Spline Surface Model Preserving Physical Object Features
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Solution Overview
Problem
Existing methods for constructing smooth spline surfaces from unstructured quadrilateral meshes are limited in accuracy and efficiency, particularly when dealing with irregular nodes on features or boundaries of physical objects.
Innovation Solution
The method involves adding one or more edge points to the quadrilateral mesh around irregular nodes, determining knot interval vectors for these additional points, and evaluating the irregular elements based on these vectors to generate a smooth spline surface with high continuity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing methods are used to construct smooth spline surfaces from unstructured quadrilateral meshes with irregular nodes on features or boundaries, then the method allows irregular nodes to be on a boundary or feature, but only achieves C0 continuity around the irregular nodes, resulting in jagged or unsmooth regions
Solution Approach 1:
The method segments the quadrilateral mesh into regular and irregular elements, applying different continuity requirements and basis functions to each segment. Regular elements use standard C2 continuous basis functions, while irregular elements use specially constructed basis functions that maintain C1 continuity along feature edges and C2 continuity elsewhere, resolving the contradiction between allowing irregular nodes on features and achieving smooth surfaces.
Solution Approach 2:
The invention applies local quality by using different basis functions for different regions of the mesh. Specifically, it uses C1 continuous basis functions along feature edges containing irregular nodes and C2 continuous basis functions in regular regions, allowing the surface to have different continuity levels in different locations to simultaneously preserve features and achieve smoothness.
2Reliability
If Rational basis functions are used to overcome the partition of unity problem, then the partition of unity problem is resolved, but the analysis process slows down
Solution Approach 1:
The method uses simple polynomial basis functions instead of complex Rational basis functions, sacrificing the ability to handle certain complex geometries in exchange for computational efficiency. The polynomial basis functions satisfy partition of unity and achieve the required continuity without the computational overhead of Rational functions, maintaining fast analysis speed.
Solution Approach 2:
The invention changes the parameters of the basis functions from Rational to polynomial form, which simplifies the mathematical operations required during analysis. This parameter change maintains the essential properties needed for finite element analysis while significantly reducing computational complexity and improving analysis speed.
3Manufacturing precision
If existing methods are used, then C1 continuity smoothness is achieved around irregular nodes, but irregular nodes cannot be on a boundary or feature of the physical object
Solution Approach 1:
The method dynamically adjusts the continuity requirements and basis function selection based on the location and type of irregular nodes. When irregular nodes are located on feature edges, the system adapts by using C1 continuous basis functions along those edges while maintaining C2 continuity elsewhere, allowing the model to both preserve features and achieve high continuity where appropriate.
Solution Approach 2:
The invention applies different continuity levels to different parts of the mesh based on local geometric features. Irregular nodes on feature edges receive C1 continuous treatment to preserve the feature, while other regions maintain C2 continuity for smoothness, allowing the model to adapt to various boundary and feature configurations.
Data Source
AI summary
A method and a system of generating a smooth spline surface from a quadrilateral mesh representing a physical object, is described. Edge points are added to the quadrilateral mesh to preserve a feature or a boundary. The edge points are added to an edge of the quadrilateral mesh having one or more irregular nodes representing a feature edge of the physical object and/or the edge points are added to an edge of the quadrilateral mesh extending between the feature edge and an irregular node. Knot interval vectors are extracted for each edge point and used to evaluate an irregular element having the edge points to generate the smooth spline surface. The smooth spline surface is highly continuous and can be displayed to model the physical object, modify a design of the physical object, or used directly in a simulation to evaluate the physical object. Other embodiments are also described and claimed.