| Irrlicht 3D Engine |

triangle3d.h
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    00001 // Copyright (C) 2002-2012 Nikolaus Gebhardt
    00002 // This file is part of the "Irrlicht Engine".
    00003 // For conditions of distribution and use, see copyright notice in irrlicht.h
    00004
    00005 #ifndef __IRR_TRIANGLE_3D_H_INCLUDED__
    00006 #define __IRR_TRIANGLE_3D_H_INCLUDED__
    00007
    00008 #include "vector3d.h"
    00009 #include "line3d.h"
    00010 #include "plane3d.h"
    00011 #include "aabbox3d.h"
    00012
    00013 namespace irr
    00014 {
    00015 namespace core
    00016 {
    00017
    00019     template <class T>
    00020     class triangle3d
    00021     {
    00022     public:
    00023
    00025         triangle3d() {}
    00027         triangle3d(vector3d<T> v1, vector3d<T> v2, vector3d<T> v3) : pointA(v1), pointB(v2), pointC(v3) {}
    00028
    00030         bool operator==(const triangle3d<T>& other) const
    00031         {
    00032             return other.pointA==pointA && other.pointB==pointB && other.pointC==pointC;
    00033         }
    00034
    00036         bool operator!=(const triangle3d<T>& other) const
    00037         {
    00038             return !(*this==other);
    00039         }
    00040
    00042
    00044         bool isTotalInsideBox(const aabbox3d<T>& box) const
    00045         {
    00046             return (box.isPointInside(pointA) &&
    00047                 box.isPointInside(pointB) &&
    00048                 box.isPointInside(pointC));
    00049         }
    00050
    00052
    00054         bool isTotalOutsideBox(const aabbox3d<T>& box) const
    00055         {
    00056             return ((pointA.X > box.MaxEdge.X && pointB.X > box.MaxEdge.X && pointC.X > box.MaxEdge.X) ||
    00057
    00058                 (pointA.Y > box.MaxEdge.Y && pointB.Y > box.MaxEdge.Y && pointC.Y > box.MaxEdge.Y) ||
    00059                 (pointA.Z > box.MaxEdge.Z && pointB.Z > box.MaxEdge.Z && pointC.Z > box.MaxEdge.Z) ||
    00060                 (pointA.X < box.MinEdge.X && pointB.X < box.MinEdge.X && pointC.X < box.MinEdge.X) ||
    00061                 (pointA.Y < box.MinEdge.Y && pointB.Y < box.MinEdge.Y && pointC.Y < box.MinEdge.Y) ||
    00062                 (pointA.Z < box.MinEdge.Z && pointB.Z < box.MinEdge.Z && pointC.Z < box.MinEdge.Z));
    00063         }
    00064
    00066
    00068         core::vector3d<T> closestPointOnTriangle(const core::vector3d<T>& p) const
    00069         {
    00070             const core::vector3d<T> rab = line3d<T>(pointA, pointB).getClosestPoint(p);
    00071             const core::vector3d<T> rbc = line3d<T>(pointB, pointC).getClosestPoint(p);
    00072             const core::vector3d<T> rca = line3d<T>(pointC, pointA).getClosestPoint(p);
    00073
    00074             const T d1 = rab.getDistanceFrom(p);
    00075             const T d2 = rbc.getDistanceFrom(p);
    00076             const T d3 = rca.getDistanceFrom(p);
    00077
    00078             if (d1 < d2)
    00079                 return d1 < d3 ? rab : rca;
    00080
    00081             return d2 < d3 ? rbc : rca;
    00082         }
    00083
    00085         /*
    00086         \param p Point to test. Assumes that this point is already
    00087         on the plane of the triangle.
    00088         \return True if the point is inside the triangle, otherwise false. */
    00089         bool isPointInside(const vector3d<T>& p) const
    00090         {
    00091             vector3d<f64> af64((f64)pointA.X, (f64)pointA.Y, (f64)pointA.Z);
    00092             vector3d<f64> bf64((f64)pointB.X, (f64)pointB.Y, (f64)pointB.Z);
    00093             vector3d<f64> cf64((f64)pointC.X, (f64)pointC.Y, (f64)pointC.Z);
    00094             vector3d<f64> pf64((f64)p.X, (f64)p.Y, (f64)p.Z);
    00095             return (isOnSameSide(pf64, af64, bf64, cf64) &&
    00096                 isOnSameSide(pf64, bf64, af64, cf64) &&
    00097                 isOnSameSide(pf64, cf64, af64, bf64));
    00098         }
    00099
    00101
    00108         bool isPointInsideFast(const vector3d<T>& p) const
    00109         {
    00110             const vector3d<T> a = pointC - pointA;
    00111             const vector3d<T> b = pointB - pointA;
    00112             const vector3d<T> c = p - pointA;
    00113
    00114             const f64 dotAA = a.dotProduct( a);
    00115             const f64 dotAB = a.dotProduct( b);
    00116             const f64 dotAC = a.dotProduct( c);
    00117             const f64 dotBB = b.dotProduct( b);
    00118             const f64 dotBC = b.dotProduct( c);
    00119
    00120             // get coordinates in barycentric coordinate system
    00121             const f64 invDenom =  1/(dotAA * dotBB - dotAB * dotAB);
    00122             const f64 u = (dotBB * dotAC - dotAB * dotBC) * invDenom;
    00123             const f64 v = (dotAA * dotBC - dotAB * dotAC ) * invDenom;
    00124
    00125             // We count border-points as inside to keep downward compatibility.
    00126             // Rounding-error also needed for some test-cases.
