Geo_Triangle.h

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#ifndef SimTK_SIMMATH_GEO_TRIANGLE_H_
#define SimTK_SIMMATH_GEO_TRIANGLE_H_

/* -------------------------------------------------------------------------- *
 *                        Simbody(tm): SimTKmath                              *
 * -------------------------------------------------------------------------- *
 * This is part of the SimTK biosimulation toolkit originating from           *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody.  *
 *                                                                            *
 * Portions copyright (c) 2011-12 Stanford University and the Authors.        *
 * Authors: Michael Sherman                                                   *
 * Contributors:                                                              *
 *                                                                            *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may    *
 * not use this file except in compliance with the License. You may obtain a  *
 * copy of the License at http://www.apache.org/licenses/LICENSE-2.0.         *
 *                                                                            *
 * Unless required by applicable law or agreed to in writing, software        *
 * distributed under the License is distributed on an "AS IS" BASIS,          *
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   *
 * See the License for the specific language governing permissions and        *
 * limitations under the License.                                             *
 * -------------------------------------------------------------------------- */

#include "SimTKcommon.h"
#include "simmath/internal/common.h"
#include "simmath/internal/Geo.h"
#include "simmath/internal/Geo_Point.h"
#include "simmath/internal/Geo_LineSeg.h"

#include <cassert>
#include <cmath>
#include <algorithm>

namespace SimTK {

//==============================================================================
//                              GEO TRIANGLE
//==============================================================================
template <class P>
class Geo::Triangle_ {
typedef P               RealP;
typedef Vec<2,P>        Vec2P;
typedef Vec<3,P>        Vec3P;
typedef UnitVec<P,1>    UnitVec3P;
public:
Triangle_() {}
Triangle_(const Vec3P& v0, const Vec3P& v1, const Vec3P& v2)
{  setVertices(v0,v1,v2); }
explicit Triangle_(const Vec3P* vertices)
{   setVertices(vertices); }
explicit Triangle_(const Vec3P** vertexPointers)
{   setVertices(*vertexPointers[0], *vertexPointers[1], *vertexPointers[2]); }

Triangle_& setVertex(int i, const Vec3P& p)
{   assert(0<=i && i<3); v[i] = p; return *this; }
Triangle_& setVertices(const Vec3P& v0, const Vec3P& v1, const Vec3P& v2)
{   v[0]=v0; v[1]=v1; v[2]=v2; return *this; }
Triangle_& setVertices(const Vec3P* vertices)
{   v[0]=vertices[0]; v[1]=vertices[1]; v[2]=vertices[2]; return *this; }

const Vec3P& getVertex(int i) const
{   SimTK_INDEXCHECK(i,3,"Geo::Triangle_::getVertex()"); 
    return v[i]; }
Vec3P& updVertex(int i)
{   SimTK_INDEXCHECK(i,3,"Geo::Triangle_::updVertex()");  
    return v[i]; }

const Vec3P& operator[](int i) const {return getVertex(i);}
Vec3P& operator[](int i) {return updVertex(i);}

LineSeg_<P> getEdge(int i) const
{   SimTK_INDEXCHECK(i,3,"Geo::Triangle_::getEdge()");
    return LineSeg_<P>(v[i],v[(i+1)%3]); }

Vec3P findPoint(const Vec2P& uv) const
{   return uv[0]*v[0] + uv[1]*v[1] + (1-uv[0]-uv[1])*v[2]; }

Vec3P findCentroid() const
{   return (v[0]+v[1]+v[2]) / RealP(3); }

UnitVec3P calcUnitNormal() const 
{   return UnitVec3P((v[1]-v[0]) % (v[2]-v[0])); }

Sphere_<P> calcBoundingSphere() const
{   return Geo::Point_<P>::calcBoundingSphere(v[0],v[1],v[2]); }

RealP calcArea() const 
{   return ((v[1]-v[0]) % (v[2]-v[0])).norm() / 2; }

RealP calcAreaSqr() const 
{   return ((v[1]-v[0]) % (v[2]-v[0])).normSqr() / 4; }

Vec3P findNearestPoint(const Vec3P& position, Vec2P& uv) const
{SimTK_ASSERT_ALWAYS(!"implemented", 
"Geo::Triangle_::findNearestPoint(): Not implemented yet.");
return Vec3P();}

bool intersectsRay(const Vec3P& origin, const UnitVec3P& direction, 
                   RealP& distance, Vec2P& uv) const
{SimTK_ASSERT_ALWAYS(!"implemented", 
"Geo::Triangle_::intersectsRay(): Not implemented yet."); return false;}

SimTK_SIMMATH_EXPORT bool overlapsTriangle(const Triangle_<P>& other) const;
SimTK_SIMMATH_EXPORT bool intersectsTriangle(const Triangle_<P>& other, LineSeg_<P>& seg,
                        bool& isCoplanar) const;

private:
// Vertices in the order they were supplied in the constructor.
Vec3P   v[3];   
};

} // namespace SimTK

#endif // SimTK_SIMMATH_GEO_TRIANGLE_H_