/// <summary>
/// Returns all the intersections the line has with this polygon.
/// </summary>
/// <param name="line"></param>
/// <returns></returns>
public PointF2D[] Intersections(LineF2D line)
{
List <PointF2D> points = new List <PointF2D>();
foreach (LineF2D polygon_line in this.LineEnumerator)
{
// calculate the intersection.
PrimitiveF2D primitive = line.Intersection(polygon_line);
// the primitive not null.
if (primitive != null)
{
if (primitive is LineF2D)
{ // primitive is a line; convert.
LineF2D intersect_line =
(primitive as LineF2D);
// we are sure the line is a segment.
// if the line is not a segment this means that the polygon contains an line with infinite length; impossible.
// TODO: how to determine the order?
points.Add(intersect_line.Point1);
points.Add(intersect_line.Point2);
}
else if (primitive is PointF2D)
{ // primitive is a point; convert.
PointF2D point = (primitive as PointF2D);
points.Add(point);
}
}
}
return(points.ToArray());
}
public static PointF2D PositionAtPosition(double[] x, double[] y, double position)
{
if (x.Length < 2)
{
throw new ArgumentOutOfRangeException("Given coordinates do not represent a polyline.");
}
double num1 = 0.0;
for (int index = 1; index < x.Length; ++index)
{
double num2 = x[index - 1] - x[index];
double num3 = y[index - 1] - y[index];
double num4 = System.Math.Sqrt(num2 * num2 + num3 * num3);
if (num1 + num4 > position)
{
LineF2D lineF2D = new LineF2D(new PointF2D(x[index - 1], y[index - 1]), new PointF2D(x[index], y[index]));
double num5 = position - num1;
VectorF2D vectorF2D = lineF2D.Direction.Normalize() * num5;
return(lineF2D.Point1 + vectorF2D);
}
num1 += num4;
}
LineF2D lineF2D1 = new LineF2D(new PointF2D(x[x.Length - 2], y[x.Length - 2]), new PointF2D(x[x.Length - 1], y[x.Length - 1]));
return(lineF2D1.Point1 + lineF2D1.Direction.Normalize() * (position - num1));
}
/// <summary>
/// Returns a position on the given polyline corresponding with the given position. (0 smaller than position smaller than polyline.lenght).
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="position"></param>
/// <returns></returns>
public static PointF2D PositionAtPosition(double[] x, double[] y, double position)
{
if (x.Length < 2)
{
throw new ArgumentOutOfRangeException("Given coordinates do not represent a polyline.");
}
double lenght = 0;
LineF2D localLine = null;
for (int idx = 1; idx < x.Length; idx++)
{
localLine = new LineF2D(new PointF2D(x[idx - 1], y[idx - 1]),
new PointF2D(x[idx], y[idx]));
double localLength = localLine.Length;
if (lenght + localLength > position)
{ // position is between point at idx and idx + 1.
double localPosition = position - lenght;
VectorF2D vector = localLine.Direction.Normalize() * localPosition;
return(localLine.Point1 + vector);
}
lenght = lenght + localLength;
}
return(localLine.Point1 + (localLine.Direction.Normalize() * (position - lenght)));
}
/// <summary>
/// Returns a position on the given polyline corresponding with the given position. (0 smaller than position smaller than polyline.lenght).
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="position"></param>
/// <returns></returns>
public static PointF2D PositionAtPosition(double[] x, double[] y, double position)
{
if (x.Length < 2) throw new ArgumentOutOfRangeException("Given coordinates do not represent a polyline.");
double lenght = 0;
LineF2D localLine;
for (int idx = 1; idx < x.Length; idx++)
{
double xDiff = (x [idx - 1] - x [idx]);
double yDiff = (y [idx - 1] - y [idx]);
double localLength = System.Math.Sqrt ((xDiff * xDiff) + (yDiff * yDiff));
if(lenght + localLength > position)
{ // position is between point at idx and idx + 1.
localLine = new LineF2D(new PointF2D(x[idx - 1], y[idx - 1]),
new PointF2D(x[idx], y[idx]));
double localPosition = position - lenght;
VectorF2D vector = localLine.Direction.Normalize() * localPosition;
return localLine.Point1 + vector;
}
lenght = lenght + localLength;
}
localLine = new LineF2D(new PointF2D(x[x.Length - 2], y[x.Length - 2]),
new PointF2D(x[x.Length - 1], y[x.Length - 1]));
return localLine.Point1 + (localLine.Direction.Normalize() * (position - lenght));
}
/// <summary>
/// Fits this rectangle to the given points.
/// </summary>
/// <param name="points">The points to wrap the rectangle around.</param>
/// <param name="percentage">The margin in percentage.</param>
/// <returns></returns>
public RectangleF2D Fit(PointF2D[] points, double percentage)
{
if (points == null)
{
throw new ArgumentNullException("points");
}
if (points.Length < 2)
{
throw new ArgumentOutOfRangeException("Rectangle fit needs at least two points.");
}
// calculate the center.
double[] center = new double[] { points[0][0], points[0][1] };
for (int idx = 1; idx < points.Length; idx++)
{
center[0] = center[0] + points[idx][0];
center[1] = center[1] + points[idx][1];
}
center[0] = center[0] / points.Length;
center[1] = center[1] / points.Length;
PointF2D centerPoint = new PointF2D(center);
LineF2D line = null;
// calculate the width.
double width = 0;
for (int idx = 0; idx < points.Length; idx++)
{
line = new LineF2D(points[idx], points[idx] + this._vectorY);
double distance = line.Distance(centerPoint);
if (distance > width)
{ // the distance is larger.
width = distance;
}
}
width = width * 2;
// calculate the height.
double height = 0;
for (int idx = 0; idx < points.Length; idx++)
{
line = new LineF2D(points[idx], points[idx] + this._vectorX);
double distance = line.Distance(centerPoint);
if (distance > height)
{ // this distance is larger.
height = distance;
}
}
height = height * 2;
// expand with the given percentage.
width = width + (width / 100.0 * percentage);
height = height + (height / 100.0 * percentage);
return(RectangleF2D.FromBoundsAndCenter(width, height, centerPoint[0], centerPoint[1],
this.DirectionY));
}
/// <summary>
/// Transforms the given the coordinates to a coordinate system defined inside this rectangle.
/// </summary>
/// <param name="width">Width.</param>
/// <param name="height">Height.</param>
/// <param name="reverseX">If set to <c>true</c> reverse x.</param>
/// <param name="reverseY">If set to <c>true</c> reverse y.</param>
/// <param name="point">Point.</param>
/// <param name="transformed">Transformed.</param>
public void TransformTo(double width, double height, bool reverseX, bool reverseY,
PointF2D point, double[] transformed)
{
if (transformed == null)
{
throw new ArgumentNullException();
}
if (transformed.Length != 2)
{
throw new ArgumentException("Tranformed array needs to be of length 2.");
}
PointF2D reference = _bottomLeft;
VectorF2D vectorX = _vectorX;
VectorF2D vectorY = _vectorY;
if (reverseX && !reverseY)
{
reference = this.BottomRight;
vectorX = _vectorX * -1;
}
else if (!reverseX && reverseY)
{
reference = this.TopLeft;
vectorY = _vectorY * -1;
}
else if (reverseX && reverseY)
{
reference = this.TopRight;
vectorX = _vectorX * -1;
vectorY = _vectorY * -1;
}
LineF2D xLine = new LineF2D(point, point + vectorX, false);
PointF2D yIntersection = xLine.Intersection(new LineF2D(reference, reference + vectorY)) as PointF2D;
VectorF2D yIntersectionVector = (yIntersection - reference);
double yFactor = yIntersectionVector.Size / vectorY.Size;
if (!yIntersectionVector.CompareNormalized(vectorY, 0.0001))
{
yFactor = -yFactor;
}
LineF2D yLine = new LineF2D(point, point + vectorY);
PointF2D xIntersection = yLine.Intersection(new LineF2D(reference, reference + vectorX)) as PointF2D;
VectorF2D xIntersectionVector = (xIntersection - reference);
double xFactor = xIntersectionVector.Size / vectorX.Size;
if (!xIntersectionVector.CompareNormalized(vectorX, 0.0001))
{
xFactor = -xFactor;
}
transformed [0] = xFactor * width;
transformed [1] = yFactor * height;
}
public bool Intersects(LineF2D line)
{
PointF2D[] corners = this.Corners;
LinePointPosition linePointPosition = line.PositionOfPoint(corners[0]);
for (int index = 1; index <= corners.Length; ++index)
{
if (line.PositionOfPoint(corners[index]) != linePointPosition)
{
return(true);
}
}
return(false);
}
/// <summary>
/// Transforms the given the coordinates to a coordinate system defined inside this rectangle.
