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

namespace Assimp {

// -------------------------------------------------------------------------------
/** Compute the signed area of a triangle.
 *  The function accepts an unconstrained template parameter for use with
 *  both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
template <typename T>
inline double GetArea2D(const T& v1, const T& v2, const T& v3)
{
    return 0.5 * (v1.x * ((double)v3.y - v2.y) + v2.x * ((double)v1.y - v3.y) + v3.x * ((double)v2.y - v1.y));
}

// -------------------------------------------------------------------------------
/** Test if a given point p2 is on the left side of the line formed by p0-p1.
 *  The function accepts an unconstrained template parameter for use with
 *  both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
template <typename T>
inline bool OnLeftSideOfLine2D(const T& p0, const T& p1,const T& p2)
{
    return GetArea2D(p0,p2,p1) > 0;
}

// -------------------------------------------------------------------------------
/** Test if a given point is inside a given triangle in R2.
 * The function accepts an unconstrained template parameter for use with
 *  both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
template <typename T>
inline bool PointInTriangle2D(const T& p0, const T& p1,const T& p2, const T& pp)
{
    // Point in triangle test using baryzentric coordinates
    const aiVector2D v0 = p1 - p0;
    const aiVector2D v1 = p2 - p0;
    const aiVector2D v2 = pp - p0;

    double dot00 = v0 * v0;
    double dot01 = v0 * v1;
    double dot02 = v0 * v2;
    double dot11 = v1 * v1;
    double dot12 = v1 * v2;

    const double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
    dot11 = (dot11 * dot02 - dot01 * dot12) * invDenom;
    dot00 = (dot00 * dot12 - dot01 * dot02) * invDenom;

    return (dot11 > 0) && (dot00 > 0) && (dot11 + dot00 < 1);
}


// -------------------------------------------------------------------------------
/** Check whether the winding order of a given polygon is counter-clockwise.
 *  The function accepts an unconstrained template parameter, but is intended
 *  to be used only with aiVector2D and aiVector3D (z axis is ignored, only
 *  x and y are taken into account).
 * @note Code taken from http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Ian/applet1.html and translated to C++
 */
template <typename T>
inline bool IsCCW(T* in, size_t npoints) {
    double aa, bb, cc, b, c, theta;
    double convex_turn;
    double convex_sum = 0;

    ai_assert(npoints >= 3);

    for (size_t i = 0; i < npoints - 2; i++) {
        aa = ((in[i+2].x - in[i].x) * (in[i+2].x - in[i].x)) +
            ((-in[i+2].y + in[i].y) * (-in[i+2].y + in[i].y));

        bb = ((in[i+1].x - in[i].x) * (in[i+1].x - in[i].x)) +
            ((-in[i+1].y + in[i].y) * (-in[i+1].y + in[i].y));

        cc = ((in[i+2].x - in[i+1].x) *
            (in[i+2].x - in[i+1].x)) +
            ((-in[i+2].y + in[i+1].y) *
            (-in[i+2].y + in[i+1].y));

        b = std::sqrt(bb);
        c = std::sqrt(cc);
        theta = std::acos((bb + cc - aa) / (2 * b * c));

        if (OnLeftSideOfLine2D(in[i],in[i+2],in[i+1])) {
            //  if (convex(in[i].x, in[i].y,
            //      in[i+1].x, in[i+1].y,
            //      in[i+2].x, in[i+2].y)) {
            convex_turn = AI_MATH_PI_F - theta;
            convex_sum += convex_turn;
        }
        else {
            convex_sum -= AI_MATH_PI_F - theta;
        }
    }
    aa = ((in[1].x - in[npoints-2].x) *
        (in[1].x - in[npoints-2].x)) +
        ((-in[1].y + in[npoints-2].y) *
        (-in[1].y + in[npoints-2].y));

    bb = ((in[0].x - in[npoints-2].x) *
        (in[0].x - in[npoints-2].x)) +
        ((-in[0].y + in[npoints-2].y) *
        (-in[0].y + in[npoints-2].y));

    cc = ((in[1].x - in[0].x) * (in[1].x - in[0].x)) +
        ((-in[1].y + in[0].y) * (-in[1].y + in[0].y));

    b = std::sqrt(bb);
    c = std::sqrt(cc);
    theta = std::acos((bb + cc - aa) / (2 * b * c));

    //if (convex(in[npoints-2].x, in[npoints-2].y,
    //  in[0].x, in[0].y,
    //  in[1].x, in[1].y)) {
    if (OnLeftSideOfLine2D(in[npoints-2],in[1],in[0])) {
        convex_turn = AI_MATH_PI_F - theta;
        convex_sum += convex_turn;
    }
    else {
        convex_sum -= AI_MATH_PI_F - theta;
    }

    return convex_sum >= (2 * AI_MATH_PI_F);
}


// -------------------------------------------------------------------------------
/** 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 <int ofs_x, int ofs_y, int ofs_z, typename TReal>
inline void NewellNormal (aiVector3t<TReal>& out, int num, TReal* x, TReal* y, TReal* z)
{
    // 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 (int 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);
}

} // ! Assimp

#endif