public static void ClosestPointOnPolygon(RenderVertex3D[] rgv, Vertex2D pvin, bool fClosed, out Vertex2D pvOut, out int piSeg)
{
var count = rgv.Length;
var minDist = Constants.FloatMax;
piSeg = -1; // in case we are not next to the line
pvOut = new Vertex2D();
var loopCount = count;
if (!fClosed)
{
--loopCount; // Don"t check segment running from the end point to the beginning point
}
// Go through line segment, calculate distance from point to the line
// then pick the shortest distance
for (var i = 0; i < loopCount; ++i)
{
var p2 = i < count - 1 ? i + 1 : 0;
var rgvi = new RenderVertex3D();
rgvi.Set(rgv[i].X, rgv[i].Y, rgv[i].Z);
var rgvp2 = new RenderVertex3D();
rgvp2.Set(rgv[p2].X, rgv[p2].Y, rgv[p2].Z);
var a = rgvi.Y - rgvp2.Y;
var b = rgvp2.X - rgvi.X;
var c = -(a * rgvi.X + b * rgvi.Y);
var dist = MathF.Abs(a * pvin.X + b * pvin.Y + c) / MathF.Sqrt(a * a + b * b);
if (dist < minDist)
{
// Assuming we got a segment that we are closet to, calculate the intersection
// of the line with the perpendicular line projected from the point,
// to find the closest point on the line
var d = -b;
var f = -(d * pvin.X + a * pvin.Y);
var det = a * a - b * d;
var invDet = det != 0.0f ? 1.0f / det : 0.0f;
var intersectX = (b * f - a * c) * invDet;
var intersectY = (c * d - a * f) * invDet;
// If the intersect point lies on the polygon segment
// (not out in space), then make this the closest known point
if (intersectX >= MathF.Min(rgvi.X, rgvp2.X) - 0.1 &&
intersectX <= MathF.Max(rgvi.X, rgvp2.X) + 0.1 &&
intersectY >= MathF.Min(rgvi.Y, rgvp2.Y) - 0.1 &&
intersectY <= MathF.Max(rgvi.Y, rgvp2.Y) + 0.1)
{
minDist = dist;
var seg = i;
pvOut.X = intersectX;
pvOut.Y = intersectY;
piSeg = seg;
}
}
}
}
private static bool AdvancePoint(IReadOnlyList <IRenderVertex> rgv, IReadOnlyList <int> poly, int a, int b, int c, int pre, int post)
{
var pv1 = rgv[a];
var pv2 = rgv[b];
var pv3 = rgv[c];
var pvPre = rgv[pre];
var pvPost = rgv[post];
if (GetDot(pv1, pv2, pv3) < 0 ||
// Make sure angle created by new triangle line falls inside existing angles
// If the existing angle is a concave angle, then new angle must be smaller,
// because our triangle can"t have angles greater than 180
GetDot(pvPre, pv1, pv2) > 0 &&
GetDot(pvPre, pv1, pv3) < 0 || // convex angle, make sure new angle is smaller than it
GetDot(pv2, pv3, pvPost) > 0 && GetDot(pv1, pv3, pvPost) < 0)
{
return(false);
}
// Now make sure the interior segment of this triangle (line ac) does not
// intersect the polygon anywhere
// sort our static line segment
var minX = MathF.Min(pv1.GetX(), pv3.GetX());
var maxX = MathF.Max(pv1.GetX(), pv3.GetX());
var minY = MathF.Min(pv1.GetY(), pv3.GetY());
var maxY = MathF.Max(pv1.GetY(), pv3.GetY());
for (var i = 0; i < poly.Count; ++i)
{
var pvCross1 = rgv[poly[i]];
var pvCross2 = rgv[poly[i < poly.Count - 1 ? i + 1 : 0]];
if (pvCross1 != pv1 && pvCross2 != pv1 && pvCross1 != pv3 && pvCross2 != pv3 &&
(pvCross1.GetY() >= minY || pvCross2.GetY() >= minY) &&
(pvCross1.GetY() <= maxY || pvCross2.GetY() <= maxY) &&
(pvCross1.GetX() >= minX || pvCross2.GetX() >= minX) &&
(pvCross1.GetX() <= maxX || pvCross2.GetX() <= maxX) &&
LinesIntersect(pv1, pv3, pvCross1, pvCross2))
{
return(false);
}
}
return(true);
}
private static bool LinesIntersect(IRenderVertex start1, IRenderVertex start2, IRenderVertex end1, IRenderVertex end2)
{
var x1 = start1.GetX();
var y1 = start1.GetY();
var x2 = start2.GetX();
var y2 = start2.GetY();
var x3 = end1.GetX();
var y3 = end1.GetY();
var x4 = end2.GetX();
var y4 = end2.GetY();
var d123 = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1);
if (d123 == 0.0) // p3 lies on the same line as p1 and p2
{
return(x3 >= MathF.Min(x1, x2) && x3 <= MathF.Max(x2, x1));
}
var d124 = (x2 - x1) * (y4 - y1) - (x4 - x1) * (y2 - y1);
if (d124 == 0.0) // p4 lies on the same line as p1 and p2
{
return(x4 >= MathF.Min(x1, x2) && x4 <= MathF.Max(x2, x1));
}
if (d123 * d124 >= 0.0)
{
return(false);
}
var d341 = (x3 - x1) * (y4 - y1) - (x4 - x1) * (y3 - y1);
if (d341 == 0.0) // p1 lies on the same line as p3 and p4
{
return(x1 >= MathF.Min(x3, x4) && x1 <= MathF.Max(x3, x4));
}
var d342 = d123 - d124 + d341;
if (d342 == 0.0) // p1 lies on the same line as p3 and p4
{
return(x2 >= MathF.Min(x3, x4) && x2 <= MathF.Max(x3, x4));
}
return(d341 * d342 < 0.0);
}