/// </summary>
/// <param name="width">The width of the rectangle in the coordinate system of the given coordinates.</param>
/// <param name="height">The height of the rectangle in the coordinate system of the given coordinates.</param>
/// <param name="reverseX">Assumes that the origin of the x-axis is on the top of this rectangle if false.</param>
/// <param name="reverseY">Assumes that the origin of the y-axis is on the right of this rectangle if false.</param>
/// <param name="x">The x-coordinate to transform.</param>
/// <param name="y">The y-coordinate to transform.</param>
public double[][] TransformTo(double width, double height, bool reverseX, bool reverseY,
double[] x, double[] y)
{
PointF2D reference = _bottomLeft;
VectorF2D vectorX = _vectorX;
VectorF2D vectorY = _vectorY;
if (reverseX && !reverseY)
{
reference = this.BottomRight;
vectorX = _vectorX * -1;
}
else if (!reverseX && reverseY)
{
reference = this.TopLeft;
vectorY = _vectorY * -1;
}
else if (reverseX && reverseY)
{
reference = this.TopRight;
vectorX = _vectorX * -1;
vectorY = _vectorY * -1;
}
double[][] transformed = new double[x.Length][];
for (int idx = 0; idx < x.Length; idx++)
{
PointF2D point = new PointF2D(x [idx], y [idx]);
LineF2D xLine = new LineF2D(point, point + vectorX, false);
PointF2D yIntersection = xLine.Intersection(new LineF2D(reference, reference + vectorY)) as PointF2D;
VectorF2D yIntersectionVector = (yIntersection - reference);
double yFactor = yIntersectionVector.Size / vectorY.Size;
if (!yIntersectionVector.CompareNormalized(vectorY, 0.0001))
{
yFactor = -yFactor;
}
LineF2D yLine = new LineF2D(point, point + vectorY);
PointF2D xIntersection = yLine.Intersection(new LineF2D(reference, reference + vectorX)) as PointF2D;
VectorF2D xIntersectionVector = (xIntersection - reference);
double xFactor = xIntersectionVector.Size / vectorX.Size;
if (!xIntersectionVector.CompareNormalized(vectorX, 0.0001))
{
xFactor = -xFactor;
}
transformed[idx] = new double[] { xFactor *width, yFactor *height };
}
return(transformed);
}
public bool Intersects(PointF2D point1, PointF2D point2)
{
PointF2D[] corners = this.Corners;
LineF2D lineF2D = new LineF2D(point1, point2, true);
LinePointPosition linePointPosition = lineF2D.PositionOfPoint(corners[0]);
for (int index = 1; index < corners.Length; ++index)
{
if (lineF2D.PositionOfPoint(corners[index]) != linePointPosition)
{
return(true);
}
}
return(false);
}
public RectangleF2D Fit(PointF2D[] points, double percentage)
{
if (points == null)
{
throw new ArgumentNullException("points");
}
if (points.Length < 2)
{
throw new ArgumentOutOfRangeException("Rectangle fit needs at least two points.");
}
double[] values = new double[2]
{
points[0][0],
points[0][1]
};
for (int index = 1; index < points.Length; ++index)
{
values[0] = values[0] + points[index][0];
values[1] = values[1] + points[index][1];
}
values[0] = values[0] / (double)points.Length;
values[1] = values[1] / (double)points.Length;
PointF2D p = new PointF2D(values);
double num1 = 0.0;
for (int index = 0; index < points.Length; ++index)
{
double num2 = new LineF2D(points[index], points[index] + this._vectorY).Distance(p);
if (num2 > num1)
{
num1 = num2;
}
}
double num3 = num1 * 2.0;
double num4 = 0.0;
for (int index = 0; index < points.Length; ++index)
{
double num2 = new LineF2D(points[index], points[index] + this._vectorX).Distance(p);
if (num2 > num4)
{
num4 = num2;
}
}
double num5 = num4 * 2.0;
return(RectangleF2D.FromBoundsAndCenter(num3 + num3 / 100.0 * percentage, num5 + num5 / 100.0 * percentage, p[0], p[1], this.DirectionY));
}
/// <summary>
/// Projects a point onto the given line.
///
/// (= intersection of the line with an angle 90° different from this line through the given point)
/// </summary>
/// <param name="point"></param>
/// <returns>The projection point if it occurs inside the segmented line.</returns>
public PointF2D ProjectOn(PointF2D point)
{
if (this.Length == 0 && this.IsSegment)
{ // cannot project on a line of length zero.
return(null);
}
// get the direction.
VectorF2D direction = this.Direction;
// rotate.
VectorF2D rotated = direction.Rotate90(true);
// create second point
PointF2D point2 = new PointF2D((point + rotated).ToArray());
if (point[0] != point2[0] || point[1] != point2[1])
{
// create line.
LineF2D line = new LineF2D(
point,
point2,
false,
false);
// intersect.
PrimitiveF2D primitive =
this.Intersection(line, true);
if (primitive == null)
{
return(null);
}
else if (primitive is PointF2D)
{
return(primitive as PointF2D);
}
else
{
throw new InvalidOperationException();
}
}
else
{
return(point2);
}
}
/// <summary>
/// Transforms the given the coordinates to a coordinate system defined inside this rectangle.
/// </summary>
/// <param name="width">The width of the rectangle in the coordinate system of the given coordinates.</param>
/// <param name="height">The height of the rectangle in the coordinate system of the given coordinates.</param>
/// <param name="reverseX">Assumes that the origin of the x-axis is on the top of this rectangle if false.</param>
/// <param name="reverseY">Assumes that the origin of the y-axis is on the right of this rectangle if false.</param>
/// <param name="point">The coordinate to transform.</param>
public double[] TransformTo(double width, double height, bool reverseX, bool reverseY,
PointF2D point)
{
PointF2D reference = _bottomLeft;
VectorF2D vectorX = _vectorX;
VectorF2D vectorY = _vectorY;
if (reverseX && !reverseY)
{
reference = this.BottomRight;
vectorX = _vectorX * -1;
}
else if (!reverseX && reverseY)
{
reference = this.TopLeft;
vectorY = _vectorY * -1;
}
else if (reverseX && reverseY)
{
reference = this.TopRight;
vectorX = _vectorX * -1;
vectorY = _vectorY * -1;
}
LineF2D xLine = new LineF2D(point, point + vectorX, false);
PointF2D yIntersection = xLine.Intersection(new LineF2D(reference, reference + vectorY)) as PointF2D;
VectorF2D yIntersectionVector = (yIntersection - reference);
double yFactor = yIntersectionVector.Size / vectorY.Size;
if (!yIntersectionVector.CompareNormalized(vectorY, 0.0001))
{
yFactor = -yFactor;
}
LineF2D yLine = new LineF2D(point, point + vectorY);
PointF2D xIntersection = yLine.Intersection(new LineF2D(reference, reference + vectorX)) as PointF2D;
VectorF2D xIntersectionVector = (xIntersection - reference);
double xFactor = xIntersectionVector.Size / vectorX.Size;
if (!xIntersectionVector.CompareNormalized(vectorX, 0.0001))
{
xFactor = -xFactor;
}
return(new double[] { xFactor *width, yFactor *height });
}
/// <summary>
/// Returns true if the line intersects with this bounding box.
