//
// Is this segment perpendicular to the given segment in terms of the coordinatization from the UI?
//
public Point CoordinatePerpendicular(Segment thatSegment)
{
//
// Do these segments intersect within both sets of stated endpoints?
//
Point intersection = this.FindIntersection(thatSegment);
if (!this.PointLiesOnAndBetweenEndpoints(intersection))
{
return(null);
}
if (!thatSegment.PointLiesOnAndBetweenEndpoints(intersection))
{
return(null);
}
//
// Special Case
//
if ((IsVertical() && thatSegment.IsHorizontal()) || (thatSegment.IsVertical() && IsHorizontal()))
{
return(intersection);
}
// Does m1 * m2 = -1 (opposite reciprocal slopes)
return(Utilities.CompareValues(thatSegment.Slope * this.Slope, -1) ? intersection : null);
}
//
// Parallel and not Coinciding
//
public bool IsPerpendicularTo(Segment thatSegment)
{
if (IsVertical() && thatSegment.IsHorizontal())
{
return(true);
}
if (IsHorizontal() && thatSegment.IsVertical())
{
return(true);
}
return(Utilities.CompareValues(thatSegment.Slope * this.Slope, -1));
}
//
// Determine if the given segment is collinear with this segment (same slope and they share a point)
//
public bool IsCollinearWith(Segment otherSegment)
{
// If the segments are vertical, just compare the X values of one point of each
if (this.IsVertical() && otherSegment.IsVertical())
{
return(Utilities.CompareValues(this.Point1.X, otherSegment.Point1.X));
}
// If the segments are horizontal, just compare the Y values of one point of each; this is redundant
if (this.IsHorizontal() && otherSegment.IsHorizontal())
{
return(Utilities.CompareValues(this.Point1.Y, otherSegment.Point1.Y));
}
return(Utilities.CompareValues(this.Slope, otherSegment.Slope) &&
this.PointLiesOn(otherSegment.Point1) && this.PointLiesOn(otherSegment.Point2)); // Check both endpoints just to be sure
}
//
// Parallel and not Coinciding
//
public bool IsParallelWith(Segment s)
{
if (IsCollinearWith(s))
{
return(false);
}
if (IsVertical() && s.IsVertical())
{
return(true);
}
if (IsHorizontal() && s.IsHorizontal())
{
return(true);
}
return(Utilities.CompareValues(s.Slope, this.Slope));
}
//
// Given the secant, there is a midpoint along the secant (wrt to the circle), given the distance,
// find the two points of intersection between the secant and the circle.
// Return the resultant chord segment.
//
private Segment ConstructChord(Segment secantSegment, Point midpt, double distance, List<Point> figPoints)
{
// distance
// circPt1 _____ circPt2
//
// Find the exact coordinates of the two 'circ' points.
//
double deltaX = 0;
double deltaY = 0;
if (secantSegment.IsVertical())
{
deltaX = 0;
deltaY = distance;
}
else if (secantSegment.IsHorizontal())
{
deltaX = distance;
deltaY = 0;
}
else
{
deltaX = Math.Sqrt(Math.Pow(distance, 2) / (1 + Math.Pow(secantSegment.Slope, 2)));
deltaY = secantSegment.Slope * deltaX;
}
Point circPt1 = Utilities.AcquirePoint(figPoints, new Point("", midpt.X + deltaX, midpt.Y + deltaY));
// intersection is the midpoint of circPt1 and pt2.
Point circPt2 = Utilities.AcquirePoint(figPoints, new Point("", 2 * midpt.X - circPt1.X, 2 * midpt.Y - circPt1.Y));
// Create the actual chord
return new Segment(circPt1, circPt2);
}
//
// Parallel and not Coinciding
//
public bool IsPerpendicularTo(Segment thatSegment)
{
if (IsVertical() && thatSegment.IsHorizontal()) return true;
if (IsHorizontal() && thatSegment.IsVertical()) return true;
return Utilities.CompareValues(thatSegment.Slope * this.Slope, -1);
}
//
// Parallel and not Coinciding
//
public bool IsParallelWith(Segment s)
{
if (IsCollinearWith(s)) return false;
if (IsVertical() && s.IsVertical()) return true;
if (IsHorizontal() && s.IsHorizontal()) return true;
return Utilities.CompareValues(s.Slope, this.Slope);
}
//
// Determine if the given segment is collinear with this segment (same slope and they share a point)
//
public bool IsCollinearWith(Segment otherSegment)
{
// If the segments are vertical, just compare the X values of one point of each
if (this.IsVertical() && otherSegment.IsVertical())
{
return Utilities.CompareValues(this.Point1.X, otherSegment.Point1.X);
}
// If the segments are horizontal, just compare the Y values of one point of each; this is redundant
if (this.IsHorizontal() && otherSegment.IsHorizontal())
{
return Utilities.CompareValues(this.Point1.Y, otherSegment.Point1.Y);
}
return Utilities.CompareValues(this.Slope, otherSegment.Slope) &&
this.PointLiesOn(otherSegment.Point1) && this.PointLiesOn(otherSegment.Point2); // Check both endpoints just to be sure
}
public Point FindIntersection(Segment thatSegment)
{
// Special Case: Collinear, but non-overlapping.
