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axmol/cocos/3d/CCOBB.cpp

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/****************************************************************************
Copyright (c) 2014 Chukong Technologies Inc.
http://www.cocos2d-x.org
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
****************************************************************************/
#include "3d/CCOBB.h"
NS_CC_BEGIN
#define ROTATE(a,i,j,k,l) g=a.m[i + 4 * j]; h=a.m[k + 4 * l]; a.m[i + 4 * j]=(float)(g-s*(h+g*tau)); a.m[k + 4 * l]=(float)(h+s*(g-h*tau));
static Mat4 _convarianceMatrix(const Vec3* aVertPos, int nVertCount)
{
int i;
Mat4 Cov;
double S1[3];
double S2[3][3];
S1[0] = S1[1] = S1[2] = 0.0;
S2[0][0] = S2[1][0] = S2[2][0] = 0.0;
S2[0][1] = S2[1][1] = S2[2][1] = 0.0;
S2[0][2] = S2[1][2] = S2[2][2] = 0.0;
// get center of mass
for(i=0; i<nVertCount; i++)
{
S1[0] += aVertPos[i].x;
S1[1] += aVertPos[i].y;
S1[2] += aVertPos[i].z;
S2[0][0] += aVertPos[i].x * aVertPos[i].x;
S2[1][1] += aVertPos[i].y * aVertPos[i].y;
S2[2][2] += aVertPos[i].z * aVertPos[i].z;
S2[0][1] += aVertPos[i].x * aVertPos[i].y;
S2[0][2] += aVertPos[i].x * aVertPos[i].z;
S2[1][2] += aVertPos[i].y * aVertPos[i].z;
}
float n = (float)nVertCount;
// now get covariances
Cov.m[0] = (float)(S2[0][0] - S1[0]*S1[0] / n) / n;
Cov.m[5] = (float)(S2[1][1] - S1[1]*S1[1] / n) / n;
Cov.m[10] = (float)(S2[2][2] - S1[2]*S1[2] / n) / n;
Cov.m[4] = (float)(S2[0][1] - S1[0]*S1[1] / n) / n;
Cov.m[9] = (float)(S2[1][2] - S1[1]*S1[2] / n) / n;
Cov.m[8] = (float)(S2[0][2] - S1[0]*S1[2] / n) / n;
Cov.m[1] = Cov.m[4];
Cov.m[2] = Cov.m[8];
Cov.m[6] = Cov.m[9];
return Cov;
}
static float& _getElement( Vec3& point, int index)
{
if (index == 0)
return point.x;
if (index == 1)
return point.y;
if (index == 2)
return point.z;
CC_ASSERT(0);
return point.x;
}
static void _eigenVectors(Mat4* vout, Vec3* dout, Mat4 a)
{
int n = 3;
int j,iq,ip,i;
double tresh,theta,tau,t,sm,s,h,g,c;
int nrot;
Vec3 b;
Vec3 z;
Mat4 v;
Vec3 d;
v = Mat4::IDENTITY;
for(ip=0; ip<n; ip++)
{
_getElement(b, ip) = a.m[ip + 4 * ip];
_getElement(d, ip) = a.m[ip + 4 * ip];
_getElement(z, ip) = 0.0;
}
nrot = 0;
for(i=0; i<50; i++)
{
sm=0.0;
for(ip=0; ip<n; ip++) for(iq=ip+1;iq<n;iq++) sm+=fabs(a.m[ip + 4 * iq]);
if( sm == 0.0 )
{
v.transpose();
*vout = v;
*dout = d;
return;
}
if (i < 3) tresh = 0.2 * sm / (n*n);
else tresh=0.0;
for(ip=0; ip<n; ip++)
{
for(iq=ip+1; iq<n; iq++)
{
g = 100.0*fabs(a.m[ip + iq * 4]);
float dmip = _getElement(d, ip);
float dmiq = _getElement(d, iq);
if( i>3 && fabs(dmip)+g==fabs(dmip) && fabs(dmiq)+g==fabs(dmiq) )
a.m[ip + 4 * iq]=0.0;
else if (fabs(a.m[ip + 4 * iq])>tresh)
{
h = dmiq-dmip;
if (fabs(h)+g == fabs(h))
t=(a.m[ip + 4 * iq])/h;
else
{
theta=0.5*h/(a.m[ip + 4 * iq]);
t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
if (theta < 0.0) t = -t;
}
c=1.0/sqrt(1+t*t);
s=t*c;
tau=s/(1.0+c);
h=t*a.m[ip + 4 * iq];
_getElement(z, ip) -= (float)h;
_getElement(z, iq) += (float)h;
