Boolean Operations Using Facet Triangles
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Solution Overview
Problem
Current Boolean operation methods in CAD/CG systems require complex data structures like Constructive Solid Geometry (CSG) or Boundary Representation (B-REP), which can be cumbersome for creating complex geometric models, especially when working with various geometric object types and facets.
Innovation Solution
A set of simplified data structures and algorithms that directly operate on triangles decomposed from geometric facets, performing Boolean operations such as combination, intersection, exclusion, difference, and division without relying on CSG or B-REP, by finding intersection lines, splitting triangles, and regrouping them to form new geometric models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If CSG or B-REP data structures are used for Boolean operations, then the operations can be performed on geometric objects, but the system becomes complex and cumbersome for creating complex geometric models
Solution Approach 1:
The patent extracts the essential geometric information (facets, vertices, normals) from complex CSG/B-REP structures and operates directly on these extracted elements. By taking out only the necessary geometric data and discarding the complex hierarchical structures, the system achieves simpler Boolean operations while maintaining accuracy.
Solution Approach 2:
The patent segments geometric objects into discrete facets and triangles, allowing Boolean operations to be performed on individual geometric elements rather than requiring complex global data structures. This segmentation enables local operations that are computationally efficient and easier to implement.
2Adaptability or versatility
If CSG or B-REP methods are used, then Boolean operations can be performed, but the implementation becomes cumbersome and less flexible for various geometric object types
Solution Approach 1:
The patent creates a universal facet-based data structure that can represent any geometric object type (polyhedra, swept objects, extruded objects) without requiring type-specific handling. This universal approach allows the same Boolean operation algorithms to work on diverse geometric objects, increasing versatility while reducing complexity.
3Productivity
If traditional Boolean operation methods are used, then geometric models can be built, but the process is complex and time-consuming
Solution Approach 1:
The patent performs preliminary triangulation of geometric facets before Boolean operations, converting all surfaces into triangle meshes. This preliminary action standardizes the input data structure, allowing subsequent Boolean operations to proceed efficiently without repeated data conversions or complex case handling.
Solution Approach 2:
The patent uses triangle copying and regeneration techniques during Boolean operations, where intersecting triangles are copied and modified to form the result geometry. This copying approach is computationally more efficient than traditional methods that require extensive data structure manipulation and validation.
Data Source
AI summary
A method for performing Boolean operations using a computer to create geometric models from primary geometric objects and their facets, comprises mapping rendering facets to extended triangles that contain neighbors, building intersection lines, splitting each triangle through which an intersection line passes, determining each triangle is obscure or visible, and regrouping the triangles to form one or more geometric objects. This method does not utilize the most popular data structures CSG and B-REP in CAD/CG/Solid Modeling systems, but has the advantages of both CSG and B-REP: easy to implement and so flexible that it can handle concave and convex geometric shapes, swept and extruded geometric objects, and it is able to generate variant and editable models.