public static float PointToLine(Vertex2 point, Vertex2 lineStart, Vertex2 lineEnd)
{
Vertex2 v = lineEnd - lineStart;
Vertex2 w = point - lineStart;
float c1 = Vertex2.Dot(w, v);
float c2 = Vertex2.Dot(v, v);
float b = c1 / c2;
Vertex2 pb = lineStart + b * v;
return(Vertex2.Distance(point, pb));
}
public static float PointToLineSegment(Vertex2 point, Vertex2 segmentStart, Vertex2 segmentEnd)
{
Vertex2 v = segmentEnd - segmentStart;
Vertex2 w = point - segmentStart;
float c1 = Vertex2.Dot(w, v);
if (c1 <= 0)
{
return(Vertex2.Distance(point, segmentStart));
}
float c2 = Vertex2.Dot(v, v);
if (c2 <= c1)
{
return(Vertex2.Distance(point, segmentEnd));
}
float b = c1 / c2;
Vertex2 pb = segmentStart + b * v;
return(Vertex2.Distance(point, pb));
}
public static float LineSegmentToLineSegment(Segment2 S1, Segment2 S2)
{
Vertex2 u = S1.b - S1.a;
Vertex2 v = S2.b - S2.a;
Vertex2 w = S1.a - S2.a;
float a = Vertex2.Dot(u, u); // always >= 0
float b = Vertex2.Dot(u, v);
float c = Vertex2.Dot(v, v); // always >= 0
float d = Vertex2.Dot(u, w);
float e = Vertex2.Dot(v, w);
float D = a * c - b * b; // always >= 0
float sN, sD = D; // sc = sN / sD, default sD = D >= 0
float tN, tD = D; // tc = tN / tD, default tD = D >= 0
// compute the line parameters of the two closest points
if (D < Mathf.Epsilon)
{
// the lines are almost parallel
sN = 0; // force using point P0 on segment S1
sD = 1; // to prevent possible division by 0.0 later
tN = e;
tD = c;
}
else
{
// get the closest points on the infinite lines
sN = (b * e - c * d);
tN = (a * e - b * d);
if (sN < 0)
{
// sc < 0 => the s=0 edge is visible
sN = 0;
tN = e;
tD = c;
}
else if (sN > sD)
{
// sc > 1 => the s=1 edge is visible
sN = sD;
tN = e + b;
tD = c;
}
}
if (tN < 0)
{
// tc < 0 => the t=0 edge is visible
tN = 0;
// recompute sc for this edge
if (-d < 0)
{
sN = 0;
}
else if (-d > a)
{
sN = sD;
}
else
{
sN = -d;
sD = a;
}
}
else if (tN > tD)
{
// tc > 1 => the t=1 edge is visible
tN = tD;
// recompute sc for this edge
if ((-d + b) < 0)
{
sN = 0;
}
else if ((-d + b) > a)
{
sN = sD;
}
else
{
sN = (-d + b);
sD = a;
}
}
// finally do the division to get sc and tc
float sc = (Mathf.Abs(sN) < Mathf.Epsilon ? 0 : sN / sD);
float tc = (Mathf.Abs(tN) < Mathf.Epsilon ? 0 : tN / tD);
// get the difference of the two closest points
Vertex2 dP = w + (sc * u) - (tc * v); // = S1(sc) - S2(tc)
return(dP.magnitude); // return the closest distance
}