Bullet Collision Detection & Physics Library
btGrahamScan2dConvexHull.h
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1 /*
2 Bullet Continuous Collision Detection and Physics Library
3 Copyright (c) 2011 Advanced Micro Devices, Inc. http://bulletphysics.org
4 
5 This software is provided 'as-is', without any express or implied warranty.
6 In no event will the authors be held liable for any damages arising from the use of this software.
7 Permission is granted to anyone to use this software for any purpose,
8 including commercial applications, and to alter it and redistribute it freely,
9 subject to the following restrictions:
10 
11 1. 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.
12 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
13 3. 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  }
31 };
32 
34 {
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 
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
void push_back(const T &_Val)
The btAlignedObjectArray template class uses a subset of the stl::vector interface for its methods It...
void btPlaneSpace1(const T &n, T &p, T &q)
Definition: btVector3.h:1251
bool operator()(const GrahamVector3 &a, const GrahamVector3 &b) const
void swap(int index0, int index1)
btVector3 btCross(const btVector3 &v1, const btVector3 &v2)
Return the cross product of two vectors.
Definition: btVector3.h:918
btScalar dot(const btVector3 &v) const
Return the dot product.
Definition: btVector3.h:229
btScalar btAtan2Fast(btScalar y, btScalar x)
Definition: btScalar.h:533
btVector3 can be used to represent 3D points and vectors.
Definition: btVector3.h:80
int size() const
return the number of elements in the array
btAngleCompareFunc(const btVector3 &anchor)
void GrahamScanConvexHull2D(btAlignedObjectArray< GrahamVector3 > &originalPoints, btAlignedObjectArray< GrahamVector3 > &hull, const btVector3 &normalAxis)
GrahamVector3(const btVector3 &org, int orgIndex)
void quickSortInternal(const L &CompareFunc, int lo, int hi)
float btScalar
The btScalar type abstracts floating point numbers, to easily switch between double and single floati...
Definition: btScalar.h:294