/// <summary>
/// Rotates the currrent point around another point at a given angle from the origin.
/// </summary>
/// <param name="angle">The angle from the origin.</param>
/// <param name="point">The point about which to rotate.</param>
public void RotatePoint(double angle, DoublePoint point)
{
// Convert angle to radians
double radianAngle = MathUtils.toRadians(angle);
// Decrement this point by the given point about which to rotate
this -= point;
// Copy off the X/Y position values
double tempX = X;
double tempY = Y;
// Perform the actual rotation
X = Math.Cos(radianAngle)* tempX - Math.Sin(radianAngle)* tempY;
Y = Math.Sin(radianAngle)* tempX + Math.Cos(radianAngle)* tempY;
// Add the coordinates that had been offset back in
this += point;
}
/// <summary>
/// Construct line segment with the specified start and end points.
/// </summary>
/// <param name="startPoint">The start point.</param>
/// <param name="endPoint">The end point.</param>
public DoubleLine(DoublePoint startPoint, DoublePoint endPoint)
{
Start = startPoint;
End = endPoint;
}
/// <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>
/// Calculate Manhattan distance between a point and x and y coordinates in two-dimensional space.
/// </summary>
/// <param name="a">The point in two-dimensional space.</param>
/// <param name="x">The x-coordinate in two-dimensiona space.</param>
/// <param name="y">The y-coordinate in two-dimensiona space.</param>
/// <returns>The manhattan distance.</returns>
public static double CalculateManhattanDistance(DoublePoint a, int x, int y)
{
var xDelta = Math.Abs(a.X - x);
var yDelta = Math.Abs(a.Y - y);
return xDelta + yDelta;
}
/// <summary>
/// Calculate Manhattan distance between two points in two-dimensional space.
/// </summary>
/// <param name="a">The first point in two-dimensional space.</param>
/// <param name="b">The second point in two-dimensional space.</param>
/// <returns>The manhattan distance.</returns>
public static double CalculateManhattanDistance(DoublePoint a, DoublePoint b)
{
var xDelta = Math.Abs(a.X - b.X);
var yDelta = Math.Abs(a.Y - b.Y);
return xDelta + yDelta;
}
/// <summary>
/// Calculate Euclidean distance between two points.
/// <param name="a">The point in two-dimensional space.</param>
/// <param name="x">The x-coordinate in two-dimensiona space.</param>
/// <param name="y">The y-coordinate in two-dimensiona space.</param>
/// <returns>The Euclidean distance.</returns>
/// </summary>
public static double CalculateEuclideanDistance(DoublePoint a, int x, int y)
{
var xDelta = (a.X - x);
var yDelta = (a.Y - y);
return Math.Sqrt(xDelta*xDelta + yDelta*yDelta);
}
/// <summary>
/// Calculate Euclidean distance between two points.
/// </summary>
/// <param name="a">The first point in two-dimensional space.</param>
/// <param name="b">The second point in two-dimensional space.</param>
/// <returns>The Euclidean distance.</returns>
public static double CalculateEuclideanDistance(DoublePoint a, DoublePoint b)
{
var xDelta = (a.X - b.X);
var yDelta = (a.Y - b.Y);
return Math.Sqrt(xDelta*xDelta + yDelta*yDelta);
}
/// <summary>
/// Calculate the squared distance between two points.
/// </summary>
/// <param name="a">The first point in two-dimensional space.</param>
/// <param name="b">The second point in two-dimensional space.</param>
/// <returns>The squared distance.</returns>
public static double CalculateSquaredDistance(DoublePoint a, DoublePoint b)
{
var xDelta = a.X - b.X;
var yDelta = a.Y - b.Y;
return xDelta*xDelta + yDelta*yDelta;
}
#pragma warning restore 1591
#region Static Methods
/// <summary>
/// Calculates the angle that the given point makes with the origin in radians.
/// </summary>
/// <param name="a">The point whose position to compare with the origin.</param>
/// <returns>The angle (in degrees) that the given point makes with the origin.</returns>
public static double CalculateAngleFromOrigin(DoublePoint a)
{
// If we're both X and Y are zero, the point is at the origin, but consider
// this to be 90 degrees
if (a.X == 0)
{
if (a.Y == 0)
{
return 90;
}
// If only X is 0 but Y isn't, we still can't calculate the slope so
// consider this to be 270 degrees
return 270;
}
// Calculate the slope (this would just be Y/X since it's compared to the
// origin) and take the arc tangent (which yields the angle in radians)
var angle = MathUtils.toDegrees(Math.Atan(a.Y/a.X));
// If the X coordinate is positive, just return the calculated angle
if (a.X > 0)
return angle;
// Otherwise, return the angle plus 180 degrees
return angle + 180;
}