GteIntpLinearNonuniform3.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

// Linear interpolation of a network of triangles whose vertices are of the
// form (x,y,z,f(x,y,z)).  The function samples are F[i] and represent
// f(x[i],y[i],z[i]), where i is the index of the input vertex
// (x[i],y[i],z[i]) to Delaunay3.
//
// The TetrahedronMesh interface must support the following:
//   int GetContainingTetrahedron(Vector3<Real> const&) const;
//   bool GetIndices(int, std::array<int, 4>&) const;
//   bool GetBarycentrics(int, Vector3<Real> const&, Real[4]) const;

#include <LowLevel/GteLogger.h>
#include <Mathematics/GteVector3.h>

namespace gte
{

template <typename Real, typename TetrahedronMesh>
class IntpLinearNonuniform3
{
public:
    // Construction.
    IntpLinearNonuniform3(TetrahedronMesh const& mesh, Real const* F);

    // Linear interpolation.  The return value is 'true' if and only if the
    // input point is in the convex hull of the input vertices, in which case
    // the interpolation is valid.
    bool operator()(Vector3<Real> const& P, Real& F) const;

private:
    TetrahedronMesh const* mMesh;
    Real const* mF;
};


template <typename Real, typename TetrahedronMesh>
IntpLinearNonuniform3<Real, TetrahedronMesh>::IntpLinearNonuniform3(
    TetrahedronMesh const& mesh, Real const* F)
    :
    mMesh(&mesh),
    mF(F)
{
    LogAssert(mF != nullptr, "Invalid input.");
}

template <typename Real, typename TetrahedronMesh>
bool IntpLinearNonuniform3<Real, TetrahedronMesh>::operator()(
    Vector3<Real> const& P, Real& F) const
{
    int t = mMesh->GetContainingTetrahedron(P);
    if (t == -1)
    {
        // The point is outside the tetrahedralization.
        return false;
    }

    // Get the barycentric coordinates of P with respect to the tetrahedron,
    // P = b0*V0 + b1*V1 + b2*V2 + b3*V3, where b0 + b1 + b2 + b3 = 1.
    std::array<Real, 4> bary;
    if (!mMesh->GetBarycentrics(t, P, bary))
    {
        LogWarning("P is in a needle-like, flat, or degenerate tetrahedron.");
        return false;
    }

    // The result is a barycentric combination of function values.
    std::array<int, 4> indices;
    mMesh->GetIndices(t, indices);
    F = bary[0] * mF[indices[0]] + bary[1] * mF[indices[1]] +
        bary[2] * mF[indices[2]] + bary[3] * mF[indices[4]];
    return true;
}


}