public clsPoint Intersect(clsArc c1)
{
double a = 0;
double b = 0;
double c = 0;
double xc = 0;
double yc = 0;
double lambda1 = 0;
double lambda2 = 0;
if (c1.Centre.Dist(this) > c1.Radius)
{
return(null);
}
xc = c1.Centre.X;
yc = c1.Centre.Y;
a = Pow((X2 - X1), 2) + Pow((Y2 - Y1), 2);
b = 2 * ((X2 - X1) * (X1 - xc) + (Y2 - Y1) * (Y1 - yc));
c = Pow((X1 - xc), 2) + Pow((Y1 - yc), 2) - Pow((c1.Radius), 2);
lambda1 = (-b + Sqrt(Abs(Pow(b, 2) - 4 * a * c))) / (2 * a);
lambda2 = (-b - Sqrt(Abs(Pow(b, 2) - 4 * a * c))) / (2 * a);
if (lambda2 < lambda1 & lambda2 > 0)
{
lambda1 = lambda2;
}
return(new clsPoint(X1 + lambda1 * (X2 - X1), Y1 + lambda1 * (Y2 - Y1)));
}
public clsArc ArcTanPlus(bool atStart, bool downSide, bool avoidLeadInOut = false)
{
clsPoint pt1;
double a1;
double a2;
clsArc c1;
if (atStart == true)
{
pt1 = P1;
}
else
{
pt1 = P2;
}
if (downSide)
{
a1 = 3 * PI / 2;
a2 = 3 * PI / 2 + Angle;
}
else
{
a1 = 3 * PI / 2 + Angle;
a2 = 3 * PI / 2 + PI / 4;
}
c1 = new clsArc(new clsPoint(pt1.x - 250 * Sin(Angle), pt1.y + 250 * Cos(Angle)), 250, a1, a2, 1);
if (avoidLeadInOut == false)
{
if (downSide)
{
c1.Move(-c1.EndStraight());
}
else
{
c1.Move(c1.StartStraight());
}
}
return(c1);
}
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));
}