public static double DistanceFrom(this Point p, LineSegment line)
{
var s = p.LerpProjectOnto(line);
if (s < 0) return p.DistanceFrom(line.Start);
if (s > 1) return p.DistanceFrom(line.End);
return p.DistanceFrom(line.LerpAcross(s));
}
/// <summary>
/// Returns the point where a linear cut path intersects a line segment whose ends points are following linear paths.
/// Returns null if there is no such point.
/// Also returns the normalized 'direction' of the cut.
/// </summary>
public static Tuple <Point, Vector> TryGetCut(this LineSegment cutPath, LineSegment endPath1, LineSegment endPath2)
{
var e = new[] { endPath1, endPath2 }
.Select(line => new LineSegment(line.Start, line.Delta - cutPath.Delta))
.ToArray();
var c = GeometryUtilities.LineDefinedByMovingEndPointsCrossesOrigin(e[0], e[1], origin: cutPath.Start);
if (!c.HasValue)
{
return(null);
}
var p = cutPath.LerpAcross(c.Value.T);
var v = cutPath.Delta - endPath1.Delta.LerpTo(endPath2.Delta, c.Value.S);
return(Tuple.Create(p, v.Normal()));
}
public static IntersectionParameters? LineDefinedByMovingEndPointsCrossesOrigin(LineSegment endPath1,
LineSegment endPath2,
Point origin = default(Point)) {
var b = endPath1.Start - origin;
var d = endPath2.Start - endPath1.Start;
var db = endPath1.Delta;
var dd = endPath2.Delta - endPath1.Delta;
return (from t in QuadraticRoots(dd.Cross(db),
d.Cross(db) + dd.Cross(b),
d.Cross(b))
where t >= 0 && t <= 1
let p0 = endPath1.LerpAcross(t)
let p1 = endPath2.LerpAcross(t)
let s = origin.LerpProjectOnto(p0.To(p1))
where s >= 0 && s <= 1
select (IntersectionParameters?)new IntersectionParameters {T = t, S = s}
).FirstOrDefault();
}
public static IntersectionParameters?LineDefinedByMovingEndPointsCrossesOrigin(LineSegment endPath1,
LineSegment endPath2,
Point origin = default(Point))
{
var b = endPath1.Start - origin;
var d = endPath2.Start - endPath1.Start;
var db = endPath1.Delta;
var dd = endPath2.Delta - endPath1.Delta;
return((from t in QuadraticRoots(dd.Cross(db),
d.Cross(db) + dd.Cross(b),
d.Cross(b))
where t >= 0 && t <= 1
let p0 = endPath1.LerpAcross(t)
let p1 = endPath2.LerpAcross(t)
let s = origin.LerpProjectOnto(p0.To(p1))
where s >= 0 && s <= 1
select(IntersectionParameters?) new IntersectionParameters {
T = t, S = s
}
).FirstOrDefault());
}