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+/*
+Open Asset Import Library (assimp)
+----------------------------------------------------------------------
+
+Copyright (c) 2006-2022, assimp team
+
+All rights reserved.
+
+Redistribution and use of this software in source and binary forms,
+with or without modification, are permitted provided that the
+following conditions are met:
+
+* Redistributions of source code must retain the above
+ copyright notice, this list of conditions and the
+ following disclaimer.
+
+* Redistributions in binary form must reproduce the above
+ copyright notice, this list of conditions and the
+ following disclaimer in the documentation and/or other
+ materials provided with the distribution.
+
+* Neither the name of the assimp team, nor the names of its
+ contributors may be used to endorse or promote products
+ derived from this software without specific prior
+ written permission of the assimp team.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+----------------------------------------------------------------------
+*/
+
+/** @file PolyTools.h, various utilities for our dealings with arbitrary polygons */
+
+#pragma once
+#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 dot11 = v1 * v1;
+ const double dot01 = v0 * v1;
+ const double dot02 = v0 * v2;
+ const double dot12 = v1 * v2;
+ const double denom = dot00 * dot11 - dot01 * dot01;
+ if (denom == 0.0) {
+ return false;
+ }
+
+ const double invDenom = 1.0 / denom;
+ 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);
+}
+
+} // ! namespace Assimp
+
+#endif // AI_POLYTOOLS_H_INCLUDED