public int Intersect(LineSegment seg, Point2D pt0, Point2D pt1)
{
if (pt0 == null)
pt0 = new Point2D();
if (pt1 == null)
pt1 = new Point2D();
// Solution is found by parameterizing the line segment and
// substituting those values into the ellipse equation.
// Results in a quadratic equation.
double x1 = _center.X;
double y1 = _center.Y;
double u1 = seg.A.X;
double v1 = seg.A.Y;
double u2 = seg.B.X;
double v2 = seg.B.Y;
double dx = u2 - u1;
double dy = v2 - v1;
double q0 = _k1 * Sqr(u1 - x1) + _k2 * (u1 - x1) * (v1 - y1) + _k3
* Sqr(v1 - y1) - 1;
double q1 = (2 * _k1 * dx * (u1 - x1)) + (_k2 * dx * (v1 - y1))
+ (_k2 * dy * (u1 - x1)) + (2 * _k3 * dy * (v1 - y1));
double q2 = (_k1 * Sqr(dx)) + (_k2 * dx * dy) + (_k3 * Sqr(dy));
// Compare q1^2 to 4*q0*q2 to see how quadratic solves
double d = Sqr(q1) - (4 * q0 * q2);
if (d < 0)
{
// Roots are complex valued. Line containing the segment does
// not intersect the ellipse
return 0;
}
if (d == 0)
{
// One real-valued root - line is tangent to the ellipse
double t = -q1 / (2 * q2);
if (0 <= t && t <= 1)
{
// Intersection occurs along line segment
pt0.X = u1 + t * dx;
pt0.Y = v1 + t * dy;
return 1;
}
return 0;
}
else
{
// Two distinct real-valued roots. Solve for the roots and see if
// they fall along the line segment
int n = 0;
double q = Math.Sqrt(d);
double t = (-q1 - q) / (2 * q2);
if (0 <= t && t <= 1)
{
// Intersection occurs along line segment
pt0.X = u1 + t * dx;
pt0.Y = v1 + t * dy;
n++;
}
// 2nd root
t = (-q1 + q) / (2 * q2);
if (0 <= t && t <= 1)
{
if (n == 0)
{
pt0.X = u1 + t * dx;
pt0.Y = v1 + t * dy;
n++;
}
else
{
pt1.X = u1 + t * dx;
pt1.Y = v1 + t * dy;
n++;
}
}
return n;
}
}
public int Intersect(LineSegment seg, Point2D pt0, Point2D pt1)
{
if (pt0 == null)
{
pt0 = new Point2D();
}
if (pt1 == null)
{
pt1 = new Point2D();
}
// Solution is found by parameterizing the line segment and
// substituting those values into the ellipse equation.
// Results in a quadratic equation.
double x1 = _center.X;
double y1 = _center.Y;
double u1 = seg.A.X;
double v1 = seg.A.Y;
double u2 = seg.B.X;
double v2 = seg.B.Y;
double dx = u2 - u1;
double dy = v2 - v1;
double q0 = _k1 * Sqr(u1 - x1) + _k2 * (u1 - x1) * (v1 - y1) + _k3
* Sqr(v1 - y1) - 1;
double q1 = (2 * _k1 * dx * (u1 - x1)) + (_k2 * dx * (v1 - y1))
+ (_k2 * dy * (u1 - x1)) + (2 * _k3 * dy * (v1 - y1));
double q2 = (_k1 * Sqr(dx)) + (_k2 * dx * dy) + (_k3 * Sqr(dy));
// Compare q1^2 to 4*q0*q2 to see how quadratic solves
double d = Sqr(q1) - (4 * q0 * q2);
if (d < 0)
{
// Roots are complex valued. Line containing the segment does
// not intersect the ellipse
return(0);
}
if (d == 0)
{
// One real-valued root - line is tangent to the ellipse
double t = -q1 / (2 * q2);
if (0 <= t && t <= 1)
{
// Intersection occurs along line segment
pt0.X = u1 + t * dx;
pt0.Y = v1 + t * dy;
return(1);
}
return(0);
}
else
{
// Two distinct real-valued roots. Solve for the roots and see if
// they fall along the line segment
int n = 0;
double q = Math.Sqrt(d);
double t = (-q1 - q) / (2 * q2);
if (0 <= t && t <= 1)
{
// Intersection occurs along line segment
pt0.X = u1 + t * dx;
pt0.Y = v1 + t * dy;
n++;
}
// 2nd root
t = (-q1 + q) / (2 * q2);
if (0 <= t && t <= 1)
{
if (n == 0)
{
pt0.X = u1 + t * dx;
pt0.Y = v1 + t * dy;
n++;
}
else
{
pt1.X = u1 + t * dx;
pt1.Y = v1 + t * dy;
n++;
}
}
return(n);
}
}
public IntersectCase Intersect(Rectangle rectangle)
{
// Test if all 4 corners of the rectangle are inside the ellipse
var ul = new Point2D(rectangle.MinPt.X, rectangle.MaxPt.Y);
var ur = new Point2D(rectangle.MaxPt.X, rectangle.MaxPt.Y);
var ll = new Point2D(rectangle.MinPt.X, rectangle.MinPt.Y);
var lr = new Point2D(rectangle.MaxPt.X, rectangle.MinPt.Y);
if (Contains(ul) && Contains(ur) && Contains(ll) && Contains(lr)) return IntersectCase.CONTAINS;
// Test if any of the rectangle edges intersect
Point2D pt0 = new Point2D(), pt1 = new Point2D();
var bottom = new LineSegment(ll, lr);
if (Intersect(bottom, pt0, pt1) > 0)
return IntersectCase.INTERSECTS;
var top = new LineSegment(ul, ur);
if (Intersect(top, pt0, pt1) > 0)
return IntersectCase.INTERSECTS;
var left = new LineSegment(ll, ul);
if (Intersect(left, pt0, pt1) > 0)
return IntersectCase.INTERSECTS;
var right = new LineSegment(lr, ur);
if (Intersect(right, pt0, pt1) > 0)
return IntersectCase.INTERSECTS;
// Ellipse does not intersect any edge : since the case for the ellipse
// containing the rectangle was considered above then if the center
// is inside the ellipse is fully inside and if center is outside
// the ellipse is fully outside
return (rectangle.Contains(_center)) ? IntersectCase.WITHIN : IntersectCase.OUTSIDE;
}