_getElement(d, ip) -= (float)h;
_getElement(d, iq) += (float)h;
a.m[ip + 4 * iq]=0.0;
for(j=0;j<ip;j++) { ROTATE(a,j,ip,j,iq); }
for(j=ip+1;j<iq;j++) { ROTATE(a,ip,j,j,iq); }
for(j=iq+1;j<n;j++) { ROTATE(a,ip,j,iq,j); }
for(j=0;j<n;j++) { ROTATE(v,j,ip,j,iq); }
nrot++;
}
}
}
for(ip=0;ip<n;ip++)
{
_getElement(b, ip) += _getElement(z, ip);
_getElement(d, ip) = _getElement(b, ip);
_getElement(z, ip) = 0.0f;
}
}
v.transpose();
*vout = v;
*dout = d;
return;
}
static Mat4 _GetOBBOrientation(const Vec3* aVertPos, int nVertCount)
{
Mat4 Cov;
if (nVertCount <= 0)
return Mat4::IDENTITY;
Cov = _convarianceMatrix(aVertPos, nVertCount);
// now get eigenvectors
Mat4 Evecs;
Vec3 Evals;
_eigenVectors(&Evecs, &Evals, Cov);
Evecs.transpose();
return Evecs;
}
OBB::OBB()
{
reset();
}
OBB::OBB(const AABB& aabb)
{
reset();
_center = (aabb._min + aabb._max);
_center.scale(0.5f);
_xAxis = Vec3(1.0f, 0.0f, 0.0f);
_yAxis = Vec3(0.0f, 1.0f, 0.0f);
_zAxis = Vec3(0.0f, 0.0f, 1.0f);
_extents = aabb._max - aabb._min;
_extents.scale(0.5f);
}
OBB::OBB(const Vec3* verts, int nVerts)
{
if (!nVerts) return;
reset();
Mat4 matTransform = _GetOBBOrientation(verts, nVerts);
// For matTransform is orthogonal, so the inverse matrix is just rotate it;
matTransform.transpose();
Vec3 vecMax = matTransform * Vec3(verts[0].x, verts[0].y, verts[0].z);
Vec3 vecMin = vecMax;
for (int i=1; i < nVerts; i++)
{
Vec3 vect = matTransform * Vec3(verts[i].x, verts[i].y, verts[i].z);
vecMax.x = vecMax.x > vect.x ? vecMax.x : vect.x;
vecMax.y = vecMax.y > vect.y ? vecMax.y : vect.y;
vecMax.z = vecMax.z > vect.z ? vecMax.z : vect.z;
vecMin.x = vecMin.x < vect.x ? vecMin.x : vect.x;
vecMin.y = vecMin.y < vect.y ? vecMin.y : vect.y;
vecMin.z = vecMin.z < vect.z ? vecMin.z : vect.z;
}
matTransform.transpose();
_xAxis = Vec3(matTransform.m[0], matTransform.m[1], matTransform.m[2]);
_yAxis = Vec3(matTransform.m[4], matTransform.m[5], matTransform.m[6]);
_zAxis = Vec3(matTransform.m[8], matTransform.m[9], matTransform.m[10]);
_center = 0.5f * (vecMax + vecMin);
_center *= matTransform;
_xAxis.normalize();
_yAxis.normalize();
_zAxis.normalize();
_extents = 0.5f * (vecMax - vecMin);
}
bool OBB::containPoint(const Vec3& point) const
{
Vec3 vd = point - _center;
float d = vd.dot(_xAxis);
if (d > _extents.x || d < -_extents.x)
return false;
d = vd.dot(_yAxis);
if (d > _extents.y || d < -_extents.y)
return false;
d = vd.dot(_zAxis);
if (d > _extents.z || d < -_extents.z)
return false;
return true;
}
void OBB::set(const Vec3& center, const Vec3& xAxis, const Vec3& yAxis, const Vec3& zAxis, const Vec3& extents)
{
_center = center;
_xAxis = xAxis;
_yAxis = yAxis;
_zAxis = zAxis;
_extents = extents;
}
void OBB::reset()
{
memset(this, 0, sizeof(OBB));
}
void OBB::getCorners(Vec3* verts) const
{
Vec3 extX = _xAxis * _extents.x;
Vec3 extY = _yAxis * _extents.y;
Vec3 extZ = _zAxis * _extents.z;
verts[0] = _center - extX + extY + extZ; // left top front
verts[1] = _center - extX - extY + extZ; // left bottom front
