Isotopologic Parameterized Surfaces for Mesh Continuity
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current CAD systems struggle to create parameterized surfaces from meshes with open base meshes and tri-rectangular patterns, resulting in insufficient continuity and quality, especially at extraordinary vertices, and lack algorithms suitable for handling irregular vertices and sharp edges.
Innovation Solution
A process that provides different types of parameterized surfaces based on vertex and edge sharpness values, applying specific surface types for regular, semi-regular, and irregular vertices to maintain geometrical continuity, using a local, linear resolution algorithm to ensure stability and adapt to various mesh topologies, including Catmull-Clark subdivision surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional conversion algorithms are used to convert meshes to parameterized surfaces, then the process can handle basic mesh types, but it fails to provide sufficient continuity and quality at extraordinary vertices and cannot properly handle open base meshes and tri-rectangular patterns
Solution Approach 1:
The patent applies different types of parameterized surfaces (first, second, and third types) to different face categories based on their vertex characteristics. Regular faces receive one type of surface while semi-regular and irregular faces receive different types, allowing each region to have the appropriate surface representation for maintaining continuity and quality at extraordinary vertices.
Solution Approach 2:
The patent divides the mesh conversion process into multiple stages: providing a mesh with regular and irregular vertices, classifying faces into different types based on vertex sharpness values, and applying different parameterized surface types to each face category. This segmentation allows systematic handling of complex mesh topologies.
2Manufacturing precision
If a single type of parameterized surface is applied to all faces, then the process is simple, but it cannot maintain geometrical continuity at extraordinary vertices and irregular faces
Solution Approach 1:
The patent evaluates sharpness values at vertices and edges to classify faces into different types (regular, semi-regular, irregular) and applies different parameterized surface types accordingly. This local differentiation ensures that surfaces are optimized for their specific geometric context, maintaining continuity at extraordinary vertices while using simpler surfaces where appropriate.
3Manufacturing precision
If high-order surface conversion is applied to ensure continuity, then surface quality improves, but the number of control points increases and computational complexity rises
Solution Approach 1:
The patent applies different levels of surface refinement locally based on face classification. Irregular faces with extraordinary vertices receive more complex parameterized surfaces with additional control points to ensure continuity, while regular faces use simpler surfaces with fewer control points, optimizing the balance between continuity and computational complexity.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
The invention is directed to a process for creating from a mesh an isotopologic set of parameterized surfaces. Said process comprises a step of providing a mesh having a plurality of vertices connected by edges, defining faces, the vertices comprising regular vertices of valence 4 and irregular vertices of valence different from 4. The mesh provided is for example a Catmull-Clark subdivided mesh. Said mesh further has a sharpness value defined on at least one vertex or edge, with a default value, the sharpness being representative of the attractiveness of the vertex or edge on the surface modeled by the mesh. In other words, the sharpness measures the difference between the mesh as it stands at a given subdivision level and the initial mesh. The process further comprises providing at least three different types of parameterized surfaces; and - for a face with regular vertices and a default value of sharpness on vertices and edges of the face, applying a first type of parameterized surface; - for a face with regular vertices and at least one vertex or edge with a non-default value of sharpness, applying a second type of parameterized surface; and - for a face with at least one irregular vertex, applying a third type of parameterized surface.