/// <summary>
/// The y-coordinate of the intersection of the vertically projected line with the provided segment.
/// </summary>
/// <param name="xPtN">The x-coordinate of pt n, where the projection starts.</param>
/// <param name="ptI">Vertex i of the segment.</param>
/// <param name="ptJ">Vertex j of the segment.</param>
/// <returns>System.Double.</returns>
public static double IntersectionPointY(
double xPtN,
CartesianCoordinate ptI,
CartesianCoordinate ptJ)
{
if (LinearCurve.IsVertical(ptI, ptJ))
{
throw new ArgumentException("Segment is vertical, so intersection point is either infinity or NAN.");
}
LinearCurve curve = new LinearCurve(ptI, ptJ);
return(curve.Y(xPtN));
}
/// <summary>
/// The numbers of shape boundary intersections a horizontal line makes when projecting to the right from the provided point.
/// An odd number indicates the point is inside the shape.
/// An even number indicates the point is outside the shape.
/// If the point is on a vertex or segment, the function returns 0.
/// </summary>
/// <param name="coordinate">The coordinate.</param>
/// <param name="shapeBoundary">The shape boundary composed of n points.</param>
/// <param name="tolerance">The tolerance.</param>
/// <returns>System.Int32.</returns>
/// <exception cref="System.ArgumentException">Shape boundary describes a shape. Closure to the shape boundary is needed.</exception>
public static int NumberOfIntersectionsOnHorizontalProjection(
CartesianCoordinate coordinate,
CartesianCoordinate[] shapeBoundary,
double tolerance = GeometryLibrary.ZeroTolerance)
{
if (shapeBoundary[0] != shapeBoundary[shapeBoundary.Length - 1])
{
throw new ArgumentException("Shape boundary describes a shape. Closure to the shape boundary is needed.");
}
// 1. Check horizontal line projection from a pt. n to the right
// 2. Count # of intersections of the line with shape edges
int currentNumberOfIntersections = 0;
for (int i = 0; i < shapeBoundary.Length - 1; i++)
{
CartesianCoordinate vertexI = shapeBoundary[i];
if (PointIntersection.IsOnPoint(coordinate, vertexI))
{ // Pt lies on vertex
return(0);
}
CartesianCoordinate vertexJ = shapeBoundary[i + 1];
LineSegment segment = new LineSegment(vertexI, vertexJ);
if (segment.IncludesCoordinate(coordinate))
{ // Pt lies on boundary
return(0);
}
if (!PointIsLeftOfLineEndInclusive(coordinate.X, vertexI, vertexJ))
{ // Pt is to the right of the line segment.
continue;
}
if (!PointIsWithinLineHeightInclusive(coordinate.Y, vertexI, vertexJ))
{ // Pt is out of vertical bounds of the line segment.
continue;
}
LinearCurve segmentCurve = segment.Curve;
if (segmentCurve.IsHorizontal())
{ // Projection is tangent to segment
continue;
}
if (pointHorizontalProjectionIntersectsVertex(coordinate, vertexI))
{ // Projection hits vertex at point I. Do offset check on current segment
if (slopeIsDownwardBetweenCoordinates(vertexI, vertexJ, tolerance))
{
continue;
}
currentNumberOfIntersections++;
continue;
}
if (pointHorizontalProjectionIntersectsVertex(coordinate, vertexJ))
{ // Projection hits vertex at point J. Do offset check on current segment
if (slopeIsDownwardBetweenCoordinates(vertexJ, vertexI, tolerance))
{
continue;
}
currentNumberOfIntersections++;
continue;
}
if (segmentCurve.IsVertical())
{ // Projection hits vertical segment
currentNumberOfIntersections++;
continue;
}
currentNumberOfIntersections += numberOfIntersectionsHorizontal(coordinate, vertexI, vertexJ);
}
return(currentNumberOfIntersections);
}