private bool turn_left(Vector p1, Vector p2, Vector p3)
{
var v1 = GeomMath.Subtract(p2, p1);
var v2 = GeomMath.Subtract(p3, p2);
return((v1.X * v2.Y - v2.X * v1.Y) > 0);
}
private int FindAngles(int[] e, double[] a, Vector v, Vector n)
{
Vector[] u = new Vector[4];
//for (int i = 0; i < 4; i++)
// u[i] = (m_chull[(e[i] + 1) % size] - m_chull[e[i]]).normalize();
int size = hull.Count;
for (int i = 0; i < 4; i++)
{
u[i] = GeomMath.Subtract(hull[(e[i] + 1) % size], hull[e[i]]).normalize();
}
int w = 0;
//a[0] = fabs(v * u[0]);
//a[1] = fabs(n * u[1]); if (a[1] > a[w]) { w = 1; } //larger dot product means smaller angle
//a[2] = fabs(v * u[2]); if (a[2] > a[w]) { w = 2; }
//a[3] = fabs(n * u[3]); if (a[3] > a[w]) { w = 3; }
a[0] = Math.Abs(GeomMath.DotProduct(v, u[0]));
a[1] = Math.Abs(GeomMath.DotProduct(n, u[1]));
if (a[1] > a[w])
{
w = 1;
}
a[2] = Math.Abs(GeomMath.DotProduct(v, u[2]));
if (a[2] > a[w])
{
w = 2;
}
a[3] = Math.Abs(GeomMath.DotProduct(n, u[3]));
if (a[3] > a[w])
{
w = 3;
}
return(w);
}
private BoundingBox CreateBoundingBox(int[] e, Vector v, Vector n)
{
//box.corners[0] = m_chull[e[0]] + v * ((m_chull[e[1]] - m_chull[e[0]]) * v);
//box.corners[3] = m_chull[e[0]] + v * ((m_chull[e[3]] - m_chull[e[0]]) * v);
//box.corners[1] = m_chull[e[2]] + v * ((m_chull[e[1]] - m_chull[e[2]]) * v);
//box.corners[2] = m_chull[e[2]] + v * ((m_chull[e[3]] - m_chull[e[2]]) * v);
//box.width = fabs((m_chull[e[3]] - m_chull[e[1]]) * v);
//box.height = fabs((m_chull[e[2]] - m_chull[e[0]]) * n);
var box = new BoundingBox();
box.Corners[0] = GeomMath.Add(hull[e[0]], GeomMath.Multiply(v, GeomMath.DotProduct(GeomMath.Subtract(hull[e[1]], hull[e[0]]), v)));
box.Corners[3] = GeomMath.Add(hull[e[0]], GeomMath.Multiply(v, GeomMath.DotProduct(GeomMath.Subtract(hull[e[3]], hull[e[0]]), v)));
box.Corners[1] = GeomMath.Add(hull[e[2]], GeomMath.Multiply(v, GeomMath.DotProduct(GeomMath.Subtract(hull[e[1]], hull[e[2]]), v)));
box.Corners[2] = GeomMath.Add(hull[e[2]], GeomMath.Multiply(v, GeomMath.DotProduct(GeomMath.Subtract(hull[e[3]], hull[e[2]]), v)));
box.Width = Math.Abs(GeomMath.DotProduct(GeomMath.Subtract(hull[e[3]], hull[e[1]]), v));
box.Height = Math.Abs(GeomMath.DotProduct(GeomMath.Subtract(hull[e[2]], hull[e[0]]), n));
return(box);
}
public BoundingBox FindSmallestBoundingBox()
{
// mathtool::Vector2d v, n;
// int e[4]; //vertex indices of extreme points
// float a[4]; //angles
// int w; //index (0~3), so that e[w] has the smallest value a[w]
// int hullsize = m_chull.size();
Vector v, n = new Vector();
int[] e = new int[4];
double[] a = new double[4];
int w;
//int hullsize = hull.Count;
// //init extreme points
// e[0] = 0;
// v = (m_chull[1] - m_chull[0]).normalize();
// n.set(-v[1], v[0]);
// const mathtool::Vector2d v0 = v;
e[0] = 0;
v = GeomMath.Subtract(hull[1], hull[0]).normalize();
n.X = -v.Y;
n.Y = v.X;
//Vector v0 = v;
// float max_v = -FLT_MAX, min_v = FLT_MAX, max_n = -FLT_MAX;
// for (int i = 2; i < hullsize; i++)
// {
// auto & pt = m_chull[i];
// double dv = (pt - m_chull[0]) * v;
// double dn = (pt - m_chull[0]) * n;
// if (dv > max_v) { max_v = dv; e[1] = i; }
// if (dv < min_v) { min_v = dv; e[3] = i; }
// if (dn > max_n) { max_n = dn; e[2] = i; }
// }
double max_v = Double.MinValue;
double min_v = Double.MaxValue;
double max_n = Double.MinValue;
for (int i = 2; i < hull.Count; i++)
{
Vector pt = hull[i];
double dv = GeomMath.DotProduct(GeomMath.Subtract(pt, hull[0]), v);
double dn = GeomMath.DotProduct(GeomMath.Subtract(pt, hull[0]), n);
if (dv > max_v)
{
max_v = dv;
e[1] = i;
}
if (dv < min_v)
{
min_v = dv;
e[3] = i;
}
if (dn > max_n)
{
max_n = dn;
e[2] = i;
}
}
// w = findAngles(e, a, v, n);
w = FindAngles(e, a, v, n);
// //update extreme points
// char svg_filename[256];
// for (int i = 0; i < m_chull.size(); i++)
// {
//#if DEBUG
// cout << "box=" << box << endl;
// sprintf(svg_filename, "%s%03d.svg", "DEBUG_", i);
// saveSVG(svg_filename, m_chull_ply, box);
// //saveSVG(svg_filename,m_ply.front(),box);
//#endif
// }
double smallestArea = Double.MaxValue;
BoundingBox smallestBox = null;
for (int i = 0; i < hull.Count; i++)
{
// //create a box from v,n,e[4]
// obb box = createOBB(e, v, n);
var box = CreateBoundingBox(e, v, n);
double area = box.Width * box.Height;
if (smallestBox == null)
{
smallestBox = box;
smallestArea = area;
}
else if (area < smallestArea)
{
smallestBox = box;
smallestArea = area;
}
Console.WriteLine("Bounding Box #" + i + ": " + area);
// //check if this box solve the problem
// if (problem.solved(box)) break;
// //update
// int ne = (e[w] + 1) % hullsize;
// mathtool::Vector2d nev = (m_chull[ne] - m_chull[e[w]]).normalize();
// if (w == 0 || w == 2)
// {
// v = nev;
// n.set(-v[1], v[0]);
// }
// else
// {
// n = nev;
// v.set(-n[1], n[0]);
// }
// e[w] = ne;
// w = findAngles(e, a, v, n);
int ne = (e[w] + 1) % hull.Count;
Vector nev = GeomMath.Subtract(hull[ne], hull[e[w]]).normalize();
if (w == 0 || w == 2)
{
v = nev;
n.X = -v.Y;
n.Y = v.X;
}
else
{
n = nev;
v.X = -n.Y;
v.Y = n.X;
}
e[w] = ne;
w = FindAngles(e, a, v, n);
}
return(smallestBox);
}