Abstract: Developable surfaces are generated by interactively evolving curves on a 2D surface embedded in 3D space using an iterative process to produce a model for the construction of a stylized three dimensional sculpture. Each iteration includes tessellating loops formed by the curves on the surface and unfolding the resulting tessellated strips onto a 2D plane. Collisions between the unfolded tessellated strips in 2D and between the loops in 3D are resolved, and the rendered evolved curve in 3D and tessellated strips in 2D are displayed simultaneously during the evolution. A graphical user interface allows the curve network, tessellated strips, and curve evolution parameters to be modified by a user. 2D textures may be mapped to the unfolded tessellated strips, and a set of tool paths may be output for cutting a 2D material.

Abstract: Complex labyrinth curves are interactively generated by an iterative process that spatially modulates curve evolution by an image or other function defined on the evolution space. After curves and evolution parameters are initialized [100], the iterative process resamples the curves [104], and spatially modulates the curves according to the evolution parameters [106]. The spatial modulation includes computing sample point displacements by calculating distances between each of the sample points and neighboring points using a surface distance metric that estimates a geodesic distance metric in a two-dimensional non-Euclidean evolution space. The evolved labyrinth curves are may be processed [110] for use in various applications. The evolved curves can also be triangulated and projected to a plane to create patterns for manufacturing developable surfaces.

Abstract: Complex labyrinth curves are interactively generated by an iterative process that spatially modulates curve evolution by an image or other function defined on the evolution space. After curves and evolution parameters are initialized [100], the iterative process allows the curve and evolution parameters to be interactively modified by a user [102], resamples the curves [104], and spatially modulates the curves according to the evolution parameters [106]. The evolved labyrinth curves are may be processed [110] for use in various applications including animation, maze creation, intricate artistic patterns, and graphical user interfaces that map linearly ordered data to the evolved curve and allow the data to be navigated using the rendered curve. The evolved curves can also be triangulated and projected to a plane to create patterns for manufacturing developable surfaces.