></a>00084 <span class="comment">// Compute paraboloid inverse mapping</span>
<a name="l00085"></a>00085 phit = ray(thit);
<a name="l00086"></a>00086 phi = atan2f(phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>, phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>);
<a name="l00087"></a>00087 <span class="keywordflow">if</span> (phi < 0.) phi += 2.f*<a class="code" href="pbrt_8h.html#e71449b1cc6e6250b91f539153a7a0d3">M_PI</a>;
<a name="l00088"></a>00088 <span class="comment">// Test paraboloid intersection against clipping parameters</span>
<a name="l00089"></a>00089 <span class="keywordflow">if</span> (phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> < <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> || phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> > <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> || phi > <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>) {
<a name="l00090"></a>00090 <span class="keywordflow">if</span> (thit == t1) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00091"></a>00091 thit = t1;
<a name="l00092"></a>00092 <span class="keywordflow">if</span> (t1 > ray.<a class="code" href="classRay.html#aa6c29ceae8edc5c9d37e879daa1557a">maxt</a>) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00093"></a>00093 <span class="comment">// Compute paraboloid inverse mapping</span>
<a name="l00094"></a>00094 phit = ray(thit);
<a name="l00095"></a>00095 phi = atan2f(phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>, phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>);
<a name="l00096"></a>00096 <span class="keywordflow">if</span> (phi < 0.) phi += 2.f*<a class="code" href="pbrt_8h.html#e71449b1cc6e6250b91f539153a7a0d3">M_PI</a>;
<a name="l00097"></a>00097 <span class="keywordflow">if</span> (phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> < <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> || phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> > <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> || phi > <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>)
<a name="l00098"></a>00098 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00099"></a>00099 }
<a name="l00100"></a>00100 <span class="comment">// Find parametric representation of paraboloid hit</span>
<a name="l00101"></a>00101 <span class="keywordtype">float</span> u = phi / <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>;
<a name="l00102"></a>00102 <span class="keywordtype">float</span> v = (phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>-<a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>) / (<a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a>-<a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>);
<a name="l00103"></a>00103 <span class="comment">// Compute parabaloid \dpdu and \dpdv</span>
<a name="l00104"></a>00104 <a class="code" href="classVector.html">Vector</a> dpdu(-<a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a> * phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>, <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a> * phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>, 0.);
<a name="l00105"></a>00105 <a class="code" href="classVector.html">Vector</a> dpdv = (<a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> - <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>) *
<a name="l00106"></a>00106 <a class="code" href="classVector.html">Vector</a>(phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> / (2.f * phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>), phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a> / (2.f * phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>), 1.);
<a name="l00107"></a>00107 <span class="comment">// Compute parabaloid \dndu and \dndv</span>
<a name="l00108"></a>00108 <a class="code" href="classVector.html">Vector</a> d2Pduu = -<a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a> * <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a> *
<a name="l00109"></a>00109 <a class="code" href="classVector.html">Vector</a>(phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>, phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>, 0);
<a name="l00110"></a>00110 Vector d2Pduv = (<a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> - <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>) * <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a> *