/// </summary>
/// <param name="line"></param>
/// <returns></returns>
public bool Intersects(LineF2D line)
{
// if all points have the same relative position with respect to the line
// there is no intersection. In the other case there is.
PointF2D[] corners = this.Corners;
LinePointPosition first_position = line.PositionOfPoint(corners[0]);
for (int idx = 1; idx <= corners.Length; idx++)
{
if (line.PositionOfPoint(corners[idx]) != first_position)
{
return(true);
}
}
return(false);
}
/// <summary>
/// Simplify the specified points using epsilon.
/// </summary>
/// <param name="points">Points.</param>
/// <param name="epsilon">Epsilon.</param>
/// <param name="first">First.</param>
/// <param name="last">Last.</param>
public static PointF2D[] SimplifyBetween(PointF2D[] points, double epsilon, int first, int last)
{
if (points == null)
throw new ArgumentNullException ("points");
if (epsilon <= 0)
throw new ArgumentOutOfRangeException("epsilon");
if (first > last)
throw new ArgumentException(string.Format("first[{0}] must be smaller or equal than last[{1}]!",
first, last));
if (first + 1 != last) {
// find point with the maximum distance.
double maxDistance = 0;
int foundIndex = -1;
// create the line between first-last.
LineF2D line = new LineF2D (points[first], points [last]);
for (int idx = first + 1; idx < last; idx++) {
double distance = line.Distance (points[idx]);
if (distance > maxDistance) {
// larger distance found.
maxDistance = distance;
foundIndex = idx;
}
}
if (foundIndex > 0 && maxDistance > epsilon) { // a point was found and it is far enough.
PointF2D[] before = SimplifyCurve.SimplifyBetween (points, epsilon, first, foundIndex);
PointF2D[] after = SimplifyCurve.SimplifyBetween (points, epsilon, foundIndex, last);
// build result.
PointF2D[] result = new PointF2D[before.Length + after.Length - 1];
for (int idx = 0; idx < before.Length - 1; idx++) {
result [idx] = before [idx];
}
for (int idx = 0; idx < after.Length; idx++) {
result [idx + before.Length - 1] = after [idx];
}
return result;
}
}
return new PointF2D[] { points[first], points[last] };
}
public override double Distance(PointF2D p)
{
double num1 = new LineF2D(this.BottomLeft, this.BottomRight, true).Distance(p);
double num2 = new LineF2D(this.BottomRight, this.TopRight, true).Distance(p);
if (num2 < num1)
{
num1 = num2;
}
double num3 = new LineF2D(this.TopRight, this.TopLeft, true).Distance(p);
if (num3 < num1)
{
num1 = num3;
}
double num4 = new LineF2D(this.TopLeft, this.BottomLeft, true).Distance(p);
if (num4 < num1)
{
num1 = num4;
}
return(num1);
}
public PointF2D[] Intersections(LineF2D line)
{
List<PointF2D> pointF2DList = new List<PointF2D>();
foreach (LineF2D line1 in this.LineEnumerator)
{
PrimitiveF2D primitiveF2D = line.Intersection(line1);
if (primitiveF2D != null)
{
if (primitiveF2D is LineF2D)
{
LineF2D lineF2D = primitiveF2D as LineF2D;
pointF2DList.Add(lineF2D.Point1);
pointF2DList.Add(lineF2D.Point2);
}
else if ((object) (primitiveF2D as PointF2D) != null)
{
PointF2D pointF2D = primitiveF2D as PointF2D;
pointF2DList.Add(pointF2D);
}
}
}
return pointF2DList.ToArray();
}
/// <summary>
/// Calculates and returns the line intersection.
/// </summary>
/// <param name="line"></param>
/// <param name="doSegment"></param>
/// <returns></returns>
public PrimitiveF2D Intersection(LineF2D line, bool doSegment)
{
if (line == this)
{ // if the lines equal, the full lines intersect.
return line;
}
else if (line.A == this.A
&& line.B == this.B
&& line.C == this.C)
{ // if the lines equal in direction and position; return the smallest segment.
KeyValuePair<double, PointF2D> point1 = new KeyValuePair<double, PointF2D>(
0, this.Point1);
KeyValuePair<double, PointF2D> point2 = new KeyValuePair<double, PointF2D>(
this.Point1.Distance(this.Point2), this.Point2);
// sort.
KeyValuePair<double, PointF2D> temp;
if (point2.Key < point1.Key)
{ // point2 smaller than point1.
temp = point2;
point2 = point1;
point1 = temp;
}
KeyValuePair<double, PointF2D> point = new KeyValuePair<double, PointF2D>(
this.Point1.Distance(line.Point1), line.Point1);
if (point.Key < point2.Key) // sort.
{ // point smaller than point2.
temp = point;
point = point2;
point2 = temp;
}
if (point2.Key < point1.Key)
{ // point2 smaller than point1.
temp = point2;
point2 = point1;
point1 = temp;
}
point = new KeyValuePair<double, PointF2D>(
this.Point1.Distance(line.Point2), line.Point2);
if (point.Key < point2.Key) // sort.
{ // point smaller than point2.
temp = point;
point = point2;
point2 = temp;
}
if (point2.Key < point1.Key)
{ // point2 smaller than point1.
temp = point2;
point2 = point1;
point1 = temp;
}
// this line is a segment.
if (doSegment && (this.IsSegment1 || this.IsSegment2))
{ // test where the intersection lies.
double this_distance =
this.Point1.Distance(this.Point2);
if (this.IsSegment)
{ // if in any directions one of the points are further away from the point.
double this_distance_1 = System.Math.Min(this.Point1.Distance(point1.Value),
this.Point1.Distance(point2.Value));
if (this_distance_1 > this_distance)
{ // the point is further away.
return null;
}
}
else if (this.IsSegment1)
{ // if in any directions one of the points are further away from the point.
double this_distance_1 = this.Point1.Distance(point1.Value);
if (this_distance_1 > this_distance)
{ // the point is further away.
return null;
}
}
else if (this.IsSegment2)
{ // if in any directions one of the points are further away from the point.
double this_distance_2 = this.Point2.Distance(point1.Value);
if (this_distance_2 > this_distance)
{ // the point is further away.
return null;
}
}
}
// other line is a segment.
if (doSegment && (line.IsSegment1 || line.IsSegment2))
{ // test where the intersection lies.
double this_distance =
line.Point1.Distance(line.Point2);
if (line.IsSegment)
{// if in any directions one of the points are further away from the point.
double this_distance_1 = System.Math.Min(line.Point1.Distance(point1.Value),
line.Point1.Distance(point2.Value));
if (this_distance_1 > this_distance)
{ // the point is further away.
return null;
}
}
else if (line.IsSegment1)
{ // if in any directions one of the points are further away from the point.
double this_distance_1 = line.Point1.Distance(point1.Value);
if (this_distance_1 > this_distance)
{ // the point is further away.
return null;
}
}
else if (line.IsSegment2)
{ // if in any directions one of the points are further away from the point.
double this_distance_2 = line.Point2.Distance(point2.Value);
if (this_distance_2 > this_distance)
{ // the point is further away.
return null;
}
}
}
return new LineF2D(
point1.Value,
point2.Value,
true);
}
else
{ // line.A = A1, line.B = B1, line.C = C1, this.A = A2, this.B = B2, this.C = C2
double det = (line.A * this.B - this.A * line.B);
if (det == 0) // TODO: implement an accuracy threshold epsilon.
