math_utils.h

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**  FougTools
**  Copyright Fougue (30 Mar. 2015)
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**
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#pragma once

#include "occtools.h"

#include <utility>
#include <gp_Ax3.hxx>
#include <gp_Vec.hxx>
#include <gp_Trsf.hxx>
#include <TopAbs_Orientation.hxx>
class Poly_Triangle;
class TColgp_Array1OfPnt;

namespace occ {

class OCCTOOLS_EXPORT MathUtils
{
public:
    static gp_Trsf displacement(const gp_Ax3& srcSys, const gp_Ax3& dstSys);
    static gp_Trsf transformation(const gp_Ax3& srcSys, const gp_Ax3& dstSys);
    static gp_Trsf transformation(const gp_Ax3& dstSys);
    static gp_Trsf transformation(const gp_Quaternion& q, const gp_Vec& vec);

    static gp_Pnt projectPointOnPlane(const gp_Pnt& p, const gp_Vec& n);
    static std::pair<gp_Pnt, bool> projectPointOnTriangle(
            const gp_Pnt& p,
            const gp_Pnt& v0, const gp_Pnt& v1, const gp_Pnt& v2);

    static Standard_Real euclideanNorm(const gp_Vec& vec);
    static Standard_Real squaredEuclideanNorm(const gp_Vec& vec);
    static Standard_Real manhattanNorm(const gp_Vec& vec);
    static Standard_Real maximumNorm(const gp_Vec& vec);

    template<typename NORM>
    static bool isNull(const gp_Vec& vec, const NORM& norm);

    static gp_Vec triangleNormal(
            const TColgp_Array1OfPnt& nodes,
            const Poly_Triangle& triangle,
            TopAbs_Orientation ori = TopAbs_FORWARD);

    template<typename OCC_PNT_VEC, typename TEXT_STREAM>
    static TEXT_STREAM& printOccPntVec(TEXT_STREAM& ts, const OCC_PNT_VEC& v);
};

const gp_Pnt2d origin2d(0, 0);
const gp_Dir2d xDir2d(1, 0);
const gp_Dir2d yDir2d(0, 1);

const gp_Pnt origin3d(0, 0, 0);
const gp_Dir xDir3d(1, 0, 0);
const gp_Dir yDir3d(0, 1, 0);
const gp_Dir zDir3d(0, 0, 1);

} // namespace occ

OCCTOOLS_EXPORT gp_Vec operator-(const gp_Pnt& p1, const gp_Pnt& p2);
OCCTOOLS_EXPORT gp_Pnt operator-(const gp_Pnt& p, const gp_Vec& v);
OCCTOOLS_EXPORT gp_Pnt operator+(const gp_Pnt& p, const gp_Vec& v);

template<typename TEXT_STREAM>
TEXT_STREAM& operator<<(TEXT_STREAM& ts, const gp_Pnt& p);

template<typename TEXT_STREAM>
TEXT_STREAM& operator<<(TEXT_STREAM& ts, const gp_Vec& v);

template<typename TEXT_STREAM>
TEXT_STREAM& operator<<(TEXT_STREAM& ts, const gp_Dir& d);

//--
//-- Implementation
//--

template<typename NORM>
bool occ::MathUtils::isNull(const gp_Vec& vec, const NORM& norm)
{
    return norm(vec) <= 0.000000000001;
}

template<typename OCC_PNT_VEC, typename TEXT_STREAM>
TEXT_STREAM &occ::MathUtils::printOccPntVec(TEXT_STREAM &ts, const OCC_PNT_VEC &v)
{
    return ts << "(" << v.X() << ", " << v.Y() << ", " << v.Z() << ")";
}

template<typename TEXT_STREAM>
TEXT_STREAM& operator<<(TEXT_STREAM& ts, const gp_Pnt& p)
{
    return occ::MathUtils::printOccPntVec(ts, p);
}

template<typename TEXT_STREAM>
TEXT_STREAM& operator<<(TEXT_STREAM& ts, const gp_Vec& v)
{
    return occ::MathUtils::printOccPntVec(ts, v);
}

template<typename TEXT_STREAM>
TEXT_STREAM& operator<<(TEXT_STREAM& ts, const gp_Dir& d)
{
    return occ::MathUtils::printOccPntVec(ts, d);
}