Conics in Geometric Constraint Solving

As their name implies, conic sections (or just “conics”) are curves that are created by intersecting a conical surface with a plane. They are usually divided into three types:     

  

In the latest release of the D-Cubed 2D DCM, we have introduced direct support for conics. As discussed in my previous post, adding a new geometry type to the 2D DCM is a significant undertaking and I’d like to talk about the benefits that this brings to users.    

One of the best explanations I have seen of why conics are used in CAD is from Adam O’Hern on the cadjunkie.com site, in the Conics 101 tutorial. I definitely recommend viewing the video. 

One of the points made by Adam is that conics can be defined in many different ways – for example: through 5 points, or tangent to 2 lines and through 3 points. This is where support for conics in a geometric constraint solver brings major benefits. In 2 dimensions, a conic has 5 degrees of freedom and the 2D DCM allows any consistent set of dimensions and constraints to be used to take up these freedoms and fully define the curve. 

The following video shows examples of conics being manipulated in the 2D DCM demo application: 

 

With 2D DCM conics, engineers and designers have access to easy to use, powerful, constraint-driven methods which can create a wider range of models. 

If you have any questions about conics get in touch and I’ll do my best to help. Also, you can request a copy of the D-Cubed demo application and try them yourself.   

Mike