fundamentals of surface modeling

We will be placing tutorials & base files for all 7 forms in the “periodic table of form“ (located above) up on df. The text below is an excerpt from the core 77 article entitled “A Periodic Table of Form: the secret language of surface and meaning in product design”, by Gray Holland. It serves as a wonderful conceptual bootstrapping mechanism for our Rhino Boot-Camp Workshop 001.

“If there is an empirical meaning behind form then, how does it manifest across the natural and into the man-made world? Going further with this notion, let’s deconstruct the meaning of form naturally, and then distill that meaning into some simplified geometric categories technically. In order to define these categories, I will ironically employ a three-level definition of surface continuity from the engineering CAD lexicon: Positional, Tangential, and Curvature continuities.

It’s useful to think of these three types as steps in a ladder, with each building on the definition of the last. Positional continuity [C⁰ or G⁰] refers to the hard edge created when 2 surfaces intersect. Tangential continuity [C¹ or G¹] is the next level, defined by a circular arc creating a relatively smooth transition between these surfaces. The quality of this transition is best visualized by a straight line drawn between two circles: the line’s only point of contact with each circle is tangential. This level of continuity is often described as a basic fillet in most solid modeling systems. Although smooth, there is a characteristic “break line” of tangency denoting where the circle meets the line.

Curvature continuity [C² or G²] is a bit trickier to describe. Technically, it occurs when the rate of curvature between 2 continuous surfaces are the same. Visually, it is when one cannot tell when one surface ends and another begins. In the CAD world this is often referred to as class A surfacing, and is the domain of surface-based modeling software like Alias, Rhino, and Catia. The primary benefit of Curvature’s quality is the ability to control smooth reflections across multiple surfaces, generating the elegant sculptural results necessary in the automotive industry. The technical renderings below illustrate these visual qualities better than any verbal description could. Please pay attention to the subtle differences, particularly the Tangential line marking the fillet’s point of contact with its adjacent surface, and how the reflections break there as well.”

To read the rest of the article please go to core 77 .