3D Geometry Decomposition into Developable Surface Patches
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Solution Overview
Problem
Existing methods fail to effectively decompose three-dimensional geometry into developable surface patches and two-dimensional cut patterns for materials that resist stretching and shearing, such as sheet metal, textiles, and wood, limiting the ability to deform these materials into desired shapes without stress.
Innovation Solution
A method that iteratively grows surface patches from seed faces in 3D geometry by adding faces with minimum distance to a patch proxy, optimizing patch boundaries, and flattening these patches into truly developable surfaces, which can be further unfolded into 2D shapes for cutting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If sheet materials are used to manufacture objects, then cost-effectiveness and ease of mass production are improved, but the ability to deform into complex 3D shapes is limited due to resistance to stretching and shearing
Solution Approach 1:
The 3D surface is segmented into multiple developable patches, each of which can be independently flattened into 2D patterns. This allows complex shapes to be constructed from multiple simpler developable surfaces that respect the material's constraints against stretching and shearing.
Solution Approach 2:
The invention transitions from 3D geometry to 2D developable patterns by flattening developable patches. This dimensional transformation enables sheet materials to be cut in 2D and then folded/assembled into complex 3D shapes without requiring in-plane stretching or shearing of the material.
2Manufacturing precision
If existing decomposition methods are used, then some 3D geometry can be converted to developable patches, but the decomposition is ineffective and cannot accurately produce stress-free cut patterns
Solution Approach 1:
The invention replaces traditional geometric decomposition algorithms with an energy minimization approach based on finite element analysis. By minimizing the energy function that penalizes stretching and shearing, the system automatically identifies optimal developable patches and their corresponding 2D patterns, achieving both high accuracy and effectiveness.
Solution Approach 2:
The energy minimization process uses feedback from the material's mechanical properties (resistance to stretching and shearing) to iteratively improve the decomposition. The system evaluates the energy state of the deformation and adjusts the patch boundaries and flattening transformations to minimize stress, ensuring accurate and stress-free results.
Data Source
AI summary
Embodiments disclosed herein provide techniques for decomposing 3D geometry into developable surface patches and cut patterns. In one embodiment, a decomposition application receives a triangulated 3D surface as input and determines approximately developable surface patches from the 3D surface using a variant of k-means clustering. Such approximately developable surface patches may have undesirable jagged boundaries, which the decomposition application may eliminate by generating a data structure separate from the mesh that contains patch boundaries and optimizing the patch boundaries or, alternatively, remeshing the mesh such that patch boundaries fall on mesh edges. The decomposition application may then flatten the patches into truly developable surfaces by re-triangulating the patches as ruled surfaces. The decomposition application may further flatten the ruled surfaces into 2D shapes and lay those shapes out on virtual sheets of material. A person, or machinery, may cut out those shapes from physical sheets of material based on the layout.