1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
|
/*
Open Asset Import Library (assimp)
----------------------------------------------------------------------
Copyright (c) 2006-2012, 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 */
#ifndef AI_POLYTOOLS_H_INCLUDED
#define AI_POLYTOOLS_H_INCLUDED
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
|
