Approximating 3D shapes with piecewise developable surfaces is an active research topic, driven by the benefits of developable geometry in fabrication. Piecewise developable surfaces are characterized by having a Gauss image that is a 1D object – a collection of curves on the Gauss sphere. We present a method for developable approximation that makes use of this classic definition from differential geometry. Our algorithm is an iterative process that alternates between thinning the Gauss image of the surface and deforming the surface itself to make its normals comply with the Gauss image. The simple, local‐global structure of our algorithm makes it easy to implement and optimize. We validate our method on developable shapes with added noise and demonstrate its effectiveness on a variety of non‐developable inputs. Compared to the state of the art, our method is more general, tessellation independent, and preserves the input mesh connectivity.
κ-curves [YSW * 17] trigonometric blending [Yuk20] 3-arcs clothoid clothoid-line-clothoid Figure 1: Interpolating curves generated from the same control points (shown in red) using κ-curves [YSW * 17], trigonometric blending [Yuk20], our 3-arcs clothoids method and our clothoid-line-clothoid method. Our approach guarantees G 2 continuity, has bounded local support and provides curvature monotonicity between control points of opposite curvature sign. The curvature normals are visualized with purple lines.
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