Conformal Toolpath Mapping on 3D NURBS Surfaces With Low Distortion
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Solution Overview
Problem
Existing methods for mapping a 2D geometry onto a 3D surface often result in substantial distortion, particularly for complex surfaces, and lack user-adjustable parameters for controlling distortion in CAD and digital printing applications.
Innovation Solution
A method utilizing non-uniform rational B-splines (NURBS) for surface representation, strain energy minimization, and interpolation using finite elements to optimize the wrapping of 2D patterns onto 3D surfaces, preserving distances or angles to minimize distortion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If 2D geometry is projected onto 3D surface, then mapping is achieved, but substantial distortion occurs
Solution Approach 1:
The patent transitions from 2D projection to 3D conformal wrapping by introducing an intermediate parametric surface representation. The method creates a 3D parametric surface that can be parameterized in two dimensions, allowing the 2D toolpath to wrap conformally around complex 3D geometries while preserving local distances and minimizing distortion through strain energy minimization.
Solution Approach 2:
The patent applies parameter changes by using Non-Uniform Rational B-Splines (NURBS) to represent the 3D surface parametrically. This allows continuous adjustment of surface parameters to optimize the wrapping process, minimizing distortion through strain energy minimization while maintaining manufacturing precision on complex 3D surfaces.
2Ease of manufacture
If standard CAD projection features are used, then wrapping is achieved, but user-adjustable distortion control is lacking
Solution Approach 1:
The patent introduces dynamic control over the wrapping process through user-adjustable parameters. The strain energy minimization approach allows real-time adjustment of distortion characteristics, enabling users to optimize the wrapping process for different applications while maintaining ease of manufacture through automated computation.
Solution Approach 2:
The patent implements feedback through the strain energy minimization process, which continuously adjusts the parametric surface representation to minimize distortion. This automated feedback mechanism provides adaptability and versatility in distortion control without requiring manual iteration, enhancing both ease of manufacture and design flexibility.
3Productivity
If 2D toolpath is wrapped onto 3D surface, then conformal printing is enabled, but distortion control is challenging
Solution Approach 1:
The patent performs preliminary action by pre-computing the optimal parametric surface representation and strain energy minimization before the actual printing process. This preliminary optimization of the toolpath wrapping ensures minimal distortion is built into the geometry before manufacturing begins, enabling both high productivity and manufacturing precision in conformal printing.
Data Source
AI summary
Presented are systems and methods that provide conformal design and motion planning that wraps a two-dimensional pattern onto a three-dimensional surface. Such systems and methods utilize a parameterization of the 3D surface in two dimensions, preferably using non-uniform rational B-splines (NURBS). Such systems and methods then provide an optimization of the parameterized surface to minimize distortion, preferably by maintaining point-to-point distances along the parametric coordinates, but with a generalizable approach to support custom constraints. Interpolation of 2D toolpath coordinates or other 2D patterns on this distorted mesh is then performed. Once complete, the parametric pattern values are remapped to 3D space using the parametric surface definition.