X-lanni
117 lines
3.2 KiB
C++
117 lines
3.2 KiB
C++
template <class NUMERIC>
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double OrientedBoundingBox<NUMERIC>::area() {
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return sqrt((ul.x - ll.x)*(ul.x - ll.x) + (ul.y - ll.y)*(ul.y - ll.y)) *
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sqrt((ul.x - ur.x)*(ul.x - ur.x) + (ul.y - ur.y)*(ul.y - ur.y)) ;
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}
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template<class NUMERIC>
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OrientedBoundingBox<NUMERIC>::OrientedBoundingBox(std::vector< point<NUMERIC> > p) {
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int nOfPoints = (int) p.size();
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// calculate the center of all points (schwerpunkt)
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// -------------------------------------------------
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double centerx = 0;
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double centery = 0;
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for (int i=0; i < nOfPoints; i++) {
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centerx += p[i].x;
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centery += p[i].y;
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}
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centerx /= (double) nOfPoints;
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centery /= (double) nOfPoints;
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// calcutae the covariance matrix
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// -------------------------------
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// covariance matrix (x1 x2, x3 x4)
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double x1 = 0.0;
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double x2 = 0.0;
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double x3 = 0.0;
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double x4 = 0.0;
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for (int i=0; i < nOfPoints; i++) {
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double cix = p[i].x - centerx;
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double ciy = p[i].y - centery;
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x1 += cix*cix;
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x2 += cix*ciy;
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x4 += ciy*ciy;
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}
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x1 /= (double) nOfPoints;
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x2 /= (double) nOfPoints;
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x3 = x2;
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x4 /= (double) nOfPoints;
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// covariance & center done
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// calculate the eigenvectors
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// ---------------------------
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// catch 1/0 or sqrt(<0)
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if ((x3 == 0) || (x2 == 0)|| (x4*x4-2*x1*x4+x1*x1+4*x2*x3 < 0 )) {
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fprintf(stderr,"error computing the Eigenvectors (%s, line %d)\nx3=%lf, x2=%lf, term=%lf\n\n",
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__FILE__, __LINE__, x3,x2, (x4*x4-2*x1*x4+x1*x1+4*x2*x3) );
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ul.x = 0;
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ul.y = 0;
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ur.x = 0;
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ur.y = 0;
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ll.x = 0;
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ll.y = 0;
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lr.x = 0;
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lr.y = 0;
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}
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// eigenvalues
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double lamda1 = 0.5* (x4 + x1 + sqrt(x4*x4 - 2.0*x1*x4 + x1*x1 + 4.0*x2*x3));
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double lamda2 = 0.5* (x4 + x1 - sqrt(x4*x4 - 2.0*x1*x4 + x1*x1 + 4.0*x2*x3));
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// eigenvector 1 with (x,y)
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double v1x = - (x4-lamda1) * (x4-lamda1) * (x1-lamda1) / (x2 * x3 * x3);
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double v1y = (x4-lamda1) * (x1-lamda1) / (x2 * x3);
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// eigenvector 2 with (x,y)
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double v2x = - (x4-lamda2) * (x4-lamda2) * (x1-lamda2) / (x2 * x3 * x3);
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double v2y = (x4-lamda2) * (x1-lamda2) / (x2 * x3);
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// norm the eigenvectors
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double lv1 = sqrt ( (v1x*v1x) + (v1y*v1y) );
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double lv2 = sqrt ( (v2x*v2x) + (v2y*v2y) );
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v1x /= lv1;
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v1y /= lv1;
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v2x /= lv2;
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v2y /= lv2;
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// eigenvectors done
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// get the points with maximal dot-product
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double x = 0.0;
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double y = 0.0;
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double xmin = 1e20;
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double xmax = -1e20;
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double ymin = 1e20;
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double ymax = -1e20;
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for(int i = 0; i< nOfPoints; i++) {
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// dot-product of relativ coordinates of every point
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x = (p[i].x - centerx) * v1x + (p[i].y - centery) * v1y;
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y = (p[i].x - centerx) * v2x + (p[i].y - centery) * v2y;
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if( x > xmax) xmax = x;
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if( x < xmin) xmin = x;
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if( y > ymax) ymax = y;
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if( y < ymin) ymin = y;
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}
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// now we can compute the corners of the bounding box
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ul.x = centerx + xmin * v1x + ymin * v2x;
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ul.y = centery + xmin * v1y + ymin * v2y;
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ur.x = centerx + xmax * v1x + ymin * v2x;
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ur.y = centery + xmax * v1y + ymin * v2y;
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ll.x = centerx + xmin * v1x + ymax * v2x;
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ll.y = centery + xmin * v1y + ymax * v2y;
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lr.x = centerx + xmax * v1x + ymax * v2x;
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lr.y = centery + xmax * v1y + ymax * v2y;
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}
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