{ // lines are parallel; no intersections.
return null;
}
else
{ // lines are not the same and not parallel so they will intersect.
double x = (this.B * line.C - line.B * this.C) / det;
double y = (line.A * this.C - this.A * line.C) / det;
// create the point.
PointF2D point = new PointF2D(new double[]{x, y});
// this line is a segment.
if (doSegment && (this.IsSegment1 || this.IsSegment2))
{ // test where the intersection lies.
double this_distance =
this.Point1.Distance(this.Point2);
if (this.IsSegment)
{// if in any directions one of the points are further away from the point.
double this_distance_1 = this.Point1.Distance(point);
if (this_distance_1 > this_distance)
{ // the point is further away.
return null;
}
double this_distance_2 = this.Point2.Distance(point);
if (this_distance_2 > this_distance)
{ // the point is further away.
return null;
}
}
else if (this.IsSegment1 && this.Point2.Distance(point) > this_distance)
{ // only check this direction and only if the points lies far enough away from point2.
VectorF2D pointDirection = point - this.Point2;
VectorF2D point2ToPoint1 = this.Direction.Inverse;
if (pointDirection.CompareNormalized(point2ToPoint1, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return null;
}
}
else if (this.IsSegment1 && this.Point1.Distance(point) > this_distance)
{ // only check this direction and only if the points lies far enough away from point1.
VectorF2D pointDirection = point - this.Point1;
VectorF2D point1ToPoint2 = this.Direction;
if (pointDirection.CompareNormalized(point1ToPoint2, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return null;
}
}
}
// line this is a segment.
if (doSegment && (line.IsSegment1 || line.IsSegment2))
{ // test where the intersection lies.
double line_distance =
line.Point1.Distance(line.Point2);
if (line.IsSegment)
{// if in any directions one of the points are further away from the point.
double line_distance_1 = line.Point1.Distance(point);
if (line_distance_1 > line_distance)
{ // the point is further away.
return null;
}
double line_distance_2 = line.Point2.Distance(point);
if (line_distance_2 > line_distance)
{ // the point is further away.
return null;
}
}
else if (line.IsSegment1 && line.Point2.Distance(point) > line_distance)
{ // only check line direction and only if the points lies far enough away from point2.
VectorF2D pointDirection = point - line.Point2;
VectorF2D point2ToPoint1 = line.Direction.Inverse;
if (pointDirection.CompareNormalized(point2ToPoint1, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return null;
}
}
else if (line.IsSegment1 && line.Point1.Distance(point) > line_distance)
{ // only check line direction and only if the points lies far enough away from point1.
VectorF2D pointDirection = point - line.Point1;
VectorF2D point1ToPoint2 = line.Direction;
if (pointDirection.CompareNormalized(point1ToPoint2, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return null;
}
}
}
// the intersection is valid.
return point;
}
}
}
/// <summary>
/// Return true if the given line intersects with this line.
/// </summary>
/// <param name="line">Line.</param>
public bool Intersects(LineF2D line)
{
return this.Intersection (line) != null;
}
/// <summary>
/// Return true if the given line intersects with this line.
/// </summary>
/// <param name="line">Line.</param>
/// <param name="doSegment"></param>
public bool Intersects(LineF2D line, bool doSegment)
{
return this.Intersection (line, doSegment) != null;
}
/// <summary>
/// Transforms the given the coordinates to a coordinate system defined inside this rectangle.
/// </summary>
public double[] TransformTo(double width, double height, bool reverseX, bool reverseY,
PointF2D point)
{
PointF2D reference = _bottomLeft;
VectorF2D vectorX = _vectorX;
VectorF2D vectorY = _vectorY;
if (reverseX && !reverseY) {
reference = this.BottomRight;
vectorX = _vectorX * -1;
} else if (!reverseX && reverseY) {
reference = this.TopLeft;
vectorY = _vectorY * -1;
} else if (reverseX && reverseY) {
reference = this.TopRight;
vectorX = _vectorX * -1;
vectorY = _vectorY * -1;
}
LineF2D xLine = new LineF2D (point, point + vectorX, false);
PointF2D yIntersection = xLine.Intersection (new LineF2D (reference, reference + vectorY)) as PointF2D;
VectorF2D yIntersectionVector = (yIntersection - reference);
double yFactor = yIntersectionVector.Size / vectorY.Size;
if (!yIntersectionVector.CompareNormalized (vectorY, 0.0001)) {
yFactor = -yFactor;
}
LineF2D yLine = new LineF2D (point, point + vectorY);
PointF2D xIntersection = yLine.Intersection (new LineF2D (reference, reference + vectorX)) as PointF2D;
VectorF2D xIntersectionVector = (xIntersection - reference);
double xFactor = xIntersectionVector.Size / vectorX.Size;
if (!xIntersectionVector.CompareNormalized (vectorX, 0.0001)) {
xFactor = -xFactor;
}
return new double[] { xFactor * width, yFactor * height };
}
/// <summary>
/// Transforms the given the coordinates to a coordinate system defined inside this rectangle.
/// </summary>
/// <param name="width">Width.</param>
/// <param name="height">Height.</param>
/// <param name="reverseX">If set to <c>true</c> reverse x.</param>
/// <param name="reverseY">If set to <c>true</c> reverse y.</param>
/// <param name="point">Point.</param>
/// <param name="transformed">Transformed.</param>
public void TransformTo(double width, double height, bool reverseX, bool reverseY,
PointF2D point, double[] transformed)
{
if (transformed == null) {
throw new ArgumentNullException ();
}
if (transformed.Length != 2) {
throw new ArgumentException ("Tranformed array needs to be of length 2.");
}
PointF2D reference = _bottomLeft;
VectorF2D vectorX = _vectorX;
VectorF2D vectorY = _vectorY;
if (reverseX && !reverseY) {
reference = this.BottomRight;
vectorX = _vectorX * -1;
} else if (!reverseX && reverseY) {
reference = this.TopLeft;
vectorY = _vectorY * -1;
} else if (reverseX && reverseY) {
reference = this.TopRight;
vectorX = _vectorX * -1;
vectorY = _vectorY * -1;
}
LineF2D xLine = new LineF2D (point, point + vectorX, false);
PointF2D yIntersection = xLine.Intersection (new LineF2D (reference, reference + vectorY)) as PointF2D;
VectorF2D yIntersectionVector = (yIntersection - reference);
double yFactor = yIntersectionVector.Size / vectorY.Size;
if (!yIntersectionVector.CompareNormalized (vectorY, 0.0001)) {
yFactor = -yFactor;
}
LineF2D yLine = new LineF2D (point, point + vectorY);
PointF2D xIntersection = yLine.Intersection (new LineF2D (reference, reference + vectorX)) as PointF2D;
VectorF2D xIntersectionVector = (xIntersection - reference);
double xFactor = xIntersectionVector.Size / vectorX.Size;
if (!xIntersectionVector.CompareNormalized (vectorX, 0.0001)) {
xFactor = -xFactor;
}
transformed [0] = xFactor * width;
transformed [1] = yFactor * height;
}
public void LinePosition2DTest()
{
PointF2D a = new PointF2D(0, 0);
PointF2D b = new PointF2D(1, 1);
LineF2D line = new LineF2D(a, b);
// test where the position lie.
Assert.AreEqual(line.PositionOfPoint(new PointF2D(0, 0.5f)), LinePointPosition.Left, "Point position should be right!");
Assert.AreEqual(line.PositionOfPoint(new PointF2D(0.5f, 0.5f)), LinePointPosition.On, "Point position should be on!");
Assert.AreEqual(line.PositionOfPoint(new PointF2D(0.5f, 0)), LinePointPosition.Right, "Point position should be left!");
}
/// <summary>
/// Simplify the specified points using epsilon.
