public void KtLine2DTest1()
{
var start = new KtPoint2D(1, 2);
var end = new KtPoint2D(3, 4);
var line = new KtLine2D(1, 2, 3, 4);
Assert.AreEqual(line.Start, start);
Assert.AreEqual(line.End, end);
}
public bool HasThePoint(KtPoint2D point)
{
var parameter = (point - Start).ToKtVector2D() / Vector;
if (parameter is null)
{
return(false);
}
return(ValidParametricValue(parameter));
}
public KtPoint2D Centroid()
{
var Atotal = 0d;
var Ad = new KtPoint2D();
foreach (var r in _regions)
{
Atotal += r.Area();
Ad += r.AreaCentroid();
}
return(Ad / Atotal);
}
public void LineIntersectionTests()
{
var watch = new Stopwatch();
var intersection = new KtPoint2D(5, 7);
var line1 = new KtLine2D((1, 1), (3, 4));
var line2 = new KtLine2D((9, 3), (7, 5));
var line3 = new KtLine2D((3, 1), (5, 4));
var ray1 = new KtRay2D((9, 3), (7, 5));
var ray2 = new KtRay2D((7, 5), (9, 3));
var ray3 = new KtRay2D((1, 1), (3, 4));
var ray4 = new KtRay2D((3, 4), (1, 1));
var segment1 = new KtSegment2D((7, 5), (9, 3));
var segment2 = new KtSegment2D((4, 8), (9, 3));
var segment3 = new KtSegment2D((1, 1), (3, 4));
var segment4 = new KtSegment2D((1, 1), (7, 10));
watch.Start();
for (int i = 0; i < 100001; i++)
{
// line to line with intersection
#pragma warning disable CS0618 // Type or member is obsolete
Assert.AreEqual(line1.IntersectWith3(line2), intersection);
//line to line parallel
Assert.IsNull(line1.IntersectWith3(line3));
// line to ray with intersection
Assert.AreEqual(line1.IntersectWith3(ray1), new KtPoint2D(5, 7));
// line to ray no Intersection
Assert.AreEqual(line1.IntersectWith3(ray2), null);
//line to segment no intersection
Assert.AreEqual(line1.IntersectWith3(segment1), null);
//line to segment with intersection
Assert.AreEqual(line1.IntersectWith3(segment2), new KtPoint2D(5, 7));
//ray to ray with intersection
Assert.AreEqual(ray3.IntersectWith3(ray1), new KtPoint2D(5, 7));
//ray to ray no intersection
Assert.AreEqual(ray3.IntersectWith3(ray2), null);
Assert.AreEqual(ray4.IntersectWith3(ray2), null);
Assert.AreEqual(ray4.IntersectWith3(ray1), null);
//ray to segment with intersection
Assert.AreEqual(ray3.IntersectWith3(segment2), new KtPoint2D(5, 7));
//ray to segment no intersection
Assert.AreEqual(ray3.IntersectWith3(segment1), null);
Assert.AreEqual(ray4.IntersectWith3(segment2), null);
//segment to segment no intersection
Assert.AreEqual(segment3.IntersectWith3(segment1), null);
//segement to segment with intersection
Assert.AreEqual(segment4.IntersectWith3(segment2), new KtPoint2D(5, 7));
#pragma warning restore CS0618 // Type or member is obsolete
}
watch.Stop();
System.Console.WriteLine(((double)watch.ElapsedMilliseconds).ToString());
//System.Windows.Forms.MessageBox.Show(watch.ElapsedMilliseconds.ToString());
}
public KtPoint2D IntersectWith3(KtLine2DBase line2)
{
var determinant = Vector.Cross(line2.Vector);
if (determinant.NearZero(5))
{
return(null);
}
var(a1, a2, b1, b2, c1, c2) = (A, line2.A, B, line2.B, C, line2.C);
var p = new KtPoint2D((b2 * c1) - (b1 * c2), (c2 * a1) - (c1 * a2)) / determinant;
return(Bounds(p) && line2.Bounds(p) ? p : null);
}
internal override bool Bounds(KtPoint2D p)
{
if (p is null)
{
return(false);
}
if (p == Start)
{
return(true);
}
var directionOfPoint = (p - Start).ToKtVector2D().Direction;
var directionOfLine = Vector.Direction;
return(directionOfPoint == directionOfLine);
}
public static KtRegion Rectangle(KtPoint2D center, double width, double height, bool solid = true)
{
if (center == null)
{
center = new KtPoint2D();
