/// <summary>
/// finds the closest point on a line segment to a given point
/// </summary>
/// <param name="point">given point</param>
/// <param name="edge">line segment</param>
/// <returns>closest point on line segment</returns>
public static Vector2 ClosestPointOnEdge(Vector2 point, LineSegment edge)
{
// vector of edge
Vector2 a = edge.Point2 - edge.Point1;
// vector from initial point of edge to our point
Vector2 b = point - edge.Point1;
// scalar projection of b onto a
float compBOntoA = Vector2.Dot(a, b) / a.Length();
if (compBOntoA < 0)
return edge.Point1;
if (compBOntoA > a.Length())
return edge.Point2;
// unit vector of a
a.Normalize();
//a = a / a.Length();
// vector projection of b onto a
Vector2 projBontoA = a * compBOntoA;
// vector projection plus initial point of edge
Vector2 pointOnEdge = edge.Point1 + projBontoA;
//pointOnEdge.X = MathHelper.Clamp(pointOnEdge.X, edge.Point1.X, edge.Point2.X);
//pointOnEdge.Y = MathHelper.Clamp(pointOnEdge.Y, edge.Point1.Y, edge.Point2.Y);
return pointOnEdge;
}
public bool ContainsPoint(Vector2 p)
{
if (p.X < MinX || p.X > MaxX || p.Y < MinY || p.Y > MaxY)
return false;
Vector2 rayStart = new Vector2(MinX - epsilon, p.Y);
Vector2 rayEnd = p;
LineSegment ray = new LineSegment(rayStart, rayEnd);
// Test the ray against all sides
int intersections = 0;
foreach (LineSegment side in sides)
{
if (Geometry.LineSegmentIntersect(ray, side))
intersections++;
}
// if odd return true
if ((intersections & 1) == 1)
return true;
// if even return false
else
return false;
}
// maybe not working
/*public static bool LineSegmentIntersect(LineSegment line1, LineSegment line2)
{
float v1x1 = line1.Point1.X;
float v1x2 = line1.Point2.X;
float v1y1 = line1.Point1.Y;
float v1y2 = line1.Point2.Y;
float v2x1 = line2.Point1.X;
float v2x2 = line2.Point2.X;
float v2y1 = line2.Point1.Y;
float v2y2 = line2.Point2.Y;
float d1, d2;
float a1, a2, b1, b2, c1, c2;
// Convert vector 1 to a line (line 1) of infinite length.
// We want the line in linear equation standard form: A*x + B*y + C = 0
// See: http://en.wikipedia.org/wiki/Linear_equation
a1 = v1y2 - v1y1;
//a1 = line1.Point2.Y - line1.Point1.Y;
b1 = v1x1 - v1x2;
//b1 = line1.Point1.X - line1.Point2.X;
c1 = (v1x2 * v1y1) - (v1x1 * v1y2);
//c1 = (line1.Point2.X * line1.Point1.Y) - (line1.Point1.X * line1.Point2.Y);
// Every point (x,y), that solves the equation above, is on the line,
// every point that does not solve it, is either above or below the line.
// We insert (x1,y1) and (x2,y2) of vector 2 into the equation above.
d1 = (a1 * v2x1) + (b1 * v2y1) + c1;
//d1 = (a1 * line2.Point1.X) + (b1 * line2.Point1.Y) + c1;
d2 = (a1 * v2x2) + (b1 * v2y2) + c1;
//d2 = (a1 * line2.Point2.X) + (b1 * line2.Point2.Y) + c1;
// If d1 and d2 both have the same sign, they are both on the same side of
// our line 1 and in that case no intersection is possible. Careful, 0 is
// a special case, that's why we don't test ">=" and "<=", but "<" and ">".
if (d1 > 0 && d2 > 0) return false;
if (d1 < 0 && d2 < 0) return false;
// We repeat everything above for vector 2.
// We start by calculating line 2 in linear equation standard form.
a2 = v2y2 - v2y1;
//a2 = line2.Point2.Y - line2.Point1.Y;
b2 = v2x1 - v2x2;
//b2 = line2.Point1.X - line2.Point2.X;
c2 = (v2x2 * v1y1) - (v2x1 * v2y2);
//c2 = (line2.Point2.X * line1.Point1.Y) - (line2.Point1.X * line2.Point2.Y);
// Calulate d1 and d2 again, this time using points of vector 1
d1 = (a2 * v1x1) + (b2 * v1y1) + c2;
//d1 = (a2 * line1.Point1.X) + (b2 * line1.Point1.Y) + c2;
d2 = (a2 * v1x2) + (b2 * v1y2) + c2;
//d2 = (a2 * line1.Point2.X) + (b2 * line1.Point2.Y) + c2;
// Again, if both have the same sign (and neither one is 0),
// no intersection is possible.
if (d1 > 0 && d2 > 0) return false;
if (d1 < 0 && d2 < 0) return false;
// If we get here, only three possibilities are left. Either the two
// vectors intersect in exactly one point or they are collinear
// (they both lie both on the same infinite line), in which case they
// may intersect in an infinite number of points or not at all.
//if ((a1 * b2) - (a2 * b1) == 0.0f) return COLLINEAR;
// If they are not collinear, they must intersect in exactly one point.
return true;
}*/
// might work
public static bool LineSegmentIntersect(LineSegment line1, LineSegment line2)
{
// Find the four orientations needed for general and
// special cases
int o1 = orientation(line1.Point1, line1.Point2, line2.Point1);
int o2 = orientation(line1.Point1, line1.Point2, line2.Point2);
int o3 = orientation(line2.Point1, line2.Point2, line1.Point1);
int o4 = orientation(line2.Point1, line2.Point2, line1.Point2);
// General case
if (o1 != o2 && o3 != o4)
return true;
return false;
}
public static LineSegment PointLinePerpendicular(Vector2 point, LineSegment line)
{
// vector of line
Vector2 a = line.Point2 - line.Point1;
// vector of point from initial point on line
Vector2 b = point - line.Point1;
// scalar projection of b onto a
float compBOntoA = Vector2.Dot(a, b) / a.Length();
// unit vector of a
a = a / a.Length();
// vector projection of b onto a
Vector2 projBontoA = a * compBOntoA;
// vector projection plus initial point of edge
Vector2 pointOnEdge = line.Point1 + projBontoA;
// return line from point on line to given point
return new LineSegment(pointOnEdge, point);
}
/// <summary>
/// finds the closest point on a polygon to a given point
/// </summary>
/// <param name="point">given point</param>
/// <param name="polygon">polygon</param>
/// <param name="closestEdge">edge the point is on</param>
/// <returns>closest point on polygon</returns>
public static Vector2 ClosestPointOnPolygon(Vector2 point, Polygon polygon, ref LineSegment closestEdge)
{
Vector2 closestPoint = Vector2.Zero;
float closestDistance = float.MaxValue;
foreach (LineSegment side in polygon.Sides)
{
Vector2 pointOnEdge = ClosestPointOnEdge(point, side);
float distance = Vector2.DistanceSquared(point, pointOnEdge);
if (distance < closestDistance)
{
closestPoint = pointOnEdge;
closestDistance = distance;
closestEdge = side;
}
}
return closestPoint;
}
