public static IntersectionResult CircleLine(GCircle circle, GLine line)
{
var result = new IntersectionResult();
float a, b, c, d, sqrt_d, t1, t2;
PointF v;
v = line.EndPoint.Sub(line.StartPoint);
a = v.Dot(v);
b = 2 * v.Dot(line.StartPoint.Sub(circle.Center));
c = line.StartPoint.Dot(line.StartPoint)
+ circle.Center.Dot(circle.Center)
- 2 * line.StartPoint.Dot(circle.Center)
- circle.Radius * circle.Radius;
d = b * b - 4 * a * c;
// no intersection
if (d < 0)
{
return(result);
}
// the line tangent to the circle
else if (d <= .0000001)
{
t1 = -b / (2 * a);
result.IntersectionType = IntersectionType.Tangent;
var p1 = new PointF(line.StartPoint.X + t1 * v.X, line.StartPoint.Y + t1 * v.Y);
result.IntersectionPoints.Add(p1);
return(result);
}
else
{
result.IntersectionType = IntersectionType.Collide;
// there is possible 2 solutions
sqrt_d = (float)Math.Sqrt(d);
t1 = (-b + sqrt_d) / (2 * a);
t2 = (-b - sqrt_d) / (2 * a);
//check if the 2 intersection point contained in the line
if ((0 <= t1 && t1 <= 1))
{
var p1 = new PointF(line.StartPoint.X + t1 * v.X, line.StartPoint.Y + t1 * v.Y);
result.IntersectionPoints.Add(p1);
}
if (0 <= t2 && t2 <= 1)
{
var p2 = new PointF(line.StartPoint.X + t2 * v.X, line.StartPoint.Y + t2 * v.Y);
result.IntersectionPoints.Add(p2);
}
return(result);
}
}
public static IntersectionResult CirclePolyLine(GCircle circle, GPolyLine pl)
{
var result = new IntersectionResult();
foreach (var line in pl.Lines)
{
var intersect = CircleLine(circle, line);
if (intersect.IntersectionPoints.Count > 0)
{
result.IntersectionPoints.
AddRange(intersect.IntersectionPoints);
}
}
return(result);
}
public static IntersectionResult CircleCircle(GCircle c1, GCircle c2)
{
IntersectionResult result = new IntersectionResult();
// the distance between 2 circles
var d = c1.Center.Distance(c2.Center);
if (d > c1.Radius + c2.Radius)
{
// return mo intersection
return(result);
}
else if (d < Math.Abs(c1.Radius - c2.Radius))
{
//Circle inside each other
// no intersections
return(result);
}
else if (d == 0 && c1.Radius == c2.Radius)
{
//then the circles are coincident
return(result);
}
else
{
result.IntersectionType = IntersectionType.Collide;
//calculate intersection points
double a, h;
a = (c1.Radius * c1.Radius - c2.Radius * c2.Radius + d * d) / (2 * d);
h = Math.Sqrt(Math.Abs(c1.Radius * c1.Radius - a * a));
var P0 = c1.Center;
var P1 = c2.Center;
PointF P2 = P0.Add(P1.Sub(P0).Scale((float)(a / d)));
float x3, y3, x4, y4;
x3 = (float)(P2.X + h * (P1.Y - P0.Y) / d);
y3 = (float)(P2.Y - h * (P1.X - P0.X) / d);
x4 = (float)(P2.X - h * (P1.Y - P0.Y) / d);
y4 = (float)(P2.Y + h * (P1.X - P0.X) / d);
result.IntersectionPoints.Add(new PointF(x3, y3));
result.IntersectionPoints.Add(new PointF(x4, y4));
return(result);
}
}
public static IntersectionResult ParabolaCircle(GParabola parabola, GCircle circle)
{
IntersectionResult result = new IntersectionResult();
// https://en.wikipedia.org/wiki/Quartic_function#Nature_of_the_roots
var h = circle.Center.X;
var k = circle.Center.Y;
var r = circle.Radius;
var poly = parabola.Polynomial;
var a = poly.A * poly.A;
var b = 2 * poly.A * poly.B;
var c = (2 * poly.A * poly.C) - (2 * poly.A * k) + (b * b) + 1;
var d = (2 * b * c) - (2 * b * k) - (2 * h);
var e = (c * c - 2 * c * k + h * h + k * k - r * r);
var p = (8 * a * c - 3 * b * b) / (8 * a * a);
var q = (b * b * b - 4 * a * b * c + 8 * a * a * d) / (8 * Pow(a, 3));
var delta_0 = c * c - 3 * b * d + 12 * a * e;
var delta_1 = 2 * c * c * c - 9 * b * c * d + 27 * b * b * e + 27 * a * d * d - 72 * a * c * e;
var delta = 256 * Pow(a, 3) * Pow(e, 3) - 192 * (a * a * b * d * e * e)
- 128 * (a * a * c * c * e * e) + 144 * (a * a * c * d * d * e)
- 27 * (a * a * Pow(d, 4)) + 144 * (a * b * b * c * e * e)
- 6 * (a * b * b * d * d * e) - 80 * (a * b * c * c * d * e)
+ 18 * (a * b * c * Pow(d, 3)) + 16 * (a * Pow(c, 4) * e)
- 4 * (a * Pow(c, 3) * d * d) - 27 * (Pow(b, 4) * e * e) +
18 * (Pow(b, 3) * c * d * e) - 4 * (Pow(b, 3) * Pow(d, 3))
- 4 * (b * b * Pow(c, 3) * e) + (b * b * c * c * d * d);
var delta_diff = -27 * delta;
double Q, S;
if (delta > 0)
{
var phy = Math.Acos(delta_1 /
(2 * Sqrt(Pow(delta_0, 3))
));
S = .5 * Sqrt(-(2 / 3) * p + (2 / 3 * a) * Sqrt(delta_0) * Cos(phy / 3));
}
else
{
Q = Pow(
(delta_1 + Sqrt(delta_diff)) / 2
, 1 / 3);
S = .5 * Sqrt(
-(2 / 3) * p + (1 / ((3 * a)) * (Q + delta_0 / Q))
);
}
if (delta != 0 && delta == 0)
{
}
float t1, t2, t3, t4;
//check for roots
var d1 = -4 * S * S - 2 * p + q / S;
if (d1 <= Setup.Tolerance)
{
t1 = (float)(-b / 4 * a - S + .5 * Sqrt(d1));
t2 = (float)(-b / 4 * a - S - .5 * Sqrt(d1));
}
var d2 = -4 * S * S - 2 * p - q / S;
if (d2 <= Setup.Tolerance)
{
t3 = (float)(-b / 4 * a - S + .5 * Sqrt(d2));
t4 = (float)(-b / 4 * a - S - .5 * Sqrt(d2));
}
return(result);
}
public static IntersectionResult ArcCircle(GCircle circle, GLine line)
{
var result = new IntersectionResult();
return(result);
}