/// </summary>
/// <param name="points">Points.</param>
/// <param name="epsilon">Epsilon.</param>
/// <param name="first">First.</param>
/// <param name="last">Last.</param>
public static double[][] SimplifyBetween(double[][] points, double epsilon, int first, int last)
{
if (points == null)
throw new ArgumentNullException("points");
if(points.Length != 2)
throw new ArgumentException();
if (epsilon <= 0)
throw new ArgumentOutOfRangeException("epsilon");
if (first > last)
throw new ArgumentException(string.Format("first[{0}] must be smaller or equal than last[{1}]!",
first, last));
if (first == last)
{ // first and last are equal, no simplification possible.
return new double[][]
{ new double[] { points[0][first] }, new double[] { points[1][first] } };
}
double[][] result;
// check for identical first and last points.
if (points[0][first] == points[0][last] &&
points[1][first] == points[1][last])
{ // first and last point are indentical.
double[][] before = SimplifyCurve.SimplifyBetween(points, epsilon, first, last - 1);
// build result.
result = new double[2][];
result[0] = new double[before[0].Length + 1];
result[1] = new double[before[0].Length + 1];
for (int idx = 0; idx < before[0].Length; idx++)
{
result[0][idx] = before[0][idx];
result[1][idx] = before[1][idx];
}
result[0][before[0].Length] = points[0][last];
result[1][before[0].Length] = points[1][last];
return result;
}
if (first + 1 != last)
{
// find point with the maximum distance.
double maxDistance = 0;
int foundIndex = -1;
// create the line between first-last.
LineF2D line = new LineF2D(new PointF2D(
points[0][first], points[1][first]),
new PointF2D(
points[0][last], points[1][last]));
for (int idx = first + 1; idx < last; idx++)
{
double distance = line.Distance(new PointF2D(
points[0][idx], points[1][idx]));
if (distance > maxDistance)
{
// larger distance found.
maxDistance = distance;
foundIndex = idx;
}
}
if (foundIndex > 0 && maxDistance > epsilon)
{ // a point was found and it is far enough.
double[][] before = SimplifyCurve.SimplifyBetween(points, epsilon, first, foundIndex);
double[][] after = SimplifyCurve.SimplifyBetween(points, epsilon, foundIndex, last);
// build result.
result = new double[2][];
result[0] = new double[before[0].Length + after[0].Length - 1];
result[1] = new double[before[0].Length + after[0].Length - 1];
for (int idx = 0; idx < before[0].Length - 1; idx++)
{
result[0][idx] = before[0][idx];
result[1][idx] = before[1][idx];
}
for (int idx = 0; idx < after[0].Length; idx++)
{
result[0][idx + before[0].Length - 1] = after[0][idx];
result[1][idx + before[0].Length - 1] = after[1][idx];
}
return result;
}
}
result = new double[2][];
result[0] = new double[] { points[0][first], points[0][last] };
result[1] = new double[] { points[1][first], points[1][last] };
return result;
}
/// <summary>
/// Return true if the given line intersects with this line.
/// </summary>
/// <param name="line">Line.</param>
public bool Intersects(LineF2D line)
{
return(this.Intersection(line) != null);
}
/// <summary>
/// Calculates and returns the line intersection.
/// </summary>
/// <param name="line"></param>
/// <returns></returns>
public PrimitiveF2D Intersection(LineF2D line)
{
return this.Intersection(line, true);
}
/// <summary>
/// Return true if the given line intersects with this line.
/// </summary>
/// <param name="line">Line.</param>
/// <param name="doSegment"></param>
public bool Intersects(LineF2D line, bool doSegment)
{
return(this.Intersection(line, doSegment) != null);
}
/// <summary>
/// Calculates and returns the line intersection.
/// </summary>
/// <param name="line"></param>
/// <returns></returns>
public PrimitiveF2D Intersection(LineF2D line)
{
return(this.Intersection(line, true));
}
/// <summary>
/// Returns true if the given coordinate is contained in this ring.
///
/// See: http://geomalgorithms.com/a03-_inclusion.html
/// </summary>
/// <param name="coordinate"></param>
/// <returns></returns>
public bool Contains(GeoCoordinate coordinate)
{
int number = 0;
if (this.Coordinates[0] == coordinate)
{ // the given point is one of the corners.
return true;
}
// loop over all edges and calculate if they possibly intersect.
for (int idx = 0; idx < this.Coordinates.Count - 1; idx++)
{
if (this.Coordinates[idx + 1] == coordinate)
{ // the given point is one of the corners.
return true;
}
bool idxRight = this.Coordinates[idx].Longitude > coordinate.Longitude;
bool idx1Right = this.Coordinates[idx + 1].Longitude > coordinate.Longitude;
if (idxRight || idx1Right)
{ // at least on of the coordinates is to the right of the point to calculate for.
if ((this.Coordinates[idx].Latitude <= coordinate.Latitude &&
this.Coordinates[idx + 1].Latitude >= coordinate.Latitude) &&
!(this.Coordinates[idx].Latitude == coordinate.Latitude &&
this.Coordinates[idx + 1].Latitude == coordinate.Latitude))
{ // idx is lower than idx+1
if (idxRight && idx1Right)
{ // no need for the left/right algorithm the result is already known.
number++;
}
else
{ // one of the coordinates is not to the 'right' now we need the left/right algorithm.
LineF2D localLine = new LineF2D(this.Coordinates[idx], this.Coordinates[idx + 1]);
if (localLine.PositionOfPoint(coordinate) == LinePointPosition.Left)
{
number++;
}
}
}
else if ((this.Coordinates[idx].Latitude >= coordinate.Latitude &&
this.Coordinates[idx + 1].Latitude <= coordinate.Latitude) &&
!(this.Coordinates[idx].Latitude == coordinate.Latitude &&
this.Coordinates[idx + 1].Latitude == coordinate.Latitude))
{ // idx is higher than idx+1
if (idxRight && idx1Right)
{ // no need for the left/right algorithm the result is already known.
number--;
}
else
{ // one of the coordinates is not to the 'right' now we need the left/right algorithm.
LineF2D localLine = new LineF2D(this.Coordinates[idx], this.Coordinates[idx + 1]);
if (localLine.PositionOfPoint(coordinate) == LinePointPosition.Right)
{
number--;
}
}
}
}
}
return number != 0;
}
/// <summary>
/// Projects a point onto the given line.
///
/// (= intersection of the line with an angle 90° different from this line through the given point)
/// </summary>
/// <param name="point"></param>
/// <returns>The projection point if it occurs inside the segmented line.</returns>
public PointF2D ProjectOn(PointF2D point)
{
// get the direction.
VectorF2D direction = this.Direction;
// rotate.
VectorF2D rotated = direction.Rotate90(true);
// create second point
PointF2D point2 = new PointF2D((point + rotated).ToArray());
if (point[0] != point2[0] || point[1] != point2[1])
{
// create line.
LineF2D line = new LineF2D(
point,
point2,
false,
false);
// intersect.
PrimitiveF2D primitive =
this.Intersection(line, true);
if (primitive == null)
{
return null;
}
else if (primitive is PointF2D)
{
return primitive as PointF2D;
}
else
{
throw new InvalidOperationException();
}
}
else
{
return point2;
}
}
/// <summary>
/// Returns true if the given coordinate is contained in this ring.
