/// <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 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 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));
}
/// <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
double numerator = (point.X - line.Start.X)*(line.End.X - line.Start.X) +
(point.Y - line.Start.Y)*(line.End.Y - line.Start.Y);
double denominator = DoublePoint.CalculateSquaredDistance(line.Start, line.End);
double 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 (xDeterminant >= Math.Min(a.Start.X, a.End.X) && xDeterminant <= Math.Max(a.Start.X, a.End.X) &&
xDeterminant >= Math.Min(b.Start.X, b.End.X) && xDeterminant <= Math.Max(b.Start.X, b.End.X) &&
yDeterminant >= Math.Min(a.Start.Y, a.End.Y) && yDeterminant <= Math.Max(a.Start.Y, a.End.Y) &&
yDeterminant >= Math.Min(b.Start.Y, b.End.Y) && 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);
}
#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);
}
