///<summary>Positions a line control to match a line segment.</summary>
public static void Reposition(this Line lineControl, LineSegment position)
{
lineControl.X1 = position.Start.X;
lineControl.Y1 = position.Start.Y;
lineControl.X2 = position.End.X;
lineControl.Y2 = position.End.Y;
}
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));
}
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 Animation Animate(Lifetime life)
{
var animation = new Animation();
var state = Ani.Anon(dt => {
var t = dt.TotalSeconds;
var x = Math.Cos(t)*100 + 150;
var y = Math.Sin(t)*100 + 150;
var vx = Math.Cos(3*t);
var vy = Math.Sin(3*t);
var c = new Point(x, y);
var v = new Vector(vx, vy);
var r = 20;
var li = new LineSegment(new Point(150 - 89, 150 - 89), new Point(150 + 50, 150 + 20));
var h = GeometryUtilities.WhenMovingCircleWillIntersectLineSegment(c, r, v, li);
return new {c, r, v, li, h};
});
animation.Things.Add(new LineSegmentDesc(state.Select(e => e.li)), life);
animation.Things.Add(
new PointDesc(
state.Select(e => e.c),
Brushes.Black,
Brushes.Gray,
state.Select(e => (double)e.r),
1.0),
life);
animation.Things.Add(new LineSegmentDesc(state.Select(e => e.c.Sweep(e.v * 1000)), Brushes.Red), life);
animation.Things.Add(new LineSegmentDesc(state.Select(e => e.c.Sweep(e.v * 1000) + e.v.Perp() * e.r), Brushes.LightGray), life);
animation.Things.Add(new LineSegmentDesc(state.Select(e => e.c.Sweep(e.v * 1000) - e.v.Perp() * e.r), Brushes.LightGray), life);
animation.Things.Add(
new PointDesc(
state.Select(e => (e.c + e.v * e.h) ?? new Point(-10000, -10000)),
Brushes.Gray,
Brushes.LightGray,
state.Select(e => (double)e.r),
1.0),
life);
return animation;
}
private static LineSegment? ClipLine(LineSegment line, Rect rect)
{
var left = new Point(rect.Left, rect.Top - 100000).To(new Point(rect.Left, rect.Bottom + 100000));
var right = new Point(rect.Right, rect.Top - 100000).To(new Point(rect.Right, rect.Bottom + 100000));
var top = new Point(rect.Left - 100000, rect.Top).To(new Point(rect.Right + 100000, rect.Top));
var bottom = new Point(rect.Left - 100000, rect.Bottom).To(new Point(rect.Right + 100000, rect.Bottom));
var p1 = line.TryIntersectionPointInside(left);
var p2 = line.TryIntersectionPointInside(right);
var p3 = line.TryIntersectionPointInside(top);
var p4 = line.TryIntersectionPointInside(bottom);
var es = new[] {line.Start, line.End};
if (p1.HasValue) return ClipLine(p1.Value.To(es.MayMaxBy(e => e.X).ForceGetValue()), rect);
if (p2.HasValue) return ClipLine(p2.Value.To(es.MayMaxBy(e => -e.X).ForceGetValue()), rect);
if (p3.HasValue) return ClipLine(p3.Value.To(es.MayMaxBy(e => e.Y).ForceGetValue()), rect);
if (p4.HasValue) return ClipLine(p4.Value.To(es.MayMaxBy(e => -e.Y).ForceGetValue()), rect);
if (!rect.Contains(line.Mid)) return null;
return line;
}
///<summary>The point on a line segment that is closest to a target point.</summary>
public static Point ClosestPointOn(this Point point, LineSegment line) {
return line.Start + line.Delta.Normal() * (point - line.Start).ScalarProjectOnto(line.Delta).Clamp(0, line.Delta.Length);
}
///<summary>Handles cutting connectors with a moving kill point.</summary>
public static void SetupMouseCutter(this Game game,
PerishableCollection<UIElement> controls,
Func<Point?> liveMousePosition,
double cutTolerance) {
var lastUsedMousePos = liveMousePosition();
game.LoopActions.Add(
step => {
// get a path between last and current mouse positions, if any
