public static clsLine LinePointToTangent(clsPoint p1, clsCircle c1)
{
double a = 0;
double b = 0;
double r = 0;
double d = 0;
clsLine l1 = new clsLine();
clsPoint p2 = new clsPoint();
r = c1.Radius;
d = p1.Dist(c1.Centre);
if (d < r)
{
return(null);
}
a = Asin(r / d);
l1 = new clsLine(p1, c1.Centre);
b = l1.Angle;
p2 = c1.Point(PI / 2 + a + b);
return(new clsLine(p1, p2));
}
public clsPoint Intersect(clsCircle c1, bool firstSolution)
{
double a = 0;
clsLine l1 = default(clsLine);
if (mdlGeometry.Dist(Centre, c1.Centre) > Radius + c1.Radius)
{
return(null);
}
if (mdlGeometry.Dist(Centre, c1.Centre) < Abs(Radius - c1.Radius))
{
return(null);
}
l1 = new clsLine(Centre.Copy(), c1.Centre.Copy());
a = Acos((Radius * Radius + l1.Length * l1.Length - c1.Radius * c1.Radius) / (2 * Radius * l1.Length));
//Cosine rule
if (firstSolution == false)
{
a = -a;
}
l1.Rotate(a);
l1.Length = Radius;
return(l1.P2);
}
public static clsLine LineTangentToArcs(clsCircle c1, clsCircle c2, int n = -1)
{
clsArc myArc1 = new clsArc();
clsArc myArc2 = new clsArc();
//n is the solution number, from 1 to 4 (see document SolutionsToTangencies.doc)
//1 = Plus - Minus
//2 = Plus - Plus
//3 = Minus - Minus
//4 = Minus - Plus
//In this case, you must pass in an arc
if (n == -1)
{
myArc1 = (clsArc)c1;
myArc2 = (clsArc)c2;
if (myArc1.Direction == 1 & myArc2.Direction == -1)
{
n = 1;
}
if (myArc1.Direction == 1 & myArc2.Direction == 1)
{
n = 2;
}
if (myArc1.Direction == -1 & myArc2.Direction == -1)
{
n = 3;
}
if (myArc1.Direction == -1 & myArc2.Direction == 1)
{
n = 4;
}
}
double x1 = 0;
double y1 = 0;
double x2 = 0;
double y2 = 0;
double r1 = 0;
double r2 = 0;
double d = 0;
double theta = 0;
double alpha = 0;
double a = 0;
clsPoint p1 = new clsPoint();
clsPoint p2 = new clsPoint();
x1 = c1.Centre.X;
y1 = c1.Centre.Y;
x2 = c2.Centre.X;
y2 = c2.Centre.Y;
r1 = c1.Radius;
r2 = c2.Radius;
d = Sqrt(Pow((x2 - x1), 2) + Pow((y2 - y1), 2));
theta = Angle(x1, y1, x2, y2);
if (n == 1)
{
if (d < r1 + r2)
{
return(null);
}
alpha = Acos((r1 + r2) / d);
a = theta - alpha;
p1 = new clsPoint(x1 + r1 * Cos(a), y1 + r1 * Sin(a));
p2 = new clsPoint(x2 - r2 * Cos(a), y2 - r2 * Sin(a));
}
else if (n == 2)
{
if (d < Abs(r2 - r1))
{
return(null);
}
alpha = Acos((r2 - r1) / d);
a = alpha - theta;
p1 = new clsPoint(x1 + r1 * Cos(a), y1 - r1 * Sin(a));
p2 = new clsPoint(x2 + r2 * Cos(a), y2 - r2 * Sin(a));
}
else if (n == 3)
{
if (d < Abs(r2 - r1))
{
return(null);
}
alpha = PI / 2 + Asin((r2 - r1) / d);
a = alpha + theta;
p1 = new clsPoint(x1 + r1 * Cos(a), y1 + r1 * Sin(a));
p2 = new clsPoint(x2 + r2 * Cos(a), y2 + r2 * Sin(a));
}
else if (n == 4)
{
if (d < r1 + r2)
{
return(null);
}
alpha = Acos((r1 + r2) / d);
a = theta + alpha;
p1 = new clsPoint(x1 + r1 * Cos(a), y1 + r1 * Sin(a));
p2 = new clsPoint(x2 - r2 * Cos(a), y2 - r2 * Sin(a));
}
else
{
return(null);
}
return(new clsLine(p1, p2));
}
