Bullet Collision Detection & Physics Library: btGrahamScan2dConvexHull.h Source File

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btGrahamScan2dConvexHull.h
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1/*
2Bullet Continuous Collision Detection and Physics Library
3Copyright (c) 2011 Advanced Micro Devices, Inc. http://bulletphysics.org
4
5This software is provided 'as-is', without any express or implied warranty.
6In no event will the authors be held liable for any damages arising from the use of this software.
7Permission is granted to anyone to use this software for any purpose,
8including commercial applications, and to alter it and redistribute it freely,
9subject to the following restrictions:
10
111. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
122. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
133. This notice may not be removed or altered from any source distribution.
14*/
15
16#ifndef GRAHAM_SCAN_2D_CONVEX_HULL_H
17#define GRAHAM_SCAN_2D_CONVEX_HULL_H
18
19#include "btVector3.h"
20#include "btAlignedObjectArray.h"
21
22 struct GrahamVector3 : public btVector3
23{
24 GrahamVector3(const btVector3& org, int orgIndex)
25 : btVector3(org),
26 m_orgIndex(orgIndex)
27 {
28 }
29 btScalar m_angle;
30 int m_orgIndex;
31};
32
33 struct btAngleCompareFunc
34{
35 btVector3 m_anchor;
36 btAngleCompareFunc(const btVector3& anchor)
37 : m_anchor(anchor)
38 {
39 }
40 bool operator()(const GrahamVector3& a, const GrahamVector3& b) const
41 {
42 if (a.m_angle != b.m_angle)
43 return a.m_angle < b.m_angle;
44 else
45 {
46 btScalar al = (a - m_anchor).length2();
47 btScalar bl = (b - m_anchor).length2();
48 if (al != bl)
49 return al < bl;
50 else
51 {
52 return a.m_orgIndex < b.m_orgIndex;
53 }
54 }
55 }
56};
57
58 inline void GrahamScanConvexHull2D(btAlignedObjectArray<GrahamVector3>& originalPoints, btAlignedObjectArray<GrahamVector3>& hull, const btVector3& normalAxis)
59{
60 btVector3 axis0, axis1;
61 btPlaneSpace1(normalAxis, axis0, axis1);
62
63 if (originalPoints.size() <= 1)
64 {
65 for (int i = 0; i < originalPoints.size(); i++)
66 hull.push_back(originalPoints[0]);
67 return;
68 }
69 //step1 : find anchor point with smallest projection on axis0 and move it to first location
70 for (int i = 0; i < originalPoints.size(); i++)
71 {
72 // const btVector3& left = originalPoints[i];
73 // const btVector3& right = originalPoints[0];
74 btScalar projL = originalPoints[i].dot(axis0);
75 btScalar projR = originalPoints[0].dot(axis0);
76 if (projL < projR)
77 {
78 originalPoints.swap(0, i);
79 }
80 }
81
82 //also precompute angles
83 originalPoints[0].m_angle = -1e30f;
84 for (int i = 1; i < originalPoints.size(); i++)
85 {
86 btVector3 ar = originalPoints[i] - originalPoints[0];
87 btScalar ar1 = axis1.dot(ar);
88 btScalar ar0 = axis0.dot(ar);
89 if (ar1 * ar1 + ar0 * ar0 < FLT_EPSILON)
90 {
91 originalPoints[i].m_angle = 0.0f;
92 }
93 else
94 {
95 originalPoints[i].m_angle = btAtan2Fast(ar1, ar0);
96 }
97 }
98
99 //step 2: sort all points, based on 'angle' with this anchor
100 btAngleCompareFunc comp(originalPoints[0]);
101 originalPoints.quickSortInternal(comp, 1, originalPoints.size() - 1);
102
103 int i;
104 for (i = 0; i < 2; i++)
105 hull.push_back(originalPoints[i]);
106
107 //step 3: keep all 'convex' points and discard concave points (using back tracking)
108 for (; i != originalPoints.size(); i++)
109 {
110 bool isConvex = false;
111 while (!isConvex && hull.size() > 1)
112 {
113 btVector3& a = hull[hull.size() - 2];
114 btVector3& b = hull[hull.size() - 1];
115 isConvex = btCross(a - b, a - originalPoints[i]).dot(normalAxis) > 0;
116 if (!isConvex)
117 hull.pop_back();
118 else
119 hull.push_back(originalPoints[i]);
120 }
121
122 if (hull.size() == 1)
123 {
124 hull.push_back(originalPoints[i]);
125 }
126 }
127}
128
129#endif //GRAHAM_SCAN_2D_CONVEX_HULL_H
btAlignedObjectArray.h
GrahamScanConvexHull2D
void GrahamScanConvexHull2D(btAlignedObjectArray< GrahamVector3 > &originalPoints, btAlignedObjectArray< GrahamVector3 > &hull, const btVector3 &normalAxis)
Definition: btGrahamScan2dConvexHull.h:58
btScalar
float btScalar
The btScalar type abstracts floating point numbers, to easily switch between double and single floati...
Definition: btScalar.h:314
btAtan2Fast
btScalar btAtan2Fast(btScalar y, btScalar x)
Definition: btScalar.h:553
btVector3.h
btPlaneSpace1
void btPlaneSpace1(const T &n, T &p, T &q)
Definition: btVector3.h:1251
btCross
btVector3 btCross(const btVector3 &v1, const btVector3 &v2)
Return the cross product of two vectors.
Definition: btVector3.h:918
btAlignedObjectArray
The btAlignedObjectArray template class uses a subset of the stl::vector interface for its methods It...
Definition: btAlignedObjectArray.h:46
btAlignedObjectArray::size
int size() const
return the number of elements in the array
Definition: btAlignedObjectArray.h:142
btAlignedObjectArray::swap
void swap(int index0, int index1)
Definition: btAlignedObjectArray.h:382
btAlignedObjectArray::push_back
void push_back(const T &_Val)
Definition: btAlignedObjectArray.h:257
btAlignedObjectArray::pop_back
void pop_back()
Definition: btAlignedObjectArray.h:185
btAlignedObjectArray::quickSortInternal
void quickSortInternal(const L &CompareFunc, int lo, int hi)
Definition: btAlignedObjectArray.h:311
btVector3
btVector3 can be used to represent 3D points and vectors.
Definition: btVector3.h:82
btVector3::dot
btScalar dot(const btVector3 &v) const
Return the dot product.
Definition: btVector3.h:229
GrahamVector3
Definition: btGrahamScan2dConvexHull.h:23
GrahamVector3::m_angle
btScalar m_angle
Definition: btGrahamScan2dConvexHull.h:29
GrahamVector3::GrahamVector3
GrahamVector3(const btVector3 &org, int orgIndex)
Definition: btGrahamScan2dConvexHull.h:24
GrahamVector3::m_orgIndex
int m_orgIndex
Definition: btGrahamScan2dConvexHull.h:30
btAngleCompareFunc
Definition: btGrahamScan2dConvexHull.h:34
btAngleCompareFunc::operator()
bool operator()(const GrahamVector3 &a, const GrahamVector3 &b) const
Definition: btGrahamScan2dConvexHull.h:40
btAngleCompareFunc::btAngleCompareFunc
btAngleCompareFunc(const btVector3 &anchor)
Definition: btGrahamScan2dConvexHull.h:36
btAngleCompareFunc::m_anchor
btVector3 m_anchor
Definition: btGrahamScan2dConvexHull.h:35