///
/// See: http://geomalgorithms.com/a03-_inclusion.html
/// </summary>
/// <param name="coordinate"></param>
/// <returns></returns>
public bool Contains(double[] coordinate)
{
int number = 0;
if (this.X[0] == coordinate[0] &&
this.Y[0] == coordinate[1])
{ // the given point is one of the corners.
return true;
}
// loop over all edges and calculate if they possibly intersect.
for (int idx = 0; idx < this.X.Length - 1; idx++)
{
if (this.X[idx + 1] == coordinate[0] &&
this.Y[idx + 1] == coordinate[1])
{ // the given point is one of the corners.
return true;
}
bool idxRight = this.X[idx] > coordinate[0];
bool idx1Right = this.X[idx + 1] > coordinate[0];
if (idxRight || idx1Right)
{ // at least one of the coordinates is to the right of the point to calculate for.
if ((this.Y[idx] <= coordinate[1] &&
this.Y[idx + 1] >= coordinate[1]) &&
!(this.Y[idx] == coordinate[1] &&
this.Y[idx + 1] == coordinate[1]))
{ // idx is lower than idx+1
if (idxRight && idx1Right)
{ // no need for the left/right algorithm the result is already known.
number++;
}
else
{ // one of the coordinates is not to the 'right' now we need the left/right algorithm.
LineF2D localLine = new LineF2D(
new PointF2D(this.X[idx], this.Y[idx]),
new PointF2D(this.X[idx + 1], this.Y[idx + 1]));
if (localLine.PositionOfPoint(new PointF2D(coordinate)) == LinePointPosition.Left)
{
number++;
}
}
}
else if ((this.Y[idx] >= coordinate[1] &&
this.Y[idx + 1] <= coordinate[1]) &&
!(this.Y[idx] == coordinate[1] &&
this.Y[idx + 1] == coordinate[1]))
{ // idx is higher than idx+1
if (idxRight && idx1Right)
{ // no need for the left/right algorithm the result is already known.
number--;
}
else
{ // one of the coordinates is not to the 'right' now we need the left/right algorithm.
LineF2D localLine = new LineF2D(
new PointF2D(this.X[idx], this.Y[idx]),
new PointF2D(this.X[idx + 1], this.Y[idx + 1]));
if (localLine.PositionOfPoint(new PointF2D(coordinate)) == LinePointPosition.Right)
{
number--;
}
}
}
}
}
return number != 0;
}
/// <summary>
/// Fits this rectangle to the given points.
/// </summary>
/// <param name="points">The points to wrap the rectangle around.</param>
/// <param name="percentage">The margin in percentage.</param>
/// <returns></returns>
public RectangleF2D Fit(PointF2D[] points, double percentage)
{
if (points == null) { throw new ArgumentNullException("points"); }
if (points.Length < 2) { throw new ArgumentOutOfRangeException("Rectangle fit needs at least two points."); }
// calculate the center.
double[] center = new double[] { points[0][0], points[0][1] };
for (int idx = 1; idx < points.Length; idx++)
{
center[0] = center[0] + points[idx][0];
center[1] = center[1] + points[idx][1];
}
center[0] = center[0] / points.Length;
center[1] = center[1] / points.Length;
PointF2D centerPoint = new PointF2D(center);
LineF2D line = null;
// calculate the width.
double width = 0;
for (int idx = 0; idx < points.Length; idx++)
{
line = new LineF2D(points[idx], points[idx] + this._vectorY);
double distance = line.Distance(centerPoint);
if (distance > width)
{ // the distance is larger.
width = distance;
}
}
width = width * 2;
// calculate the height.
double height = 0;
for (int idx = 0; idx < points.Length; idx++)
{
line = new LineF2D(points[idx], points[idx] + this._vectorX);
double distance = line.Distance(centerPoint);
if (distance > height)
{ // this distance is larger.
height = distance;
}
}
height = height * 2;
// expand with the given percentage.
width = width + (width / 100.0 * percentage);
height = height + (height / 100.0 * percentage);
return RectangleF2D.FromBoundsAndCenter(width, height, centerPoint[0], centerPoint[1],
this.DirectionY);
}
public void LineSegmentIntersectionTests()
{
// double segments.
LineF2D segment1 = new LineF2D(0, 0, 5, 0, true);
LineF2D segment2 = new LineF2D(0, 0, 0, 5, true);
LineF2D segment3 = new LineF2D(0, 3, 3, 0, true);
LineF2D segment4 = new LineF2D(1, 1, 2, 2, true);
LineF2D segment5 = new LineF2D(3, 3, 4, 4, true);
LineF2D segment6 = new LineF2D(3, 1, 3, -1, true);
PrimitiveF2D primitive = segment1.Intersection(segment2);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(0, 0), primitive as PointF2D);
primitive = segment1.Intersection(segment3);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(3, 0), primitive as PointF2D);
primitive = segment2.Intersection(segment3);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(0, 3), primitive as PointF2D);
primitive = segment3.Intersection(segment4);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(1.5, 1.5), primitive as PointF2D);
primitive = segment5.Intersection(segment1);
Assert.IsNull(primitive);
primitive = segment5.Intersection(segment2);
Assert.IsNull(primitive);
primitive = segment5.Intersection(segment3);
Assert.IsNull(primitive);
primitive = segment5.Intersection(segment4);
Assert.IsNull(primitive);
primitive = segment5.Intersection(segment6);
Assert.IsNull(primitive);
primitive = segment6.Intersection(segment3);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(3, 0), primitive as PointF2D);
primitive = segment6.Intersection(segment1);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(3, 0), primitive as PointF2D);
primitive = segment6.Intersection(segment3);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(3, 0), primitive as PointF2D);
// half segments.
LineF2D segment7 = new LineF2D(1.5, 2, 1.5, 0, true, false); // only closed upwards.
LineF2D segment9 = new LineF2D(1.5, 2, 1.5, 4, true, false); // only closed downwards.
LineF2D segment8 = new LineF2D(1.5, 1, 1.5, 0, true, false); // only closed upwards.
LineF2D segment10 = new LineF2D(1.5, 1, 1.5, 4, true, false); // only closed downwards.
primitive = segment7.Intersection(segment3);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(1.5, 1.5), primitive as PointF2D);
primitive = segment3.Intersection(segment7);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(1.5, 1.5), primitive as PointF2D);
primitive = segment9.Intersection(segment3);
Assert.IsNull(primitive);
primitive = segment3.Intersection(segment9);
Assert.IsNull(primitive);
primitive = segment10.Intersection(segment3);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(1.5, 1.5), primitive as PointF2D);
primitive = segment3.Intersection(segment10);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(1.5, 1.5), primitive as PointF2D);
primitive = segment8.Intersection(segment3);
Assert.IsNull(primitive);
primitive = segment3.Intersection(segment8);
Assert.IsNull(primitive);
LineF2D segment11 = new LineF2D(-1, 1, 0, 1, true, false);
LineF2D segment12 = new LineF2D(0, 3, 3, 0, true, true);
primitive = segment11.Intersection(segment12);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(2, 1), primitive as PointF2D);
primitive = segment12.Intersection(segment11);
Assert.IsNotNull(primitive);
Assert.IsInstanceOf<PointF2D>(primitive);
Assert.AreEqual(new PointF2D(2, 1), primitive as PointF2D);
}
/// <summary>
/// Calculates and returns the line intersection.
/// </summary>
/// <param name="line"></param>
/// <param name="doSegment"></param>
/// <returns></returns>
public PrimitiveF2D Intersection(LineF2D line, bool doSegment)
{
if (line == this)
{ // if the lines equal, the full lines intersect.
return(line);
}
else if (line.A == this.A &&
line.B == this.B &&
line.C == this.C)
{ // if the lines equal in direction and position; return the smallest segment.
KeyValuePair <double, PointF2D> point1 = new KeyValuePair <double, PointF2D>(
0, this.Point1);
KeyValuePair <double, PointF2D> point2 = new KeyValuePair <double, PointF2D>(
this.Point1.Distance(this.Point2), this.Point2);
// sort.