if (this.CoincidingWithoutOverlap(thatSegment)) return null;
// Special Case: Intersect at an endpoint
Point shared = this.SharedVertex(thatSegment);
if (shared != null) return shared;
double a, b, c, d, e, f;
if (this.IsVertical() && thatSegment.IsHorizontal()) return new Point(null, this.Point1.X, thatSegment.Point1.Y);
if (thatSegment.IsVertical() && this.IsHorizontal()) return new Point(null, thatSegment.Point1.X, this.Point1.Y);
if (this.IsVertical())
{
MakeLine(thatSegment.Point1.X, thatSegment.Point1.Y, thatSegment.Point2.X, thatSegment.Point2.Y, out a, out b, out e);
return new Point(null, this.Point1.X, EvaluateYGivenX(a, b, e, this.Point1.X));
}
if (thatSegment.IsVertical())
{
MakeLine(this.Point1.X, this.Point1.Y, this.Point2.X, this.Point2.Y, out a, out b, out e);
return new Point(null, thatSegment.Point1.X, EvaluateYGivenX(a, b, e, thatSegment.Point1.X));
}
if (this.IsHorizontal())
{
MakeLine(thatSegment.Point1.X, thatSegment.Point1.Y, thatSegment.Point2.X, thatSegment.Point2.Y, out a, out b, out e);
return new Point(null, EvaluateXGivenY(a, b, e, this.Point1.Y), this.Point1.Y);
}
if (thatSegment.IsHorizontal())
{
MakeLine(this.Point1.X, this.Point1.Y, this.Point2.X, this.Point2.Y, out a, out b, out e);
return new Point(null, EvaluateXGivenY(a, b, e, thatSegment.Point1.Y), thatSegment.Point1.Y);
}
//
// ax + by = e
// cx + dy = f
//
MakeLine(Point1.X, Point1.Y, Point2.X, Point2.Y, out a, out b, out e);
MakeLine(thatSegment.Point1.X, thatSegment.Point1.Y, thatSegment.Point2.X, thatSegment.Point2.Y, out c, out d, out f);
double overallDeterminant = a * d - b * c;
double x = determinant(e, b, f, d) / overallDeterminant;
double y = determinant(a, e, c, f) / overallDeterminant;
return new Point("Intersection", x, y);
}
//
// Is this segment perpendicular to the given segment in terms of the coordinatization from the UI?
//
public Point CoordinatePerpendicular(Segment thatSegment)
{
//
// Do these segments intersect within both sets of stated endpoints?
//
Point intersection = this.FindIntersection(thatSegment);
if (!this.PointLiesOnAndBetweenEndpoints(intersection)) return null;
if (!thatSegment.PointLiesOnAndBetweenEndpoints(intersection)) return null;
//
// Special Case
//
if ((IsVertical() && thatSegment.IsHorizontal()) || (thatSegment.IsVertical() && IsHorizontal())) return intersection;
// Does m1 * m2 = -1 (opposite reciprocal slopes)
return Utilities.CompareValues(thatSegment.Slope * this.Slope, -1) ? intersection : null;
}
public Point FindIntersection(Segment thatSegment)
{
// Special Case: Collinear, but non-overlapping.
if (this.CoincidingWithoutOverlap(thatSegment))
{
return(null);
}
// Special Case: Intersect at an endpoint
Point shared = this.SharedVertex(thatSegment);
if (shared != null)
{
return(shared);
}
double a, b, c, d, e, f;
if (this.IsVertical() && thatSegment.IsHorizontal())
{
return(new Point(null, this.Point1.X, thatSegment.Point1.Y));
}
if (thatSegment.IsVertical() && this.IsHorizontal())
{
return(new Point(null, thatSegment.Point1.X, this.Point1.Y));
}
if (this.IsVertical())
{
MakeLine(thatSegment.Point1.X, thatSegment.Point1.Y, thatSegment.Point2.X, thatSegment.Point2.Y, out a, out b, out e);
return(new Point(null, this.Point1.X, EvaluateYGivenX(a, b, e, this.Point1.X)));
}
if (thatSegment.IsVertical())
{
MakeLine(this.Point1.X, this.Point1.Y, this.Point2.X, this.Point2.Y, out a, out b, out e);
return(new Point(null, thatSegment.Point1.X, EvaluateYGivenX(a, b, e, thatSegment.Point1.X)));
}
if (this.IsHorizontal())
{
MakeLine(thatSegment.Point1.X, thatSegment.Point1.Y, thatSegment.Point2.X, thatSegment.Point2.Y, out a, out b, out e);
return(new Point(null, EvaluateXGivenY(a, b, e, this.Point1.Y), this.Point1.Y));
}
if (thatSegment.IsHorizontal())
{
MakeLine(this.Point1.X, this.Point1.Y, this.Point2.X, this.Point2.Y, out a, out b, out e);
return(new Point(null, EvaluateXGivenY(a, b, e, thatSegment.Point1.Y), thatSegment.Point1.Y));
}
//
// ax + by = e
// cx + dy = f
//
MakeLine(Point1.X, Point1.Y, Point2.X, Point2.Y, out a, out b, out e);
MakeLine(thatSegment.Point1.X, thatSegment.Point1.Y, thatSegment.Point2.X, thatSegment.Point2.Y, out c, out d, out f);
double overallDeterminant = a * d - b * c;
double x = determinant(e, b, f, d) / overallDeterminant;
double y = determinant(a, e, c, f) / overallDeterminant;
return(new Point("Intersection", x, y));
}