<a name="l00111"></a>00111 Vector(-phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a> / (2.f * phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>),
<a name="l00112"></a>00112 phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> / (2.f * phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>),
<a name="l00113"></a>00113 0);
<a name="l00114"></a>00114 Vector d2Pdvv = -(<a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> - <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>) * (<a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> - <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>) *
<a name="l00115"></a>00115 Vector(phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>/(4.f*phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>*phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>),
<a name="l00116"></a>00116 phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>/(4.f*phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>*phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>),
<a name="l00117"></a>00117 0.);
<a name="l00118"></a>00118 <span class="comment">// Compute coefficients for fundamental forms</span>
<a name="l00119"></a>00119 <span class="keywordtype">float</span> E = <a class="code" href="geometry_8h.html#ad0d36688d190693f70a5c9ef9342914">Dot</a>(dpdu, dpdu);
<a name="l00120"></a>00120 <span class="keywordtype">float</span> F = <a class="code" href="geometry_8h.html#ad0d36688d190693f70a5c9ef9342914">Dot</a>(dpdu, dpdv);
<a name="l00121"></a>00121 <span class="keywordtype">float</span> G = <a class="code" href="geometry_8h.html#ad0d36688d190693f70a5c9ef9342914">Dot</a>(dpdv, dpdv);
<a name="l00122"></a>00122 Vector <a class="code" href="util_8cpp.html#0240ac851181b84ac374872dc5434ee4">N</a> = <a class="code" href="geometry_8h.html#46448bfa3df1c2de5e3b763f163866a4">Normalize</a>(<a class="code" href="geometry_8h.html#340d6d877ba46443c9ad20e7c0d0668f">Cross</a>(dpdu, dpdv));
<a name="l00123"></a>00123 <span class="keywordtype">float</span> e = <a class="code" href="geometry_8h.html#ad0d36688d190693f70a5c9ef9342914">Dot</a>(N, d2Pduu);
<a name="l00124"></a>00124 <span class="keywordtype">float</span> f = <a class="code" href="geometry_8h.html#ad0d36688d190693f70a5c9ef9342914">Dot</a>(N, d2Pduv);
<a name="l00125"></a>00125 <span class="keywordtype">float</span> g = <a class="code" href="geometry_8h.html#ad0d36688d190693f70a5c9ef9342914">Dot</a>(N, d2Pdvv);
<a name="l00126"></a>00126 <span class="comment">// Compute \dndu and \dndv from fundamental form coefficients</span>
<a name="l00127"></a>00127 <span class="keywordtype">float</span> invEGF2 = 1.f / (E*G - F*F);
<a name="l00128"></a>00128 Vector dndu = (f*F - e*G) * invEGF2 * dpdu +
<a name="l00129"></a>00129 (e*F - f*E) * invEGF2 * dpdv;
<a name="l00130"></a>00130 Vector dndv = (g*F - f*G) * invEGF2 * dpdu +
<a name="l00131"></a>00131 (f*F - g*E) * invEGF2 * dpdv;
<a name="l00132"></a>00132 <span class="comment">// Initialize _DifferentialGeometry_ from parametric information</span>
<a name="l00133"></a>00133 *dg = <a class="code" href="structDifferentialGeometry.html">DifferentialGeometry</a>(<a class="code" href="classShape.html#7c8a34f400c3a5ad7cfd2395836cda03">ObjectToWorld</a>(phit),
<a name="l00134"></a>00134 <a class="code" href="classShape.html#7c8a34f400c3a5ad7cfd2395836cda03">ObjectToWorld</a>(dpdu),
<a name="l00135"></a>00135 <a class="code" href="classShape.html#7c8a34f400c3a5ad7cfd2395836cda03">ObjectToWorld</a>(dpdv),
<a name="l00136"></a>00136 <a class="code" href="classShape.html#7c8a34f400c3a5ad7cfd2395836cda03">ObjectToWorld</a>(dndu),
<a name="l00137"></a>00137 <a class="code" href="classShape.html#7c8a34f400c3a5ad7cfd2395836cda03">ObjectToWorld</a>(dndv),
<a name="l00138"></a>00138 u, v, <span class="keyword">this</span>);
<a name="l00139"></a>00139 <span class="comment">// Update _tHit_ for quadric intersection</span>
<a name="l00140"></a>00140 *tHit = thit;
<a name="l00141"></a>00141 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00142"></a>00142 }
<a name="l00143"></a>00143
<a name="l00144"></a><a class="code" href="classParaboloid.html#daa2f7b37d435552d09ab7456cdf6b82">00144</a> <span class="keywordtype">bool</span> <a class="code" href="classParaboloid.html#daa2f7b37d435552d09ab7456cdf6b82">Paraboloid::IntersectP</a>(<span class="keyword">const</span> <a class="code" href="classRay.html">Ray</a> &r)<span class="keyword"> const </span>{