KeyValuePair <double, PointF2D> temp;
if (point2.Key < point1.Key)
{ // point2 smaller than point1.
temp = point2;
point2 = point1;
point1 = temp;
}
KeyValuePair <double, PointF2D> point = new KeyValuePair <double, PointF2D>(
this.Point1.Distance(line.Point1), line.Point1);
if (point.Key < point2.Key) // sort.
{ // point smaller than point2.
temp = point;
point = point2;
point2 = temp;
}
if (point2.Key < point1.Key)
{ // point2 smaller than point1.
temp = point2;
point2 = point1;
point1 = temp;
}
point = new KeyValuePair <double, PointF2D>(
this.Point1.Distance(line.Point2), line.Point2);
if (point.Key < point2.Key) // sort.
{ // point smaller than point2.
temp = point;
point = point2;
point2 = temp;
}
if (point2.Key < point1.Key)
{ // point2 smaller than point1.
temp = point2;
point2 = point1;
point1 = temp;
}
// this line is a segment.
if (doSegment && (this.IsSegment1 || this.IsSegment2))
{ // test where the intersection lies.
double this_distance =
this.Point1.Distance(this.Point2);
if (this.IsSegment)
{ // if in any directions one of the points are further away from the point.
double this_distance_1 = System.Math.Min(this.Point1.Distance(point1.Value),
this.Point1.Distance(point2.Value));
if (this_distance_1 > this_distance)
{ // the point is further away.
return(null);
}
}
else if (this.IsSegment1)
{ // if in any directions one of the points are further away from the point.
double this_distance_1 = this.Point1.Distance(point1.Value);
if (this_distance_1 > this_distance)
{ // the point is further away.
return(null);
}
}
else if (this.IsSegment2)
{ // if in any directions one of the points are further away from the point.
double this_distance_2 = this.Point2.Distance(point1.Value);
if (this_distance_2 > this_distance)
{ // the point is further away.
return(null);
}
}
}
// other line is a segment.
if (doSegment && (line.IsSegment1 || line.IsSegment2))
{ // test where the intersection lies.
double this_distance =
line.Point1.Distance(line.Point2);
if (line.IsSegment)
{// if in any directions one of the points are further away from the point.
double this_distance_1 = System.Math.Min(line.Point1.Distance(point1.Value),
line.Point1.Distance(point2.Value));
if (this_distance_1 > this_distance)
{ // the point is further away.
return(null);
}
}
else if (line.IsSegment1)
{ // if in any directions one of the points are further away from the point.
double this_distance_1 = line.Point1.Distance(point1.Value);
if (this_distance_1 > this_distance)
{ // the point is further away.
return(null);
}
}
else if (line.IsSegment2)
{ // if in any directions one of the points are further away from the point.
double this_distance_2 = line.Point2.Distance(point2.Value);
if (this_distance_2 > this_distance)
{ // the point is further away.
return(null);
}
}
}
return(new LineF2D(
point1.Value,
point2.Value,
true));
}
else
{ // line.A = A1, line.B = B1, line.C = C1, this.A = A2, this.B = B2, this.C = C2
double det = (line.A * this.B - this.A * line.B);
if (det == 0) // TODO: implement an accuracy threshold epsilon.
{ // lines are parallel; no intersections.
return(null);
}
else
{ // lines are not the same and not parallel so they will intersect.
double x = (this.B * line.C - line.B * this.C) / det;
double y = (line.A * this.C - this.A * line.C) / det;
// create the point.
PointF2D point = new PointF2D(new double[] { x, y });
// this line is a segment.
if (doSegment && (this.IsSegment1 || this.IsSegment2))
{ // test where the intersection lies.
double this_distance =
this.Point1.Distance(this.Point2);
if (this.IsSegment)
{// if in any directions one of the points are further away from the point.
double this_distance_1 = this.Point1.Distance(point);
if (this_distance_1 > this_distance)
{ // the point is further away.
return(null);
}
double this_distance_2 = this.Point2.Distance(point);
if (this_distance_2 > this_distance)
{ // the point is further away.
return(null);
}
}
else if (this.IsSegment1 && this.Point2.Distance(point) > this_distance)
{ // only check this direction and only if the points lies far enough away from point2.
VectorF2D pointDirection = point - this.Point2;
VectorF2D point2ToPoint1 = this.Direction.Inverse;
if (pointDirection.CompareNormalized(point2ToPoint1, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return(null);
}
}
else if (this.IsSegment1 && this.Point1.Distance(point) > this_distance)
{ // only check this direction and only if the points lies far enough away from point1.
VectorF2D pointDirection = point - this.Point1;
VectorF2D point1ToPoint2 = this.Direction;
if (pointDirection.CompareNormalized(point1ToPoint2, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return(null);
}
}
}
// line this is a segment.
if (doSegment && (line.IsSegment1 || line.IsSegment2))
{ // test where the intersection lies.
double line_distance =
line.Point1.Distance(line.Point2);
if (line.IsSegment)
{// if in any directions one of the points are further away from the point.
double line_distance_1 = line.Point1.Distance(point);
if (line_distance_1 > line_distance)
{ // the point is further away.
return(null);
}
double line_distance_2 = line.Point2.Distance(point);
if (line_distance_2 > line_distance)
{ // the point is further away.
return(null);
}
}
else if (line.IsSegment1 && line.Point2.Distance(point) > line_distance)
{ // only check line direction and only if the points lies far enough away from point2.
VectorF2D pointDirection = point - line.Point2;
VectorF2D point2ToPoint1 = line.Direction.Inverse;
if (pointDirection.CompareNormalized(point2ToPoint1, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return(null);
}
}
else if (line.IsSegment1 && line.Point1.Distance(point) > line_distance)
{ // only check line direction and only if the points lies far enough away from point1.
VectorF2D pointDirection = point - line.Point1;
VectorF2D point1ToPoint2 = line.Direction;
if (pointDirection.CompareNormalized(point1ToPoint2, 0.001))
{ // point lies in the direction of the segmented point1 and far away from point2
return(null);
}
}
}
// the intersection is valid.
return(point);
}
}
}
/// <summary>
/// Returns true if the two points could potentially intersect this bounding box.
///
/// This is a rudemantairy quick test to rule out intersection.
/// - If false is returned there can be no intersection.
/// - If true is returned there might be intersection but it is not certain.
/// </summary>
/// <param name="line"></param>
/// <returns></returns>
public bool IntersectsPotentially(LineF2D line)
{
return(this.IntersectsPotentially(line.Point1, line.Point2));
}
public void LineDistance2DSegmentTest()
{
double delta = 0.000000000000001;
// create the line to test.
PointF2D a = new PointF2D(0, 0);
PointF2D b = new PointF2D(1, 1);
LineF2D line = new LineF2D(a, b, true, true);
// calculate the results
double sqrt_2 = (double)System.Math.Sqrt(2);
double sqrt_2_div_2 = (double)System.Math.Sqrt(2) / 2.0f;
// the point to test to.
