Curvilinear coordinate systems for 3D design: building cyclidic nets with conformal geometric algebra.

We introduce various parametric techniques to construct and manipulate triply orthogonal curvilinear lattices. Using principal contact tangent elements and the rationalization of spheres through conformal transformations, we detail their constraints and provide an inverse mapping at the boundary. We develop our approach from the perspective of a three-dimensional (3D) practitioner, working with geometric primitives to express various forms with this system. This article is part of the theme issue 'Modern applications of geometric algebra'.