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Curved Creases

Design

An interactive tool for designing curved-crease origami.

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What it does

Curved Creases is an interactive geometry simulation and optimization tool for designing curved-crease origami from ruled-surface polysurfaces. It is built for designers, researchers, and technical artists who want to explore curved-crease folding and validate whether a set of surface patches and creases can satisfy geometric conditions needed for physically plausible folding.

Workflow starts with input geometry: load a polysurface made of (untrimmed) ruled surfaces in .3dm format, or explore included examples. Curved Creases represents the geometry with B-spline control points and runs an optimizer that adjusts those control points so each surface patch becomes developable while satisfying constraints that define a valid curved-crease fold between adjacent patches.

Optimization is performed with a Gauss–Newton solver over B-spline control points, combining multiple residual types. Developability constraints enforce developable ruled patches via relationships between rulings, rails, tangents, and surface normals. Curved-crease constraints enforce that the crease curve’s osculating plane bisects the dihedral angle between neighboring patches, using conditions on crease tangent and curvature relative to the sum of normals.

Additional controls provide practical handles for interactive design and stabilization: Anchor Z keeps control point heights close to their initial values; Folding Angle softly preserves the initial dihedral angles at creases; Fairness encourages smoother curves by making consecutive control points more collinear; C1 Tangent enforces tangent continuity where rails meet; and Regression and Solver iteration settings control step size and convergence behavior.

Curved Creases also includes tools to inspect geometry layers (surfaces, creases, rulings, control points), view initial vs optimized results, and work with unrolled/merged representations via an Unroller with stitch/merge operations and 2D↔3D transfers. You can export results and print, supporting iterative exploration from input surfaces through optimized, constraint-satisfying crease-fold geometry.

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