/// <summary>Returns resulting point if this point is rotated around <paramref name='reference'/> by <paramref name='degrees'/>.</summary>
/// <param name='reference'>The center of the rotation.</param>
/// <param name='degrees'>Positive values means a counter-clockwise rotation.</param>
public WPoint Rotate(WPoint reference, double degrees)
{
WPoint a = this - reference;
WPoint b = a.RotateAroundOrigin(degrees);
return(b + reference);
}
/// <summary></summary>
public WRectangle(double width, double height, WPoint corner, double rotation)
{
Width = width;
Height = height;
Corner = corner;
Rotation = rotation;
}
/// <summary>Finds the intersection points between the edge of this circle and circle <paramref name='b'/>.</summary>
/// <returns>Null (no intersection), an array of length 1, or an array of length 2.</returns>
public WPoint[] GetIntersectionPoints(WCircle b)
{
//following the method in math/intersectionCircleCircle.png
WCircle a = this;
double d = a.Center.Distance(b.Center); //distance between centers
if (d > a.Radius + b.Radius)
{
return(null); //circles too far apart to intersect
}
if (a.ContainsOrIsContained(b))
{
return(null); //one circle is wholly inside the other
}
//the radical line is the line between the two intersecting points of the circles
//Point c is the center of the radical line, which is also on the line between the centers
double dA = (Math.Pow(a.Radius, 2) - Math.Pow(b.Radius, 2) + Math.Pow(d, 2)) / (2 * d); //distance from centerA to pointC
if (dA == a.Radius)
{
return(new WPoint[] { Geometry.PointOnLine(a.Center, b.Center, a.Radius) }); //circles intersect at single point
}
WPoint c = a.Center + dA * (b.Center - a.Center) / d;
//h is the distance from pointC to either intersection point (the hypotenus of triangle centerA-C-intersection)
double h = Math.Sqrt(Math.Pow(a.Radius, 2) - Math.Pow(dA, 2));
return(new WPoint[] {
new WPoint(c.X + (h * (b.Y - a.Y) / d), c.Y - h * (b.X - a.X) / d),
new WPoint(c.X - (h * (b.Y - a.Y) / d), c.Y + h * (b.X - a.X) / d)
});
}
/// <summary></summary>
public Intersection(WPoint point)
{
Type = IntersectionType.Point;
this.points = new List <WPoint>()
{
point
};
}
/// <exception cref='ArgumentException'>Points A and B cannot be the same.</exception>
public WLine(WPoint a, WPoint b, bool isDirected)
{
if (a == b)
{
throw new ArgumentException("Points A and B cannot be the same.");
}
A = a;
B = b;
IsDirected = isDirected;
}
/// <returns>Null (no intercepts), or array of length 1 or 2.</returns>
public WPoint[] GetIntersectionPoints(WLine line)
{
//line does not intersect if perpendicular line from circle-center to line is longer than circle-radius
WPoint perpendicularToCenter = line.GetPerpendicularIntersect(Center);
if (perpendicularToCenter.Distance(Center) > Radius)
{
return(null);
}
//equation of circle with radius r and center (h, k)
//is (x - h)^2 + (y - k)^2 = r^2
//line: y = mx + b
//circle: (x - h)^2 + (y - k)^2 = r^2
//substitute y: (x - h)^2 + (mx + b - k)^2 = r^2
//expand: x^2 - 2hx + h^2 + m^2x^2 + 2(b - k)mx + (b - k)^2 - r^2 = 0
//group: (1 + m^2)x^2 + (-2h + 2(b - k)m)x + (h^2 + (b - k)^2 - r^2) = 0
//quadratic equation: if 0 = Ax^2 + Bx + C, then x = (-B +- sqrt(B^2 - 4AC)) / 2A
double A = 1 + Math.Pow(line.Slope, 2);
double B = (-2 * Center.X) + (2 * (line.YIntercept - Center.Y) * line.Slope);
double C = Math.Pow(Center.X, 2) + Math.Pow(line.YIntercept - Center.Y, 2) - Math.Pow(Radius, 2);
double x1 = (-1 * B + Math.Sqrt(Math.Pow(B, 2) - (4 * A * C))) / (2 * A);
double x2 = (-1 * B - Math.Sqrt(Math.Pow(B, 2) - (4 * A * C))) / (2 * A);
double y1 = line.Slope * x1 + line.YIntercept;
double y2 = line.Slope * x2 + line.YIntercept;
if (line.IsVertical)
{
x1 = line.A.X;
x2 = line.A.X;
//must use circle equation instead of line equation to find y's
y1 = Center.Y + Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(x1 - Center.X, 2));
y2 = Center.Y - Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(x1 - Center.X, 2));
}
if (line.IsHorizontal)
{
y1 = line.A.Y;
y2 = line.A.Y;
}
WPoint point1 = new WPoint(x1, y1);
WPoint point2 = new WPoint(x2, y2);
List <WPoint> result = new List <WPoint>()
{
point1
};
if (point1 != point2)
{
result.Add(point2);
}
return(result.ToArray());
}
/// <summary>
/// Returns true if this wedge contains point <paramref name='b'/>, including if <paramref name='b'/> lies on one of this wedge's edges.