PointF2D c = new PointF2D(1, 0);
Assert.AreEqual(line.Distance(c), sqrt_2_div_2, delta, string.Format("Point distance should be {0}f!", sqrt_2_div_2));
// the point to test to.
c = new PointF2D(0, 1);
Assert.AreEqual(line.Distance(c), sqrt_2_div_2, delta, string.Format("Point distance should be {0}f!", sqrt_2_div_2));
// the point to test to.
c = new PointF2D(2, 2);
Assert.AreEqual(line.Distance(c), sqrt_2, delta);
// the point to test to.
c = new PointF2D(2, 3);
Assert.AreEqual(line.Distance(c), 2.23606797749979, delta, string.Format("Point distance should be {0}f!", sqrt_2_div_2));
// the point to test to.
c = new PointF2D(3, 2);
Assert.AreEqual(line.Distance(c), 2.23606797749979, delta, string.Format("Point distance should be {0}f!", sqrt_2_div_2));
// the point to test to.
c = new PointF2D(1, 0);
Assert.AreEqual(line.Distance(c), sqrt_2_div_2, delta, string.Format("Point distance should be {0}f!", sqrt_2_div_2));
// the point to test to.
c = new PointF2D(0, 1);
Assert.AreEqual(line.Distance(c), sqrt_2_div_2, delta, string.Format("Point distance should be {0}f!", sqrt_2_div_2));
// the point to test to.
c = new PointF2D(2, 2);
Assert.AreEqual(line.Distance(c), sqrt_2, delta, string.Format("Point distance should be {0}!", sqrt_2));
// the point to test to.
c = new PointF2D(2, 1);
Assert.AreEqual(line.Distance(c), 1, delta, string.Format("Point distance should be {0}f!", 1));
// the point to test to.
c = new PointF2D(1, 2);
Assert.AreEqual(line.Distance(c), 1, delta, string.Format("Point distance should be {0}f!", 1));
// the point to test to.
c = new PointF2D(-1, -1);
Assert.AreEqual(line.Distance(c), sqrt_2, delta, string.Format("Point distance should be {0}f!", 1));
// the point to test to.
c = new PointF2D(1, -1);
Assert.AreEqual(line.Distance(c), sqrt_2, delta, string.Format("Point distance should be {0}f!", 1));
}
/// <summary>
/// Returns all the intersections the line has with this polygon.
/// </summary>
/// <param name="line"></param>
/// <returns></returns>
public PointF2D[] Intersections(LineF2D line)
{
List<PointF2D> points = new List<PointF2D>();
foreach (LineF2D polygon_line in this.LineEnumerator)
{
// calculate the intersection.
PrimitiveF2D primitive = line.Intersection(polygon_line);
// the primitive not null.
if (primitive != null)
{
if (primitive is LineF2D)
{ // primitive is a line; convert.
LineF2D intersect_line =
(primitive as LineF2D);
// we are sure the line is a segment.
// if the line is not a segment this means that the polygon contains an line with infinite length; impossible.
// TODO: how to determine the order?
points.Add(intersect_line.Point1);
points.Add(intersect_line.Point2);
}
else if (primitive is PointF2D)
{ // primitive is a point; convert.
PointF2D point = (primitive as PointF2D);
points.Add(point);
}
}
}
return points.ToArray();
}
public PrimitiveF2D Intersection(LineF2D line, bool doSegment)
{
if (line == this)
{
return((PrimitiveF2D)line);
}
if (line.A == this.A && line.B == this.B && line.C == this.C)
{
KeyValuePair <double, PointF2D> keyValuePair1 = new KeyValuePair <double, PointF2D>(0.0, this.Point1);
KeyValuePair <double, PointF2D> keyValuePair2 = new KeyValuePair <double, PointF2D>(this.Point1.Distance(this.Point2), this.Point2);
if (keyValuePair2.Key < keyValuePair1.Key)
{
KeyValuePair <double, PointF2D> keyValuePair3 = keyValuePair2;
keyValuePair2 = keyValuePair1;
keyValuePair1 = keyValuePair3;
}
KeyValuePair <double, PointF2D> keyValuePair4 = new KeyValuePair <double, PointF2D>(this.Point1.Distance(line.Point1), line.Point1);
if (keyValuePair4.Key < keyValuePair2.Key)
{
KeyValuePair <double, PointF2D> keyValuePair3 = keyValuePair4;
keyValuePair4 = keyValuePair2;
keyValuePair2 = keyValuePair3;
}
if (keyValuePair2.Key < keyValuePair1.Key)
{
KeyValuePair <double, PointF2D> keyValuePair3 = keyValuePair2;
keyValuePair2 = keyValuePair1;
keyValuePair1 = keyValuePair3;
}
keyValuePair4 = new KeyValuePair <double, PointF2D>(this.Point1.Distance(line.Point2), line.Point2);
if (keyValuePair4.Key < keyValuePair2.Key)
{
KeyValuePair <double, PointF2D> keyValuePair3 = keyValuePair4;
keyValuePair4 = keyValuePair2;
keyValuePair2 = keyValuePair3;
}
if (keyValuePair2.Key < keyValuePair1.Key)
{
KeyValuePair <double, PointF2D> keyValuePair3 = keyValuePair2;
keyValuePair2 = keyValuePair1;
keyValuePair1 = keyValuePair3;
}
if (doSegment && (this.IsSegment1 || this.IsSegment2))
{
double num = this.Point1.Distance(this.Point2);
if (this.IsSegment)
{
if (System.Math.Min(this.Point1.Distance(keyValuePair1.Value), this.Point1.Distance(keyValuePair2.Value)) > num)
{
return((PrimitiveF2D)null);
}
}
else if (this.IsSegment1)
{
if (this.Point1.Distance(keyValuePair1.Value) > num)
{
return((PrimitiveF2D)null);
}
}
else if (this.IsSegment2 && this.Point2.Distance(keyValuePair1.Value) > num)
{
return((PrimitiveF2D)null);
}
}
if (doSegment && (line.IsSegment1 || line.IsSegment2))
{
double num = line.Point1.Distance(line.Point2);
if (line.IsSegment)
{
if (System.Math.Min(line.Point1.Distance(keyValuePair1.Value), line.Point1.Distance(keyValuePair2.Value)) > num)
{
return((PrimitiveF2D)null);
}
}
else if (line.IsSegment1)
{
if (line.Point1.Distance(keyValuePair1.Value) > num)
{
return((PrimitiveF2D)null);
}
}
else if (line.IsSegment2 && line.Point2.Distance(keyValuePair2.Value) > num)
{
return((PrimitiveF2D)null);
}
}
return((PrimitiveF2D) new LineF2D(keyValuePair1.Value, keyValuePair2.Value, true));
}
double num1 = line.A * this.B - this.A * line.B;
if (num1 == 0.0)
{
return((PrimitiveF2D)null);
}
PointF2D p = new PointF2D(new double[2]
{
(this.B * line.C - line.B * this.C) / num1,
(line.A * this.C - this.A * line.C) / num1
});
if (doSegment && (this.IsSegment1 || this.IsSegment2))
{
double num2 = this.Point1.Distance(this.Point2);
if (this.IsSegment)
{
if (this.Point1.Distance(p) > num2)
{
return((PrimitiveF2D)null);
}
if (this.Point2.Distance(p) > num2)
{
return((PrimitiveF2D)null);
}
}
else if (this.IsSegment1 && this.Point2.Distance(p) > num2)
{
if ((p - this.Point2).CompareNormalized(this.Direction.Inverse, 0.001))
{
return((PrimitiveF2D)null);
}
}
else if (this.IsSegment1 && this.Point1.Distance(p) > num2 && (p - this.Point1).CompareNormalized(this.Direction, 0.001))
{
return((PrimitiveF2D)null);
}
}
if (doSegment && (line.IsSegment1 || line.IsSegment2))
{
double num2 = line.Point1.Distance(line.Point2);
if (line.IsSegment)
{
if (line.Point1.Distance(p) > num2)
{
return((PrimitiveF2D)null);
}
if (line.Point2.Distance(p) > num2)
{
return((PrimitiveF2D)null);
}
}
else if (line.IsSegment1 && line.Point2.Distance(p) > num2)
{
if ((p - line.Point2).CompareNormalized(line.Direction.Inverse, 0.001))
{
return((PrimitiveF2D)null);
}
}
else if (line.IsSegment1 && line.Point1.Distance(p) > num2 && (p - line.Point1).CompareNormalized(line.Direction, 0.001))
{
return((PrimitiveF2D)null);
}
}
return((PrimitiveF2D)p);
}