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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 
     17 #ifndef GRAHAM_SCAN_2D_CONVEX_HULL_H
     18 #define GRAHAM_SCAN_2D_CONVEX_HULL_H
     19 
     20 
     21 #include "btVector3.h"
     22 #include "btAlignedObjectArray.h"
     23 
     24 struct GrahamVector3 : public btVector3
     25 {
     26 	GrahamVector3(const btVector3& org, int orgIndex)
     27 		:btVector3(org),
     28 			m_orgIndex(orgIndex)
     29 	{
     30 	}
     31 	btScalar	m_angle;
     32 	int m_orgIndex;
     33 };
     34 
     35 
     36 struct btAngleCompareFunc {
     37 	btVector3 m_anchor;
     38 	btAngleCompareFunc(const btVector3& anchor)
     39 	: m_anchor(anchor)
     40 	{
     41 	}
     42 	bool operator()(const GrahamVector3& a, const GrahamVector3& b) const {
     43 		if (a.m_angle != b.m_angle)
     44 			return a.m_angle < b.m_angle;
     45 		else
     46 		{
     47 			btScalar al = (a-m_anchor).length2();
     48 			btScalar bl = (b-m_anchor).length2();
     49 			if (al != bl)
     50 				return  al < bl;
     51 			else
     52 			{
     53 				return a.m_orgIndex < b.m_orgIndex;
     54 			}
     55 		}
     56 	}
     57 };
     58 
     59 inline void GrahamScanConvexHull2D(btAlignedObjectArray<GrahamVector3>& originalPoints, btAlignedObjectArray<GrahamVector3>& hull, const btVector3& normalAxis)
     60 {
     61 	btVector3 axis0,axis1;
     62 	btPlaneSpace1(normalAxis,axis0,axis1);
     63 
     64 
     65 	if (originalPoints.size()<=1)
     66 	{
     67 		for (int i=0;i<originalPoints.size();i++)
     68 			hull.push_back(originalPoints[0]);
     69 		return;
     70 	}
     71 	//step1 : find anchor point with smallest projection on axis0 and move it to first location
     72 	for (int i=0;i<originalPoints.size();i++)
     73 	{
     74 //		const btVector3& left = originalPoints[i];
     75 //		const btVector3& right = originalPoints[0];
     76 		btScalar projL = originalPoints[i].dot(axis0);
     77 		btScalar projR = originalPoints[0].dot(axis0);
     78 		if (projL < projR)
     79 		{
     80 			originalPoints.swap(0,i);
     81 		}
     82 	}
     83 
     84 	//also precompute angles
     85 	originalPoints[0].m_angle = -1e30f;
     86 	for (int i=1;i<originalPoints.size();i++)
     87 	{
     88 	    btVector3 ar = originalPoints[i]-originalPoints[0];
     89 	    btScalar ar1 = axis1.dot(ar);
     90 	    btScalar ar0 = axis0.dot(ar);
     91 	    if( ar1*ar1+ar0*ar0 < FLT_EPSILON )
     92 	    {
     93 	      originalPoints[i].m_angle = 0.0f;
     94 	    }
     95 	    else
     96 	    {
     97 	      originalPoints[i].m_angle = btAtan2Fast(ar1, ar0);
     98 	    }
     99 	}
    100 
    101 	//step 2: sort all points, based on 'angle' with this anchor
    102 	btAngleCompareFunc comp(originalPoints[0]);
    103 	originalPoints.quickSortInternal(comp,1,originalPoints.size()-1);
    104 
    105 	int i;
    106 	for (i = 0; i<2; i++)
    107 		hull.push_back(originalPoints[i]);
    108 
    109 	//step 3: keep all 'convex' points and discard concave points (using back tracking)
    110 	for (; i != originalPoints.size(); i++)
    111 	{
    112 		bool isConvex = false;
    113 		while (!isConvex&& hull.size()>1) {
    114 			btVector3& a = hull[hull.size()-2];
    115 			btVector3& b = hull[hull.size()-1];
    116 			isConvex = btCross(a-b,a-originalPoints[i]).dot(normalAxis)> 0;
    117 			if (!isConvex)
    118 				hull.pop_back();
    119 			else
    120 				hull.push_back(originalPoints[i]);
    121 		}
    122 
    123 	    if( hull.size() == 1 )
    124 	    {
    125 	      hull.push_back( originalPoints[i] );
    126 	    }
    127 	}
    128 }
    129 
    130 #endif //GRAHAM_SCAN_2D_CONVEX_HULL_H
    131