Ruled Free Forms

Abstract

The geometry of ruled surfaces is highly relevant for jreeform architec- tural design, owing to the fact that any negatively curved freeform shape can be approximated by a smooth union of ruled surface strips. This information is im- portant for the efficient manufacturing o f both skins and underconstructions. The present paper discusses how to algorithmically solve this approximation problem. In particular we emphasize the special class o f conoidal ruled surfaces which sug- gest new and simple ways ofsurface generation.