1/*
2Open Asset Import Library (assimp)
3----------------------------------------------------------------------
4
5Copyright (c) 2006-2017, assimp team
6
7All rights reserved.
8
9Redistribution and use of this software in source and binary forms,
10with or without modification, are permitted provided that the
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12
13* Redistributions of source code must retain the above
14 copyright notice, this list of conditions and the
15 following disclaimer.
16
17* Redistributions in binary form must reproduce the above
18 copyright notice, this list of conditions and the
19 following disclaimer in the documentation and/or other
20 materials provided with the distribution.
21
22* Neither the name of the assimp team, nor the names of its
23 contributors may be used to endorse or promote products
24 derived from this software without specific prior
25 written permission of the assimp team.
26
27THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
28"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
29LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
30A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
31OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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38
39----------------------------------------------------------------------
40*/
41
42/** @file PolyTools.h, various utilities for our dealings with arbitrary polygons */
43
44#ifndef AI_POLYTOOLS_H_INCLUDED
45#define AI_POLYTOOLS_H_INCLUDED
46
47#include <assimp/material.h>
48#include <assimp/ai_assert.h>
49
50namespace Assimp {
51
52// -------------------------------------------------------------------------------
53/** Compute the signed area of a triangle.
54 * The function accepts an unconstrained template parameter for use with
55 * both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
56template <typename T>
57inline double GetArea2D(const T& v1, const T& v2, const T& v3)
58{
59 return 0.5 * (v1.x * ((double)v3.y - v2.y) + v2.x * ((double)v1.y - v3.y) + v3.x * ((double)v2.y - v1.y));
60}
61
62// -------------------------------------------------------------------------------
63/** Test if a given point p2 is on the left side of the line formed by p0-p1.
64 * The function accepts an unconstrained template parameter for use with
65 * both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
66template <typename T>
67inline bool OnLeftSideOfLine2D(const T& p0, const T& p1,const T& p2)
68{
69 return GetArea2D(p0,p2,p1) > 0;
70}
71
72// -------------------------------------------------------------------------------
73/** Test if a given point is inside a given triangle in R2.
74 * The function accepts an unconstrained template parameter for use with
75 * both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
76template <typename T>
77inline bool PointInTriangle2D(const T& p0, const T& p1,const T& p2, const T& pp)
78{
79 // Point in triangle test using baryzentric coordinates
80 const aiVector2D v0 = p1 - p0;
81 const aiVector2D v1 = p2 - p0;
82 const aiVector2D v2 = pp - p0;
83
84 double dot00 = v0 * v0;
85 double dot01 = v0 * v1;
86 double dot02 = v0 * v2;
87 double dot11 = v1 * v1;
88 double dot12 = v1 * v2;
89
90 const double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
91 dot11 = (dot11 * dot02 - dot01 * dot12) * invDenom;
92 dot00 = (dot00 * dot12 - dot01 * dot02) * invDenom;
93
94 return (dot11 > 0) && (dot00 > 0) && (dot11 + dot00 < 1);
95}
96
97
98// -------------------------------------------------------------------------------
99/** Check whether the winding order of a given polygon is counter-clockwise.
100 * The function accepts an unconstrained template parameter, but is intended
101 * to be used only with aiVector2D and aiVector3D (z axis is ignored, only
102 * x and y are taken into account).