}
var corners = new List <KtPoint2D>
{
center + new KtPoint2D(-width / 2.0, -height / 2.0),
center + new KtPoint2D(-width / 2.0, height / 2.0),
center + new KtPoint2D(width / 2.0, height / 2.0),
center + new KtPoint2D(width / 2.0, -height / 2.0)
};
return(solid ? (KtRegion) new KtSolidRegion(corners) : new KtHollowRegion(corners));
}
protected KtLine2DBase(KtPoint2D start, KtPoint2D end)
{
if (start == end)
{
throw new ArgumentException("Cannot create zero length line where start and end are equal");
}
if (start == null || end == null)
{
throw new ArgumentNullException($"Cannot create a 2D line with points ({start}) and ({end}) where one is null");
}
Start = start;
End = end;
Vector = (end - start).ToKtVector2D();
A = Vector.Y;
B = -Vector.X;
C = Start.ToKtVector2D().Cross(Vector);
}
public static KtRegion RegularPolygon(KtPoint2D center, int cornerCount, double circumRadius, bool solid)
{
if (circumRadius.NearZero(5) || cornerCount < 2)
{
return(null);
}
if (center == null)
{
center = new KtPoint2D();
}
var corners = new List <KtPoint2D>();
var intAngle = Cycle.Create(1) / cornerCount;
for (var i = 0; i < cornerCount; i++)
{
var corner = center + (new KtVector2D(intAngle * i) * circumRadius).ToKtPoint2D();
corners.Add(corner);
}
return(solid ? (KtRegion) new KtSolidRegion(corners) : new KtHollowRegion(corners));
}
public KtSegment2D(KtPoint2D start, KtPoint2D end) : base(start, end)
{
}
public KtLine2D(KtPoint2D start, KtPoint2D end) : base(start, end)
{
}
internal static bool LiesOnSegments(this KtPoint2D point, IEnumerable <KtSegment2D> segments) => segments.Any(segment => segment.HasThePoint(point));
internal abstract bool Bounds(KtPoint2D p);
internal static bool Inscribes(this CircularStack <KtPoint2D> points, KtPoint2D point) => !points.EdgesHasThePoint(point) && !points.InteriorAngle(point).IsZero;
public KtPolygon2D Translate(KtPoint2D point) => new(_regions.Select(reg => reg.Translate(point)).ToArray());
private static bool EdgesHasThePoint(this CircularStack <KtPoint2D> points, KtPoint2D point) => points.ToEdges().Any(edge => edge.HasThePoint(point));
public KtRay2D(KtPoint2D start, KtVector2D direction) : this(start, start + direction)
{
}
public double SubstitutePoint(KtPoint2D p) => (A * p.X) + (B * p.Y) - C;
public double Distance(KtPoint2D p) => SubstitutePoint(p) / Vector.Magnitude;
internal override bool Bounds(KtPoint2D p) => p.X.IsWithin(Start.X, End.X) && p.Y.IsWithin(Start.Y, End.Y);
public static Angle TotalInternalAngle(this CircularStack <KtPoint2D> points, KtPoint2D point) => points.Aggregate(Degrees.Create(0), (total, c) => total + (c?.Next?.Value - point).ToKtVector2D().AngleBetween((c?.Value - point).ToKtVector2D()));
internal static bool Inscribes(this IEnumerable <KtPoint2D> points, KtPoint2D point) => points.ToCircularStack().Inscribes(point);
public static Angle TotalInternalAngle(this IEnumerable <KtPoint2D> points, KtPoint2D point) => points.ToCircularStack().TotalInternalAngle(point);
private static Angle InteriorAngle(this CircularStack <KtPoint2D> points, KtPoint2D point) => points.Aggregate(Degrees.Create(0.0), (total, c) => total + c.InteriorAngle(point));
public bool Inline(KtPoint2D p) => p != null && SubstitutePoint(p).NearZero() && Bounds(p);
private static Angle InteriorAngle(this CircularStackElement <KtPoint2D> c, KtPoint2D point) => (c?.Next?.Value - point).ToKtVector2D().AngleBetween((c?.Value - point).ToKtVector2D());
public KtRay2D(KtPoint2D start, KtPoint2D end) : base(start, end)
{
}