verts[2] = _center + extX - extY + extZ; // right bottom front
verts[3] = _center + extX + extY + extZ; // right top front
verts[4] = _center + extX + extY - extZ; // right top back
verts[5] = _center + extX - extY - extZ; // right bottom back
verts[6] = _center - extX - extY - extZ; // left bottom back
verts[7] = _center - extX + extY - extZ; // left top back
}
float OBB::projectPoint(const Vec3& point, const Vec3& axis)const
{
float dot = axis.dot(point);
float ret = dot * point.length();
return ret;
}
void OBB::getInterval(const OBB& box, const Vec3& axis, float &min, float &max)const
{
Vec3 corners[8];
box.getCorners(corners);
float value;
min = max = projectPoint(axis, corners[0]);
for(int i = 1; i < 8; i++)
{
value = projectPoint(axis, corners[i]);
min = MIN(min, value);
max = MAX(max, value);
}
}
Vec3 OBB::getEdgeDir(int index)const
{
Vec3 corners[8];
getCorners(corners);
Vec3 tmpLine;
switch(index)
{
case 0:// edge with x axis
tmpLine = corners[5] - corners[6];
tmpLine.normalize();
break;
case 1:// edge with y axis
tmpLine = corners[7] - corners[6];
tmpLine.normalize();
break;
case 2:// edge with z axis
tmpLine = corners[1] - corners[6];
tmpLine.normalize();
break;
}
return tmpLine;
}
Vec3 OBB::getFaceDir(int index) const
{
Vec3 corners[8];
getCorners(corners);
Vec3 faceDir, v0, v1;
switch(index)
{
case 0:// front and back
v0 = corners[2] - corners[1];
v1 = corners[0] - corners[1];
Vec3::cross(v0, v1, &faceDir);
faceDir.normalize();
break;
case 1:// left and right
v0 = corners[5] - corners[2];
v1 = corners[3] - corners[2];
Vec3::cross(v0, v1, &faceDir);
faceDir.normalize();
break;
case 2:// top and bottom
v0 = corners[1] - corners[2];
v1 = corners[5] - corners[2];
Vec3::cross(v0, v1, &faceDir);
faceDir.normalize();
break;
}
return faceDir;
}
bool OBB::intersects(const OBB& box) const
{
float min1, max1, min2, max2;
for (int i = 0; i < 3; i++)
{
getInterval(*this, getFaceDir(i), min1, max1);
getInterval(box, getFaceDir(i), min2, max2);
if (max1 < min2 || max2 < min1) return false;
}
for (int i = 0; i < 3; i++)
{
getInterval(*this, box.getFaceDir(i), min1, max1);
getInterval(box, box.getFaceDir(i), min2, max2);
if (max1 < min2 || max2 < min1) return false;
}
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
Vec3 axis;
Vec3::cross(getEdgeDir(i), box.getEdgeDir(j), &axis);
getInterval(*this, axis, min1, max1);
getInterval(box, axis, min2, max2);
if (max1 < min2 || max2 < min1) return false;
}
}
return true;
}
void OBB::transform(const Mat4& mat)
{
Vec4 newcenter = mat * Vec4(_center.x, _center.y, _center.z, 1.0f);// center;
_center.x = newcenter.x;
_center.y = newcenter.y;
_center.z = newcenter.z;
_xAxis = mat * _xAxis;
_yAxis = mat * _yAxis;
_zAxis = mat * _zAxis;
_xAxis.normalize();
_yAxis.normalize();
_zAxis.normalize();
Vec3 scale, trans;
Quaternion quat;
mat.decompose(&scale, &quat, &trans);
_extents.x *= scale.x;
_extents.y *= scale.y;
_extents.z *= scale.z;
}
NS_CC_END
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