/// </summary>
public bool Contains(WPoint b)
{
double distance = Circle.Center.Distance(b);
if (distance > Circle.Radius)
{
return(false);
}
double degrees = Circle.DegreesAtPoint(b);
return(Degrees.Overlaps(degrees));
}
/// <summary>
/// Find the two tangent points on the circle that form lines to point <paramref name='b'/>.
/// </summary>
/// <returns>Array of length 2.</returns>
public WPoint[] GetTangentPoints(WPoint b)
{
//point C and D are the tangents
WCircle a = this;
double distanceAB = a.Center.Distance(b);
double degreesAB = DegreesAtPoint(b);
double degreesAB_AC = Math.Cos(Radius / distanceAB);
WPoint c = PointAtDegrees(degreesAB + degreesAB_AC);
WPoint d = PointAtDegrees(degreesAB - degreesAB_AC);
return(new WPoint[] { c, d });
}
/// <summary>Returns true if point <paramref name='c'/> lies on this line.</summary>
public virtual bool Overlaps(WPoint c)
{
if (IsVertical)
{
return(Geometry.WithinMarginOfError(c.X, A.X));
}
if (!Geometry.WithinMarginOfError(c.Y, (Slope * c.X) + YIntercept))
{
return(false);
}
return(true);
}
//todo: better names for PointOnLine and PointPastLine, they are misleading
/// <summary>
/// Calculates point along line AB, starting at A and moving towards B
/// </summary>
/// <exception cref='ArgumentException'>Point A and B cannot be the same.</exception>
public static WPoint PointOnLine(WPoint a, WPoint b, double distance)
{
double lineLength = a.Distance(b);
if (lineLength == 0)
{
throw new ArgumentException("Point A and B cannot be the same.");
}
double lengthRatio = distance / lineLength;
double x = ((1d - lengthRatio) * a.X) + (lengthRatio * b.X);
double y = ((1d - lengthRatio) * a.Y) + (lengthRatio * b.Y);
return(new WPoint(x, y));
}
/// <summary>Returns true if point <paramref name='c'/> lies on this line segment.</summary>
public override bool Overlaps(WPoint c)
{
if (IsVertical)
{
return(Geometry.WithinMarginOfError(c.X, A.X));
}
if (!Geometry.WithinMarginOfError(c.Y, (Slope * c.X) + YIntercept))
{
return(false);
}
return(c.X >= Math.Min(A.X, B.X) && c.X <= Math.Max(A.X, B.X) &&
c.Y >= Math.Min(A.Y, B.Y) && c.Y <= Math.Max(A.Y, B.Y));
}
//todo: couldn't LineDirection be moved to Line object? probably PointOnLine and PointPastLine could to.
/// <summary>
/// Given directed line A to B, what direction is it pointing?
/// </summary>
/// <remarks>
/// North, South, East, and West answers are exact. So "North" means exactly North.
/// The inbetween directions cover all remaining values. So "NorthWest" covers all values between North and West.
/// </remarks>
/// <exception cref='NotImplementedException'>Coordinate plane not supported.</exception>
public static Direction LineDirection(WPoint a, WPoint b)
{
if (a == b)
{
return(Direction.None);
}
switch (CoordinatePlane)
{
case CoordinatePlanes.Screen: return(LineDirection_Screen(a, b));
case CoordinatePlanes.Paper: return(LineDirection_Paper(a, b));
default: throw new NotImplementedException("Coordinate plane not supported.");
}
}
//todo: verify that all line operations take vertical and horizontal lines into account
/// <summary>
/// Returns the point where a perpendicular line passing through point <paramref name='c'/> intersects this line.
/// </summary>
public WPoint GetPerpendicularIntersect(WPoint c)
{
if (IsVertical)
{
return(new WPoint(this.A.X, c.Y));
}
if (IsHorizontal)
{
return(new WPoint(c.X, this.A.Y));
}
double cSlope = PerpendicularSlope;
double cYIntercept = c.Y - (cSlope * c.X);
double x = (cYIntercept - this.YIntercept) / (this.Slope - cSlope);
double y = (this.Slope * x) + this.YIntercept;
return(new WPoint(x, y));
}
private static Direction LineDirection_Paper(WPoint a, WPoint b)
{
if (a.X == b.X)
{
return((a.Y < b.Y) ? Direction.North : Direction.South);
}
if (a.Y == b.Y)
{
return((a.X < b.X) ? Direction.East : Direction.West);
}
if (a.X < b.X)
{
return((a.Y < b.Y) ? Direction.NorthEast : Direction.SouthEast);
}
else
{
return((a.Y < b.Y) ? Direction.NorthWest : Direction.SouthWest);
}
}
/// <summary>
/// Given a line from the center of this circle to a point (<paramref name='lineEnd'/>), what degrees is the line angle at?
