四面体的重心坐标 [英] Barycentric coordinates of a tetrahedron

问题描述

我想寻求有关四面体的重心坐标的帮助：

I would like to ask for help regarding barycentric coordinates of a tetrahedron:

按照我在这里找到的方法：
http://www.cdsimpson.net/2014/10/barycentric-coordinates.html
i实现了C ++函数，用于查找四面体中点的重心坐标：

Following an approach I found here: http://www.cdsimpson.net/2014/10/barycentric-coordinates.html i implemented a C++ function for finding barycentric coordinates of a point in a tetrahedron:

float ScTP(const Vec &a, const Vec &b, const Vec &c)
{
    // computes scalar triple product
    return Dot(a, Cross(b, c));
}

Vec4f bary_tet(Vec3f a, Vec3f b, Vec3f c, Vec3f d, Vec3f p)
{
    float va, vb, vc, vd, v;
    Vec3f vap = p - a;
    Vec3f vbp = p - b;
    Vec3f vcp = p - c;
    Vec3f vdp = p - d;

    Vec3f vab = b - a;
    Vec3f vac = c - a;
    Vec3f vad = d - a;

    Vec3f vbc = c - b;
    Vec3f vbd = d - b;
    // ScTP computes the scalar triple product
    va = ScTP(vbp, vbd, vbc) * 1 / 6;
    vb = ScTP(vap, vac, vad) * 1 / 6;
    vc = ScTP(vap, vad, vab) * 1 / 6;
    vd = ScTP(vap, vab, vac) * 1 / 6;
    v = 1 / ScTP(vab, vac, vad) * 1 / 6;
    return Vec4f(va*v, vb*v, vc*v, vd*v);
}

但是，我的代码似乎计算的重心坐标略有错误-
将我的结果与此处的参考实现进行比较：
http://dennis2society.de/painless -tetrahedral-barycentric-mapping
我的四个重心值分别小于参考实现中
计算的值。

However, my code seems to calculate slightly wrong barycentric coordinates - comparing my results with a reference implementation from here: http://dennis2society.de/painless-tetrahedral-barycentric-mapping my four barycentric values are each smaller the values calculated by the reference implementation.

有人吗？在实现中发现任何错误？非常感谢您的帮助！

Does anyone spot any error in my implementation? Many thanks for help!

推荐答案

盲目猜测：

Vec4f bary_tet(const Vec3f & a, const Vec3f & b, const Vec3f & c, const Vec3f & d, const Vec3f & p)
{
    Vec3f vap = p - a;
    Vec3f vbp = p - b;

    Vec3f vab = b - a;
    Vec3f vac = c - a;
    Vec3f vad = d - a;

    Vec3f vbc = c - b;
    Vec3f vbd = d - b;
    // ScTP computes the scalar triple product
    float va6 = ScTP(vbp, vbd, vbc);
    float vb6 = ScTP(vap, vac, vad);
    float vc6 = ScTP(vap, vad, vab);
    float vd6 = ScTP(vap, vab, vac);
    float v6 = 1 / ScTP(vab, vac, vad);
    return Vec4f(va6*v6, vb6*v6, vc6*v6, vd6*v6);
}

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