var prev = lastUsedMousePos;
var cur = liveMousePosition();
lastUsedMousePos = cur;
if (!prev.HasValue || !cur.HasValue) return;
var cutPath = new LineSegment(prev.Value, cur.Value);
// cut any connectors that crossed the cut path
foreach (var cut in from e in game.Connectors.CurrentItems()
let connector = e.Value
let endPath1 = new LineSegment(connector.Parent.LastPos, connector.Parent.Pos)
let endPath2 = new LineSegment(connector.Child.LastPos, connector.Child.Pos)
let pt = cutPath.TryGetCut(endPath1, endPath2)
where pt != null
select new { pt, connector} ) {
cut.connector.CutPoint = cut.pt.Item1;
cut.connector.CutDir = cut.pt.Item2.Normal();
cut.connector.Child.Life.EndLifetime();
}
},
game.Life);
}
///<summary>Positions a line control to match a line segment.</summary>
public static void Reposition(this Line lineControl, LineSegment position) {
lineControl.X1 = position.Start.X;
lineControl.Y1 = position.Start.Y;
lineControl.X2 = position.End.X;
lineControl.Y2 = position.End.Y;
}
public static Point IntersectionPoint(this LineSegment line1, LineSegment line2)
{
var p = line1.TryIntersectionPoint(line2);
if (p == null) throw new InvalidOperationException();
return p.Value;
}
///<summary>Returns the first non-negative time, if any, where a moving circle will intersect a fixed line segment.</summary>
public static double? WhenMovingCircleWillIntersectLineSegment(Point center, double radius, Vector velocity, LineSegment line)
{
var epsilon = 0.00001;
// use whatever's earliest and is actually touching
return new[] {
WhenMovingCircleWillIntersectExtendedLine(center, radius, velocity, line.Start, line.Delta),
WhenMovingCircleWillIntersectPoint(center, radius, velocity, line.Start),
WhenMovingCircleWillIntersectPoint(center, radius, velocity, line.End)
}.OrderBy(e => e)
.FirstOrDefault(t => t.HasValue && (center + velocity * t.GetValueOrDefault()).DistanceFrom(line) <= radius + epsilon);
}
public static Point? TryIntersectionPointInside(this LineSegment line1, LineSegment line2)
{
var p = TryIntersectionPoint(line1, line2);
if (!p.HasValue) return null;
var q = p.Value;
if (q.DistanceFrom(line1.Start) < 0.001) return null;
if (q.DistanceFrom(line1.End) < 0.001) return null;
if (q.DistanceFrom(line2.Start) < 0.001) return null;
if (q.DistanceFrom(line2.End) < 0.001) return null;
return q;
}
public static Point? TryIntersectionPoint(this LineSegment line1, LineSegment line2)
{
if (line1.Delta.IsParallelTo(line2.Delta)) return null;
//[solve intersection in 2d, then transform back]
//create transformed coordinate axies [x along L1, y along L2 (with x component removed), z=0]
var u_x = line1.Delta.Normal();
var u_y = line2.Delta.PerpOnto(u_x).Normal();
//transform L2's direction vector
var u_L2_dir = new Vector(line2.Delta.ScalarProjectOnto(u_x), line2.Delta.ScalarProjectOnto(u_y));
if (u_L2_dir.Y.Abs() < 0.001) return null;
//get the transformed y-distance between L1 and L2's starting points, and convert it to a time
var u_L1_L2_dy = (line1.Start - line2.Start).ScalarProjectOnto(u_y);
var u_t = u_L1_L2_dy/u_L2_dir.Y;
//get the transformed intersection point
var c_2d = u_L2_dir * u_t;
//transform intersection point back to normal coordinates
var c_3d = line2.Start + c_2d.X * u_x + c_2d.Y * u_y;
//check that 2d intersection is in fact a 3d intersection
if (!line1.ContainsPoint(c_3d)) return null;
if (!line2.ContainsPoint(c_3d)) return null;
return c_3d;
}
