CODEWITHSUNDEEP
algorithmgeometrycurvecad
user1446072
user1446072

Reputation: 93

Creating a circular arc tangent to two curves with specified radius

The operation mentioned in the title is common in many Computer Aided Design (CAD) softwares such as AutoCAD, where it is called fillet. However, I found it is really difficult to implement this function in my own program.

The method I thought of is to use the condition that the distances of the arc center to the tangent lines of the curves are equal to the specified radius. Considering that actual curves are defined with piece-wise nonlinear functions, and the contact points could be anywhere on the curves, it is not easy to get the solution. Anyone good ideas?

Upvotes: 2

Views: 1836

Answers (2)

abenci
abenci

Reputation: 8681

To find the arc center you need two robust and strategic algorithms:

  1. Curve offset
  2. Curve intersection

What AutoCAD does to find the arc center is to offset the two curves of the arc radius distance and intersect them. Depending on the curve offset direction you can easily switch between all possible solutions to the problem.

At this point, trimming the curves at tangent points will be trivial.

Upvotes: 1

Adrian Colomitchi
Adrian Colomitchi

Reputation: 3992

Given that you don't describe in enough details the characteristics of the curves, it's hard to come with a specific/specified algo, but let's try a descriptive approach:

take a circle of the given radius and roll it on one curve until the circle touches the other one.

I assume you can parametrize you curves.

To "roll the circle" along the curve you need the tangent (or better said the normal, which of course is normal to the tangent) in the point "rolling track curve"-to-circle tangent point. You have this normal, you know the radius, you can compute your circle. You have the circle, you can see if/where it intersects the other curve.

The idea of "rolling" is to bracket your solution (parameter of the tangent-point on one curve) between a point when the circle does not intersect the other curve and another point where it intersects (possible in more than 1 point). Once you have the bracket, go with a bisection method (binary search) between the two positions until your circle becomes "tangent enough" to the other curve (i.e the intersection points with the other curve are so close that they fall below your acceptable epsilon).

You will now have two points (one on each curves) and the circle that realizes the solution: just keep the arc on this circle corresponding what make sense (based on the convergence or divergence of the two tangents).

Upvotes: 1

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