3D Surface Flattening via Wire-Patch Geodesic Projection
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Solution Overview
Problem
Current surface flattening methods for 3D to 2D conversion in design and manufacturing are inefficient, often leading to length variations and difficulties in preserving feature curves, especially for non-developable surfaces, which affects the accuracy and fit of fabricated products.
Innovation Solution
A method involving the construction of wire-patches by feature curves, computation of optimal 2D angles for wire-nodes, and determining their positions to lay out feature curves in 2D, using both progressive and global warping schemes to preserve edge lengths and minimize distortions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If non-linear optimization framework is used to minimize distance variation error, then surface flattening accuracy is improved, but computational time is excessive and feature curve length preservation is poor
Solution Approach 1:
The patent segments the surface flattening problem into two distinct stages: (1) computing geodesic distances using graph theory algorithms, and (2) projecting points onto the 2D plane using the computed distances. This segmentation allows each stage to use optimized algorithms appropriate for its specific task, avoiding the computational burden of general non-linear optimization while maintaining accuracy.
Solution Approach 2:
The patent replaces the mechanical iterative optimization process with a computational geometry approach based on graph theory. By computing geodesic distances through graph algorithms and then directly projecting points using these distances, the method eliminates the need for time-consuming non-linear optimization iterations while preserving feature curve lengths.
2Manufacturing precision
If developable ruled surfaces are used to approximate 3D surfaces, then length preservation is improved, but modeling capability for freeform surfaces is limited
Solution Approach 1:
The patent changes the fundamental parameter from assuming developable surface geometry to computing actual geodesic distances on the given 3D surface. This allows the method to work with any freeform surface topology while still achieving length preservation through accurate geodesic distance computation and 2D projection, without being constrained to ruled surface approximations.
3Manufacturing precision
If isometric mapping is applied to preserve distances, then length invariance is achieved, but this is only possible on developable surfaces
Solution Approach 1:
The patent applies isometric mapping principles partially by preserving lengths along feature curves through geodesic distance computation, while accepting that complete isometric mapping is only possible on developable surfaces. The method computes geodesic distances accurately and projects points to minimize distortion, achieving length preservation for important feature curves even on non-developable surfaces.
Data Source
AI summary
Disclosed is a method for flattening a 3D surface into a 2D piece. In one embodiment, the method is implemented by constructing a plurality of wire-patches by feature curves on a surface patch of the 3D surface, wherein each of feature curves comprises a plurality of wire-nodes; computing an optimal 2D angle for each of said wire-nodes of the constructed wire-patches; determining an optimal position for each of said wire-nodes based on the computed optimal 2D angles thereof, respectively; and laying out each of said feature curves in 2D based on the determined optimal position. A device to flatten a 3D surface into a 2D piece is also provided.