/// <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));
}
/// <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 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));
}