/// 0 degrees is East of center, increases clockwise.
/// </summary>
public double DegreesAtPoint(WPoint lineEnd)
{
if (Geometry.CoordinatePlane == Geometry.CoordinatePlanes.None)
{
throw new ArgumentException("Coordinate plane required.");
}
Geometry.Direction direction = Geometry.LineDirection(Center, lineEnd);
switch (direction)
{
case Geometry.Direction.East: return(0);
case Geometry.Direction.South: return(90);
case Geometry.Direction.West: return(180);
case Geometry.Direction.North: return(270);
}
double lineLength = Center.Distance(lineEnd);
double radians = Math.Abs(Math.Asin((lineEnd.Y - Center.Y) / lineLength));
double degrees = Shapes.WCircle.RadiansToDegrees(radians) % DEGREES_IN_CIRCLE;
switch (direction)
{
case Geometry.Direction.SouthEast: return(degrees);
case Geometry.Direction.SouthWest: return(DEGREES_IN_HALF_CIRCLE - degrees);
case Geometry.Direction.NorthWest: return(DEGREES_IN_HALF_CIRCLE + degrees);
case Geometry.Direction.NorthEast: return(DEGREES_IN_CIRCLE - degrees);
}
throw new NotImplementedException(String.Format("Direction not supported: {0}.", direction));
}
/// <summary></summary>
public WWedgeUnbound(WPoint center, WRangeCircular degreeRange)
{
Center = center;
Degrees = degreeRange;
}
/// <summary>
/// Returns true if point <paramref name='b'/> lies within or on this circle.
/// </summary>
public bool Contains(WPoint b)
{
return(Center.Distance(b) <= Radius);
}
/// <summary>Generates a vertical line through the specified point.</summary>
public static WLine Vertical(WPoint point)
{
return(new WLine(point, new WPoint(point.X, point.Y + 1)));
}
/// <summary>
/// Returns the distance between this point and point <paramref name='b'/>. Always positive.
/// </summary>
public double Distance(WPoint b)
{
return(Math.Sqrt(Math.Pow(b.X - this.X, 2) + Math.Pow(b.Y - this.Y, 2)));
}
/// <summary>Returns intersection between a line segment and another line segment.</summary>
public override Intersection GetIntersection(WLineSegment that)
{
if (this.Parallel(that))
{
bool thisAOnThat = this.A.Overlaps(that);
bool thisBOnThat = this.B.Overlaps(that);
bool thatAOnThis = that.A.Overlaps(this);
bool thatBOnThis = that.B.Overlaps(this);
if (!thisAOnThat && !thisBOnThat && !thatAOnThis && !thatBOnThis)
{
return(Intersection.NONE);
}
if (thisAOnThat && thisBOnThat)
{
return(new Intersection(this));
}
if (thatAOnThis && thatBOnThis)
{
return(new Intersection(that));
}
WPoint overlapThis = null;
WPoint overlapThat = null;
if (thisAOnThat)
{
overlapThis = this.A;
}
else if (thisBOnThat)
{
overlapThis = this.B;
}
if (thatAOnThis)
{
overlapThat = that.A;
}
else if (thatBOnThis)
{
overlapThat = that.B;
}
if (overlapThis == null || overlapThat == null)
{
//should not reach this, but just in case
return(Intersection.NONE);
}
if (overlapThis == overlapThat)
{
return(new Intersection(overlapThis));
}
return(new Intersection(new WLineSegment(overlapThis, overlapThat)));
}
Intersection possibleIntersection = (this.ToWLine()).GetIntersection(that.ToWLine());
if (possibleIntersection.IsPoint && this.Overlaps(possibleIntersection.Point) && that.Overlaps(possibleIntersection.Point))
{
return(possibleIntersection);
}
return(Intersection.NONE);
}
/// <summary></summary>
public WCircle(WPoint center, double radius)
{
X = center.X;
Y = center.Y;
Radius = radius;
}
/// <summary></summary>
public WLineSegment(WPoint a, WPoint b, bool isDirected) : base(a, b, isDirected)
{
}
/// <summary></summary>
public WLineSegment(WPoint a, WPoint b) : base(a, b)
{
}
/// <summary></summary>
public WWedgeUnbound(WPoint center, double degreesRangeStart, double degreesRangeEnd)
{
Center = center;
Degrees = new WRangeCircular(degreesRangeStart, degreesRangeEnd, WCircle.DEGREES_IN_CIRCLE);
}
/// <summary>Rotation defaults to 0 degrees.</summary>
public WRectangle(double width, double height, WPoint corner) : this(width, height, corner, 0)
{
}
/// <summary>
/// Calculates point along line AB, starting at B and moving away from A
/// </summary>
public static WPoint PointPastLine(WPoint a, WPoint b, double distance)
{
double lineLength = a.Distance(b);
return(PointOnLine(a, b, lineLength + distance));
}