An Introduction to Guided and Polar Surfacing

This paper gives an overview of two recent techniques for high-quality surface constructions: polar layout and the guided approach. We demonstrate the challenge of high-quality surface construction by examples since the notion of surface quality lacks an overarching theory. A key ingredient of high-quality constructions is a good layout of the surface pieces. Polar layout simplifies design and is natural where a high number of pieces meet. A second ingredient is separation of shape design from surface representation by creating an initial guide shape and leveraging classical approximation-theoretic tools to construct a final surface compatible with industry standards, either as a finite number of polynomial patches or as a subdivision process. An example construction generating guided C2 surfaces from patches of degree bi-3 highlights the power of the approach.