103 * @note Code taken from http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Ian/applet1.html and translated to C++
104 */
105template <typename T>
106inline bool IsCCW(T* in, size_t npoints) {
107 double aa, bb, cc, b, c, theta;
108 double convex_turn;
109 double convex_sum = 0;
110
111 ai_assert(npoints >= 3);
112
113 for (size_t i = 0; i < npoints - 2; i++) {
114 aa = ((in[i+2].x - in[i].x) * (in[i+2].x - in[i].x)) +
115 ((-in[i+2].y + in[i].y) * (-in[i+2].y + in[i].y));
116
117 bb = ((in[i+1].x - in[i].x) * (in[i+1].x - in[i].x)) +
118 ((-in[i+1].y + in[i].y) * (-in[i+1].y + in[i].y));
119
120 cc = ((in[i+2].x - in[i+1].x) *
121 (in[i+2].x - in[i+1].x)) +
122 ((-in[i+2].y + in[i+1].y) *
123 (-in[i+2].y + in[i+1].y));
124
125 b = std::sqrt(bb);
126 c = std::sqrt(cc);
127 theta = std::acos((bb + cc - aa) / (2 * b * c));
128
129 if (OnLeftSideOfLine2D(in[i],in[i+2],in[i+1])) {
130 // if (convex(in[i].x, in[i].y,
131 // in[i+1].x, in[i+1].y,
132 // in[i+2].x, in[i+2].y)) {
133 convex_turn = AI_MATH_PI_F - theta;
134 convex_sum += convex_turn;
135 }
136 else {
137 convex_sum -= AI_MATH_PI_F - theta;
138 }
139 }
140 aa = ((in[1].x - in[npoints-2].x) *
141 (in[1].x - in[npoints-2].x)) +
142 ((-in[1].y + in[npoints-2].y) *
143 (-in[1].y + in[npoints-2].y));
144
145 bb = ((in[0].x - in[npoints-2].x) *
146 (in[0].x - in[npoints-2].x)) +
147 ((-in[0].y + in[npoints-2].y) *
148 (-in[0].y + in[npoints-2].y));
149
150 cc = ((in[1].x - in[0].x) * (in[1].x - in[0].x)) +
151 ((-in[1].y + in[0].y) * (-in[1].y + in[0].y));
152
153 b = std::sqrt(bb);
154 c = std::sqrt(cc);
155 theta = std::acos((bb + cc - aa) / (2 * b * c));
156
157 //if (convex(in[npoints-2].x, in[npoints-2].y,
158 // in[0].x, in[0].y,
159 // in[1].x, in[1].y)) {
160 if (OnLeftSideOfLine2D(in[npoints-2],in[1],in[0])) {
161 convex_turn = AI_MATH_PI_F - theta;
162 convex_sum += convex_turn;
163 }
164 else {
165 convex_sum -= AI_MATH_PI_F - theta;
166 }
167
168 return convex_sum >= (2 * AI_MATH_PI_F);
169}
170
171
172// -------------------------------------------------------------------------------
173/** Compute the normal of an arbitrary polygon in R3.
174 *
175 * The code is based on Newell's formula, that is a polygons normal is the ratio
176 * of its area when projected onto the three coordinate axes.
177 *
178 * @param out Receives the output normal
179 * @param num Number of input vertices
180 * @param x X data source. x[ofs_x*n] is the n'th element.
181 * @param y Y data source. y[ofs_y*n] is the y'th element
182 * @param z Z data source. z[ofs_z*n] is the z'th element
183 *
184 * @note The data arrays must have storage for at least num+2 elements. Using
185 * this method is much faster than the 'other' NewellNormal()
186 */
187template <int ofs_x, int ofs_y, int ofs_z, typename TReal>
188inline void NewellNormal (aiVector3t<TReal>& out, int num, TReal* x, TReal* y, TReal* z)
189{
190 // Duplicate the first two vertices at the end
191 x[(num+0)*ofs_x] = x[0];
192 x[(num+1)*ofs_x] = x[ofs_x];
193
194 y[(num+0)*ofs_y] = y[0];
195 y[(num+1)*ofs_y] = y[ofs_y];
196
197 z[(num+0)*ofs_z] = z[0];
198 z[(num+1)*ofs_z] = z[ofs_z];
199
200 TReal sum_xy = 0.0, sum_yz = 0.0, sum_zx = 0.0;
201
202 TReal *xptr = x +ofs_x, *xlow = x, *xhigh = x + ofs_x*2;
203 TReal *yptr = y +ofs_y, *ylow = y, *yhigh = y + ofs_y*2;
204 TReal *zptr = z +ofs_z, *zlow = z, *zhigh = z + ofs_z*2;
205
206 for (int tmp=0; tmp < num; tmp++) {
207 sum_xy += (*xptr) * ( (*yhigh) - (*ylow) );
208 sum_yz += (*yptr) * ( (*zhigh) - (*zlow) );
209 sum_zx += (*zptr) * ( (*xhigh) - (*xlow) );
210
211 xptr += ofs_x;
212 xlow += ofs_x;
213 xhigh += ofs_x;
214
215 yptr += ofs_y;
216 ylow += ofs_y;
217 yhigh += ofs_y;
218
219 zptr += ofs_z;
220 zlow += ofs_z;
221 zhigh += ofs_z;
222 }
223 out = aiVector3t<TReal>(sum_yz,sum_zx,sum_xy);
224}
225
226} // ! Assimp
227
228#endif
229