Developable Surface Generation via Curve Evolution
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Solution Overview
Problem
Existing techniques for generating developable surface models for organic 3D shapes face limitations such as tedious assembly, visual artifacts, limited control over surface characteristics, and inefficiencies in manufacturing, particularly due to issues like self-intersections and irregular shapes, which hinder their practical application in manufacturing complex and aesthetically pleasing models.
Innovation Solution
A method for generating developable surfaces through a computer-implemented process that optimizes the number, regularity, and assembly of developable surfaces by using a curve evolution technique inspired by the anatomy of the human visual cortex, allowing for easier assembly and integration of textures, while preventing self-intersections and reducing the need for external assembly aids.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If existing techniques are used to generate developable surface models for organic 3D shapes, then the models can be created, but the assembly process becomes tedious and requires external aids
Solution Approach 1:
The patent applies the self-service principle by designing developable surfaces with self-supporting properties that enable automatic assembly without external aids. The surfaces are generated with inherent stability features that allow them to assemble themselves into complete 3D models, eliminating the need for manual intervention or additional assembly tools.
Solution Approach 2:
The patent segments the organic 3D shape into multiple developable surface patches that can be independently manufactured and then assembled. This segmentation allows each patch to be optimized for manufacturability while maintaining the overall structural integrity when combined, reducing assembly complexity through modular design.
2Shape
If existing techniques generate developable surfaces with high geometric detail, then the visual appearance improves, but the number of surfaces increases making assembly more complex
Solution Approach 1:
The patent merges multiple small developable surface patches into larger, more regular surfaces that maintain geometric detail while reducing the total number of components. This merging process combines adjacent patches with similar characteristics into unified surfaces, preserving visual fidelity while simplifying assembly operations.
Solution Approach 2:
The patent employs parameter changes by adjusting the regularization parameters during surface generation to control the balance between geometric detail and surface count. By dynamically modifying parameters such as patch size thresholds and detail preservation levels, the system optimizes the trade-off between visual appearance and assembly complexity.
3Manufacturing precision
If developable surfaces are generated with irregular shapes to fit organic forms, then the approximation accuracy improves, but self-intersections occur preventing manufacturing
Solution Approach 1:
The patent applies preliminary anti-action by implementing collision detection and resolution algorithms that prevent self-intersections before the surfaces are finalized for manufacturing. The system proactively identifies potential intersection problems during the generation phase and adjusts surface geometry to avoid these issues, ensuring manufacturability is maintained while preserving approximation accuracy.
Solution Approach 2:
The patent performs preliminary regularization and validation of developable surfaces before they are used for manufacturing. This preliminary action includes checking for self-intersections, validating geometric properties, and pre-processing surfaces to ensure they meet manufacturing requirements, thereby preventing reliability issues downstream.
4Ease of operation
If the number of developable surfaces is reduced to simplify assembly, then assembly ease improves, but control over surface characteristics is limited
Solution Approach 1:
The patent introduces dynamics by implementing an iterative optimization process that dynamically adjusts surface characteristics during generation. The system starts with a simplified surface configuration for easy assembly and progressively refines surface properties through multiple passes, allowing control over characteristics such as curvature, patch size, and boundary conditions while maintaining assembly simplicity.
Solution Approach 2:
The patent applies local quality by allowing different regions of the developable surfaces to have different characteristics optimized for their specific functions. Critical areas maintain high geometric fidelity while less critical areas use simpler representations, providing localized control over surface properties without increasing overall assembly complexity.
Data Source
AI summary
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.