Rho, Rho, Rho Your Boat: Conics in SolidWorks 2013

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SolidWorks 2013 introduces a sketch entity type that was once the soledominion of expensive Class-A surface modeling systems of yesteryear: The Conic Section.

As I learned in 10th grade, if you take a cone and slice it with a plane, depending on what angle you slice it at you will get a circle, an ellipse, a parabola, or a hyperbola. These curves are called conic sections and you can read all about them on Wikipedia (which did not exist when I was in 10th grade).

 

CAD jockeys really like conics (as these curves have been called) because they are more interesting than arcs, while being less cumbersome than splines. Many of us learned how to write and solve the formulas for conic sections while still in high school, unlike the higher math needed to manipulate cubic splines. That means conics, and their resulting surfaces, are fast and lightweight for our computers too. The nature of their combined x-squared and y-squared terms means conics have a varying curvature, but do not ever change convexity like cubic splines can do. This allows us to create smooth, flowing blends, without worrying about wrinkles or dimples or other unruly spline behaviors.

 

Creating a conic in SolidWorks is very simple. It builds much like a 3-point-arc, but instead of adjusting a radius value, we adjust a parameter called Rho (?). If you imagine the conic as a rounded corner, then Rho is the ratio of the distance of the peak of the rounded corner to the sharp corner (D1/D2). This gives us an intuitive way to adjust the curvature of the conic without having to delve into which type of conic section it is, or what its mathematical eccentricity is.

 

As the picture shows, if Rho is 0.5, then the conic is a parabola. If Rho is greater than 0.5, then the conic is a hyperbola (which we have never had before in SolidWorks!). If Rho is less than 0.5, then the conic is an ellipse. The exact Rho value which gives you a circle/arc (a special ellipse) depends on the angle of the corner; for a 90° corner, Rho for a circle is the square root of two, minus one (0.414).
 
 
The two ends of the conic can be set tangent to the adjacent entities, just as you would with an arc or partial ellipse. Unlike splines, you cannot clamp curvature continuity, but it still looks pretty darn good.

Now, are they used in boat design? Probably not.

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Jason Pancoast is Engineering Manager at CAPINC, a SolidWorks Value Added Reseller with locations across New England. He is a regular contributor to their CAPINC University blog.

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