/// <summary>
/// Calculates the squared shortest distance between a line segment and point.
/// </summary>
/// <param name="line">The line segment involved in the calculation.</param>
/// <param name="point">The point involved in the calculation.</param>
/// <returns>The shortest squared distance between the given line segment and point.</returns>
public static double CalculateSquaredDistanceFromLineToPoint(DoubleLine line, DoublePoint point)
{
// Calculate the projection of the given point onto the given line
var numerator = (point.X - line._start.X) * (line._end.X - line._start.X) +
(point.Y - line._start.Y) * (line._end.Y - line._start.Y);
var denominator = DoublePoint.CalculateSquaredDistance(line._start, line._end);
var projection = numerator / denominator;
// If the projection is beyond the segment, return the distance to
// either the start or end point on the line segment (whichever
// happens to be the shortest)
if (projection < 0 || projection > 1)
{
var distanceToStart = DoublePoint.CalculateSquaredDistance(line._start, point);
var distanceToEnd = DoublePoint.CalculateSquaredDistance(line._end, point);
return(distanceToStart < distanceToEnd ? distanceToStart : distanceToEnd);
}
// Create a point on the line segment from which to measure the distance to the given point
var segmentPoint = new DoublePoint(line._start.X + projection * (line._end.X - line._start.X),
line._start.Y + projection * (line._end.Y - line._start.Y));
// Measure the distance from this point on the segment to the given point
return(DoublePoint.CalculateSquaredDistance(segmentPoint, point));
}
#pragma warning restore 1591
#region Static Methods
/// <summary>
/// Calculates the midpoint of the given line segment.
/// </summary>
/// <param name="line">The line segment of which to find the midpoint.</param>
/// <returns>The midpoint of the given line segment.</returns>
public static DoublePoint CalculateMidpoint(DoubleLine line)
{
// Half the sum of both the start and end X and Y coordinates
var x = (line._start.X + line._end.X) / 2;
var y = (line._start.Y + line._end.Y) / 2;
// Return a new point based on those halved coordinates
return(new DoublePoint(x, y));
}
/// <summary>
/// Calculates the closest point on the line segment to the given point.
/// </summary>
/// <param name="line">The line segment on which to find the closest point.</param>
/// <param name="point">The source point.</param>
/// <returns>The closest point on the line segment.</returns>
public static DoublePoint CalculateLineSegmentClosestPoint(DoubleLine line, DoublePoint point)
{
// Calculate the projection of the given point onto the given line
var numerator = (point.X - line._start.X) * (line._end.X - line._start.X) +
(point.Y - line._start.Y) * (line._end.Y - line._start.Y);
var denominator = DoublePoint.CalculateSquaredDistance(line._start, line._end);
var projection = numerator / denominator;
// Return the intersection point on the line segment
return(new DoublePoint(line._start.X + projection * (line._end.X - line._start.X),
line._start.Y + projection * (line._end.Y - line._start.Y)));
}
/// <summary>
/// Calculates the intersection between two line segments.
/// </summary>
/// <param name="a">The first line segment.</param>
/// <param name="b">The segment line segment.</param>
/// <param name="intersectionFound">Whether or not the lines intersect.</param>
/// <returns>The point of intersection between the two given line segments.</returns>
public static DoublePoint CalculateLineIntersection(DoubleLine a, DoubleLine b, out bool intersectionFound)
{
// Calculate the determinant's denominator
var denominator = (a._start.X - a._end.X) * (b._start.Y - b._end.Y) -
(a._start.Y - a._end.Y) * (b._start.X - b._end.X);
if (denominator != 0)
{
// Calculate the determinants
var xDeterminant = ((a._start.X * a._end.Y - a._start.Y * a._end.X) * (b._start.X - b._end.X) -
(a._start.X - a._end.X) * (b._start.X * b._end.Y - b._start.Y * b._end.X)) /
denominator;
var yDeterminant = ((a._start.X * a._end.Y - a._start.Y * a._end.X) * (b._start.Y - b._end.Y) -
(a._start.Y - a._end.Y) * (b._start.X * b._end.Y - b._start.Y * b._end.X)) /
denominator;
// Ensure that the intersection point actually lies within both line segments
if (MathUtils.AlmostGreaterThanOrEqual(xDeterminant, Math.Min(a._start.X, a._end.X)) &&
MathUtils.AlmostLessThanOrEqual(xDeterminant, Math.Max(a._start.X, a._end.X)) &&
MathUtils.AlmostGreaterThanOrEqual(xDeterminant, Math.Min(b._start.X, b._end.X)) &&
MathUtils.AlmostLessThanOrEqual(xDeterminant, Math.Max(b._start.X, b._end.X)) &&
MathUtils.AlmostGreaterThanOrEqual(yDeterminant, Math.Min(a._start.Y, a._end.Y)) &&
MathUtils.AlmostLessThanOrEqual(yDeterminant, Math.Max(a._start.Y, a._end.Y)) &&
MathUtils.AlmostGreaterThanOrEqual(yDeterminant, Math.Min(b._start.Y, b._end.Y)) &&
MathUtils.AlmostLessThanOrEqual(yDeterminant, Math.Max(b._start.Y, b._end.Y))
)
{
intersectionFound = true;
return(new DoublePoint(xDeterminant, yDeterminant));
}
}
// If the denominator came out to 0 or the point isn't within both
// line segments, then the lines don't intersect
intersectionFound = false;
return(new DoublePoint(0, 0));
}
/// <summary>
/// Calculates the length of the given line segment.
/// </summary>
/// <param name="line">The line segment to measure.</param>
/// <returns>The length of the line segment.</returns>
public static double CalculateLineSegmentLength(DoubleLine line)
{
return(DoublePoint.CalculateEuclideanDistance(line._start, line._end));
}
/// <summary>
/// Calculates the squared length of the given line segment.
/// </summary>
/// <param name="line">The line segment to measure.</param>
/// <returns>The squared length of the line segment.</returns>
public static double CalculateSquaredLineSegmentLength(DoubleLine line)
{
return(DoublePoint.CalculateSquaredDistance(line._start, line._end));
}
/// <summary>
/// Calculates the euclidean shortest distance between a line segment and point.
/// </summary>
/// <param name="line">The line segment involved in the calculation.</param>
/// <param name="point">The point involved in the calculation.</param>
/// <returns>The shortest euclidean distance between the given line segment and point.</returns>
public static double CalculateEuclideanDistanceFromLineToPoint(DoubleLine line, DoublePoint point)
{
return(Math.Sqrt(CalculateSquaredDistanceFromLineToPoint(line, point)));
}
