/// <summary>
/// Returns the minimal distance between the polygon and the non-
/// overlapping other supplied polygon. The minimal distance is
/// always computed as the distance between a line segment and a
/// point. The indices of the minimal distance configuration are
/// returned in the out parameter, as the indices of points on the
/// two polygons, and wether the line segement was on this or the
/// other polygon. O(n). The returned index of the line segment is
/// the lower point index (except in case of wraparound).
/// </summary>
public static double MinDistanceTo(
this Polygon2d polygon, Polygon2d polygon1,
out int pi0, out int pi1, out bool lineOnThis)
{
var p0a = polygon.m_pointArray;
var p1a = polygon1.m_pointArray;
var p0c = polygon.m_pointCount;
var p1c = polygon1.m_pointCount;
var e0a = polygon.GetEdgeArray();
var e1a = polygon1.GetEdgeArray();
int i0 = p0a.IndexOfMinY(p0c), i1 = p1a.IndexOfMaxY(p1c);
V2d p0 = p0a[i0], e0 = e0a[i0], p1 = p1a[i1], e1 = e1a[i1];
int start0 = i0, start1 = i1;
var dir = V2d.XAxis;
var d = V2d.Distance(p0, p1);
var bestValue = double.MaxValue;
int bpi0 = -1, bpi1 = -1;
var bLineOnThis = true;
do
{
var s0 = Fun.Atan2(e0.Dot90(dir), e0.Dot(dir));
var s1 = Fun.Atan2(e1.Dot270(dir), e1.Dot180(dir));
if (s0 <= s1)
{
dir = e0a[i0];
int i0n = (i0 + 1) % p0c; var p0n = p0a[i0];
var dn = V2d.Distance(p0n, p1);
var dist = DistanceToLine(p1, p0, p0n, d, dn);
if (dist < bestValue)
{
bestValue = dist;
bLineOnThis = true; bpi0 = i0; bpi1 = i1;
}
i0 = i0n; p0 = p0n; e0 = e0a[i0]; d = dn;
}
else
{
dir = e0a[i1].Rot180;
int i1n = (i1 + 1) % p1c; var p1n = p1a[i1];
var dn = V2d.Distance(p0, p1n);
var dist = DistanceToLine(p0, p1, p1n, d, dn);
if (dist < bestValue)
{
bestValue = dist;
bLineOnThis = false; bpi0 = i0; bpi1 = i1;
}
i1 = i1n; p1 = p1n; e1 = e1a[i1]; d = dn;
}
}while (i0 != start0 || i1 != start1);
lineOnThis = bLineOnThis; pi0 = bpi0; pi1 = bpi1;
return(bestValue);
}
private static double DistanceToLine(V2d query, V2d p0, V2d p1, double d0, double d1)
{
var p0p1 = p1 - p0;
var p0q = query - p0;
var t = V2d.Dot(p0q, p0p1);
if (t <= 0)
{
return(d0);
}
var denom = p0p1.LengthSquared;
if (t >= denom)
{
return(d1);
}
t /= denom;
return(V2d.Distance(query, p0 + t * p0p1));
}