assimp/code/Common/PolyTools.h

/*
Open Asset Import Library (assimp)
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/** @file PolyTools.h, various utilities for our dealings with arbitrary polygons */

#ifndef AI_POLYTOOLS_H_INCLUDED
#define AI_POLYTOOLS_H_INCLUDED

#include <assimp/ai_assert.h>
#include <assimp/material.h>
#include <assimp/vector3.h>

namespace Assimp {

template<class T>
class TBoundingBox2D {
    T mMin, mMax;

    TBoundingBox2D( const T &min, const T &max ) :
            mMin( min ),
            mMax( max ) {
        // empty
    }
};

using BoundingBox2D = TBoundingBox2D<aiVector2D>;

// -------------------------------------------------------------------------------
/// Compute the normal of an arbitrary polygon in R3.
///
/// The code is based on Newell's formula, that is a polygons normal is the ratio
/// of its area when projected onto the three coordinate axes.
///
/// @param out Receives the output normal
/// @param num Number of input vertices
/// @param x X data source. x[ofs_x*n] is the n'th element.
/// @param y Y data source. y[ofs_y*n] is the y'th element
/// @param z Z data source. z[ofs_z*n] is the z'th element
///
/// @note The data arrays must have storage for at least num+2 elements. Using
/// this method is much faster than the 'other' NewellNormal()
// -------------------------------------------------------------------------------
template <size_t ofs_x, size_t ofs_y, size_t ofs_z, typename TReal>
inline void NewellNormal(aiVector3t<TReal> &out, size_t num, TReal *x, TReal *y, TReal *z, size_t bufferSize) {
    ai_assert(bufferSize > num);

    if (nullptr == x || nullptr == y || nullptr == z || 0 == bufferSize || 0 == num) {
        return;
    }

    // Duplicate the first two vertices at the end
    x[(num + 0) * ofs_x] = x[0];
    x[(num + 1) * ofs_x] = x[ofs_x];

    y[(num + 0) * ofs_y] = y[0];
    y[(num + 1) * ofs_y] = y[ofs_y];

    z[(num + 0) * ofs_z] = z[0];
    z[(num + 1) * ofs_z] = z[ofs_z];

    TReal sum_xy = 0.0, sum_yz = 0.0, sum_zx = 0.0;

    TReal *xptr = x + ofs_x, *xlow = x, *xhigh = x + ofs_x * 2;
    TReal *yptr = y + ofs_y, *ylow = y, *yhigh = y + ofs_y * 2;
    TReal *zptr = z + ofs_z, *zlow = z, *zhigh = z + ofs_z * 2;

    for (size_t tmp = 0; tmp < num; ++tmp ) {
        sum_xy += (*xptr) * ((*yhigh) - (*ylow));
        sum_yz += (*yptr) * ((*zhigh) - (*zlow));
        sum_zx += (*zptr) * ((*xhigh) - (*xlow));

        xptr += ofs_x;
        xlow += ofs_x;
        xhigh += ofs_x;

        yptr += ofs_y;
        ylow += ofs_y;
        yhigh += ofs_y;

        zptr += ofs_z;
        zlow += ofs_z;
        zhigh += ofs_z;
    }
    out = aiVector3t<TReal>(sum_yz, sum_zx, sum_xy);
}

// -------------------------------------------------------------------------------
// -------------------------------------------------------------------------------
template <class T>
inline aiMatrix4x4t<T> DerivePlaneCoordinateSpace(const aiVector3t<T> *vertices, size_t numVertices, bool &ok, aiVector3t<T> &norOut) {
    const aiVector3t<T> *out = vertices;
    aiMatrix4x4t<T> m;

    ok = true;

    const size_t s = numVertices;

    const aiVector3t<T> &any_point = out[numVertices - 1u];
    aiVector3t<T> nor;

    // The input polygon is arbitrarily shaped, therefore we might need some tries
    // until we find a suitable normal. Note that Newell's algorithm would give
    // a more robust result, but this variant also gives us a suitable first
    // axis for the 2D coordinate space on the polygon plane, exploiting the
    // fact that the input polygon is nearly always a quad.
    bool done = false;
    size_t idx = 0;
    for (size_t i = 0; !done && i < s - 2; done || ++i) {
        idx = i;
        for (size_t j = i + 1; j < s - 1; ++j) {
            nor = -((out[i] - any_point) ^ (out[j] - any_point));
            if (std::fabs(nor.Length()) > 1e-8f) {
                done = true;
                break;
            }
        }
    }

    if (!done) {
        ok = false;
        return m;
    }

    nor.Normalize();
    norOut = nor;

    aiVector3t<T> r = (out[idx] - any_point);
    r.Normalize();

    // Reconstruct orthonormal basis
    // XXX use Gram Schmidt for increased robustness
    aiVector3t<T> u = r ^ nor;
    u.Normalize();

    m.a1 = r.x;
    m.a2 = r.y;
    m.a3 = r.z;

    m.b1 = u.x;
    m.b2 = u.y;
    m.b3 = u.z;

    m.c1 = -nor.x;
    m.c2 = -nor.y;
    m.c3 = -nor.z;

    return m;
}

} // namespace Assimp

#endif