<a name="l00145"></a>00145 <span class="keywordtype">float</span> phi;
<a name="l00146"></a>00146 <a class="code" href="classPoint.html">Point</a> phit;
<a name="l00147"></a>00147 <span class="comment">// Transform _Ray_ to object space</span>
<a name="l00148"></a>00148 <a class="code" href="classRay.html">Ray</a> ray;
<a name="l00149"></a>00149 <a class="code" href="classShape.html#72cf45b4c359fc22b3264a02e932324e">WorldToObject</a>(r, &ray);
<a name="l00150"></a>00150 <span class="comment">// Compute quadratic paraboloid coefficients</span>
<a name="l00151"></a>00151 <span class="keywordtype">float</span> k = <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a>/(<a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>*<a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a>);
<a name="l00152"></a>00152 <span class="keywordtype">float</span> A = k*(ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#ca49165049a1e21ae47afcfc078819ed">x</a> * ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#ca49165049a1e21ae47afcfc078819ed">x</a> + ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#81be9102fca6d9beea3efef522c4c09d">y</a> * ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#81be9102fca6d9beea3efef522c4c09d">y</a>);
<a name="l00153"></a>00153 <span class="keywordtype">float</span> B = 2*k*(ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#ca49165049a1e21ae47afcfc078819ed">x</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> + ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#81be9102fca6d9beea3efef522c4c09d">y</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>) -
<a name="l00154"></a>00154 ray.<a class="code" href="classRay.html#5bbfc94e178e0a050b51200acc579069">d</a>.<a class="code" href="classVector.html#0e84237d0830d5c459bfa5676b5fbfba">z</a>;
<a name="l00155"></a>00155 <span class="keywordtype">float</span> C = k*(ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a> + ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a> * ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>) -
<a name="l00156"></a>00156 ray.<a class="code" href="classRay.html#1014d000992e8ac3b92f150ad2a5cffe">o</a>.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a>;
<a name="l00157"></a>00157 <span class="comment">// Solve quadratic equation for _t_ values</span>
<a name="l00158"></a>00158 <span class="keywordtype">float</span> t0, t1;
<a name="l00159"></a>00159 <span class="keywordflow">if</span> (!<a class="code" href="pbrt_8h.html#14bbcf80fc40915df82a84e6eb2dfb3b">Quadratic</a>(A, B, C, &t0, &t1))
<a name="l00160"></a>00160 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00161"></a>00161 <span class="comment">// Compute intersection distance along ray</span>
<a name="l00162"></a>00162 <span class="keywordflow">if</span> (t0 > ray.<a class="code" href="classRay.html#aa6c29ceae8edc5c9d37e879daa1557a">maxt</a> || t1 < ray.<a class="code" href="classRay.html#ded3b6e00c215611ebd61a6965560ba0">mint</a>)
<a name="l00163"></a>00163 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00164"></a>00164 <span class="keywordtype">float</span> thit = t0;
<a name="l00165"></a>00165 <span class="keywordflow">if</span> (t0 < ray.<a class="code" href="classRay.html#ded3b6e00c215611ebd61a6965560ba0">mint</a>) {
<a name="l00166"></a>00166 thit = t1;
<a name="l00167"></a>00167 <span class="keywordflow">if</span> (thit > ray.<a class="code" href="classRay.html#aa6c29ceae8edc5c9d37e879daa1557a">maxt</a>) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00168"></a>00168 }
<a name="l00169"></a>00169 <span class="comment">// Compute paraboloid inverse mapping</span>
<a name="l00170"></a>00170 phit = ray(thit);
<a name="l00171"></a>00171 phi = atan2f(phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>, phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>);
<a name="l00172"></a>00172 <span class="keywordflow">if</span> (phi < 0.) phi += 2.f*<a class="code" href="pbrt_8h.html#e71449b1cc6e6250b91f539153a7a0d3">M_PI</a>;
<a name="l00173"></a>00173 <span class="comment">// Test paraboloid intersection against clipping parameters</span>
<a name="l00174"></a>00174 <span class="keywordflow">if</span> (phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> < <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> || phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> > <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> || phi > <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>) {
