Marionette meshes: Modelling free-form architecture with planar facets

We introduce an intuitive method, called Marionette, for the modelling of free-form architecture with planar facets. The method takes inspiration from descriptive geometry and allows to design complex shapes with one projection and the control of elevation curves. The proposed framework achieves exact facet planarity in real time and considerably enriches previous geometrically constrained methods for free-form architecture. A discussion on the design of quadrilateral meshes with a fixed horizontal projection is first proposed, and the method is then extended to various projections and patterns. The method used is a discrete solution of a continuous problem. This relation between smooth and continuous problem is discussed and shows how to combine the marionette method with modelling tools for smooth surfaces, like non-uniform rational basis spline or T-splines. The result is a versatile tool for shape modelling, suited to engineering problems related to free-form architecture.