    00127             return (u > -ROUNDING_ERROR_f32) && (v >= 0) && (u + v < 1+ROUNDING_ERROR_f32);
    00128
    00129         }
    00130
    00131
    00133
    00136         bool getIntersectionWithLimitedLine(const line3d<T>& line,
    00137             vector3d<T>& outIntersection) const
    00138         {
    00139             return getIntersectionWithLine(line.start,
    00140                 line.getVector(), outIntersection) &&
    00141                 outIntersection.isBetweenPoints(line.start, line.end);
    00142         }
    00143
    00144
    00146
    00154         bool getIntersectionWithLine(const vector3d<T>& linePoint,
    00155             const vector3d<T>& lineVect, vector3d<T>& outIntersection) const
    00156         {
    00157             if (getIntersectionOfPlaneWithLine(linePoint, lineVect, outIntersection))
    00158                 return isPointInside(outIntersection);
    00159
    00160             return false;
    00161         }
    00162
    00163
    00165
    00169         bool getIntersectionOfPlaneWithLine(const vector3d<T>& linePoint,
    00170             const vector3d<T>& lineVect, vector3d<T>& outIntersection) const
    00171         {
    00172             // Work with f64 to get more precise results (makes enough difference to be worth the casts).
    00173             const vector3d<f64> linePointf64(linePoint.X, linePoint.Y, linePoint.Z);
    00174             const vector3d<f64> lineVectf64(lineVect.X, lineVect.Y, lineVect.Z);
    00175             vector3d<f64> outIntersectionf64;
    00176
    00177             core::triangle3d<irr::f64> trianglef64(vector3d<f64>((f64)pointA.X, (f64)pointA.Y, (f64)pointA.Z)
    00178                                         ,vector3d<f64>((f64)pointB.X, (f64)pointB.Y, (f64)pointB.Z)
    00179                                         , vector3d<f64>((f64)pointC.X, (f64)pointC.Y, (f64)pointC.Z));
    00180             const vector3d<irr::f64> normalf64 = trianglef64.getNormal().normalize();
    00181             f64 t2;
    00182
    00183             if ( core::iszero ( t2 = normalf64.dotProduct(lineVectf64) ) )
    00184                 return false;
    00185
    00186             f64 d = trianglef64.pointA.dotProduct(normalf64);
    00187             f64 t = -(normalf64.dotProduct(linePointf64) - d) / t2;
    00188             outIntersectionf64 = linePointf64 + (lineVectf64 * t);
    00189
    00190             outIntersection.X = (T)outIntersectionf64.X;
    00191             outIntersection.Y = (T)outIntersectionf64.Y;
    00192             outIntersection.Z = (T)outIntersectionf64.Z;
    00193             return true;
    00194         }
    00195
    00196
    00198
    00199         vector3d<T> getNormal() const
    00200         {
    00201             return (pointB - pointA).crossProduct(pointC - pointA);
    00202         }
    00203
    00205
    00210         bool isFrontFacing(const vector3d<T>& lookDirection) const
    00211         {
    00212             const vector3d<T> n = getNormal().normalize();
    00213             const f32 d = (f32)n.dotProduct(lookDirection);
    00214             return F32_LOWER_EQUAL_0(d);
    00215         }
    00216
    00218         plane3d<T> getPlane() const
    00219         {
    00220             return plane3d<T>(pointA, pointB, pointC);
    00221         }
    00222
    00224         T getArea() const
    00225         {
    00226             return (pointB - pointA).crossProduct(pointC - pointA).getLength() * 0.5f;
    00227
    00228         }
    00229
    00231         void set(const core::vector3d<T>& a, const core::vector3d<T>& b, const core::vector3d<T>& c)
    00232         {
    00233             pointA = a;
    00234             pointB = b;
    00235             pointC = c;
    00236         }
    00237
    00239         vector3d<T> pointA;
    00240         vector3d<T> pointB;
    00241         vector3d<T> pointC;
    00242
    00243     private:
    00244         // Using f64 instead of <T> to avoid integer overflows when T=int (maybe also less floating point troubles).
    00245         bool isOnSameSide(const vector3d<f64>& p1, const vector3d<f64>& p2,
    00246             const vector3d<f64>& a, const vector3d<f64>& b) const
    00247         {
    00248             vector3d<f64> bminusa = b - a;
    00249             vector3d<f64> cp1 = bminusa.crossProduct(p1 - a);
    00250             vector3d<f64> cp2 = bminusa.crossProduct(p2 - a);
    00251             f64 res = cp1.dotProduct(cp2);
    00252             if ( res < 0 )
    00253             {
    00254                 // This catches some floating point troubles.
    00255                 // Unfortunately slightly expensive and we don't really know the best epsilon for iszero.
    00256                 vector3d<f64> cp1 = bminusa.normalize().crossProduct((p1 - a).normalize());
    00257                 if (    core::iszero(cp1.X, (f64)ROUNDING_ERROR_f32)
    00258                     &&  core::iszero(cp1.Y, (f64)ROUNDING_ERROR_f32)
    00259                     &&  core::iszero(cp1.Z, (f64)ROUNDING_ERROR_f32) )
    00260                 {
    00261                     res = 0.f;
    00262                 }
    00263             }
    00264             return (res >= 0.0f);
    00265         }
    00266     };
    00267
    00268
    00270     typedef triangle3d<f32> triangle3df;
    00271
    00273     typedef triangle3d<s32> triangle3di;
    00274
    00275 } // end namespace core
    00276 } // end namespace irr
    00277
    00278 #endif
    00279