<a name="l00175"></a>00175 <span class="keywordflow">if</span> (thit == t1) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00176"></a>00176 thit = t1;
<a name="l00177"></a>00177 <span class="keywordflow">if</span> (t1 > ray.<a class="code" href="classRay.html#aa6c29ceae8edc5c9d37e879daa1557a">maxt</a>) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00178"></a>00178 <span class="comment">// Compute paraboloid inverse mapping</span>
<a name="l00179"></a>00179 phit = ray(thit);
<a name="l00180"></a>00180 phi = atan2f(phit.<a class="code" href="classPoint.html#6101960c8d2d4e8ea1d32c9234bbeb8d">y</a>, phit.<a class="code" href="classPoint.html#05dfe2dfbde813ad234b514f30e662f1">x</a>);
<a name="l00181"></a>00181 <span class="keywordflow">if</span> (phi < 0.) phi += 2.f*<a class="code" href="pbrt_8h.html#e71449b1cc6e6250b91f539153a7a0d3">M_PI</a>;
<a name="l00182"></a>00182 <span class="keywordflow">if</span> (phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> < <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> || phit.<a class="code" href="classPoint.html#9a666531e0e99adff132be93d2407d0c">z</a> > <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> || phi > <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>)
<a name="l00183"></a>00183 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00184"></a>00184 }
<a name="l00185"></a>00185 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00186"></a>00186 }
<a name="l00187"></a><a class="code" href="classParaboloid.html#dfca2ff655627c3063325899dfdaba9f">00187</a> <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#dfca2ff655627c3063325899dfdaba9f">Paraboloid::Area</a>()<span class="keyword"> const </span>{
<a name="l00188"></a>00188 <span class="keywordflow">return</span> <a class="code" href="classParaboloid.html#9f84ca3d9880f61e57702a3138643a0c">phiMax</a>/12.0f *
<a name="l00189"></a>00189 (powf(1+4*<a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a>, 1.5f) - powf(1+4*<a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a>, 1.5f));
<a name="l00190"></a>00190 }
<a name="l00191"></a><a class="code" href="paraboloid_8cpp.html#3ca5abc6928b2220103b7f077e0471e1">00191</a> <span class="keyword">extern</span> <span class="stringliteral">"C"</span> <a class="code" href="pbrt_8h.html#808e08638be3cba36e36759e5b150de0">DLLEXPORT</a> <a class="code" href="classShape.html">Shape</a> *<a class="code" href="cone_8cpp.html#3ca5abc6928b2220103b7f077e0471e1">CreateShape</a>(<span class="keyword">const</span> <a class="code" href="classTransform.html">Transform</a> &o2w,
<a name="l00192"></a>00192 <span class="keywordtype">bool</span> <a class="code" href="classShape.html#337c63db30f17a31ac81a8921ec97872">reverseOrientation</a>, <span class="keyword">const</span> <a class="code" href="classParamSet.html">ParamSet</a> &params) {
<a name="l00193"></a>00193 <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#3c79e0b32bcc1dfc04a383813fbc061d">radius</a> = params.<a class="code" href="classParamSet.html#87143fd8e73a75082179a110d42531a4">FindOneFloat</a>( <span class="stringliteral">"radius"</span>, 1 );
<a name="l00194"></a>00194 <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#e92c33df6de848c8cf8ec51a946f98a1">zmin</a> = params.<a class="code" href="classParamSet.html#87143fd8e73a75082179a110d42531a4">FindOneFloat</a>( <span class="stringliteral">"zmin"</span>, 0 );
<a name="l00195"></a>00195 <span class="keywordtype">float</span> <a class="code" href="classParaboloid.html#2d660d4d1dae4e4e75fb01b64ab7e3d6">zmax</a> = params.<a class="code" href="classParamSet.html#87143fd8e73a75082179a110d42531a4">FindOneFloat</a>( <span class="stringliteral">"zmax"</span>, 1 );
<a name="l00196"></a>00196 <span class="keywordtype">float</span> phimax = params.<a class="code" href="classParamSet.html#87143fd8e73a75082179a110d42531a4">FindOneFloat</a>( <span class="stringliteral">"phimax"</span>, 360 );
<a name="l00197"></a>00197 <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="classParaboloid.html#76adacc8588508839bb117158369936a">Paraboloid</a>(o2w, reverseOrientation, radius, zmin, zmax, phimax);
<a name="l00198"></a>00198 }
</pre></div></div>
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