Boolean Operations on Geometric Facets

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Solution Overview

Problem

Current Boolean operation methods for building three-dimensional geometric models in CAD/CG and Solid Modeling systems require complex data structures like Constructive Solid Geometry (CSG) or Boundary Representation (B-REP), which can be inflexible and computationally intensive, limiting the types of geometric objects that can be modeled and the efficiency of the modeling process.

Innovation Solution

The method introduces a set of simple data structures and algorithms that perform Boolean operations directly on triangles decomposed from geometric facets, eliminating the need for CSG or B-REP, allowing for five basic commands (combination, intersection, exclusion, difference, division, and surface trimming) to create complex models by selecting and defining geometric objects' facets, and uses triangle-triangle intersections, splitting, and regrouping to achieve these operations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If CSG or B-REP data structures are used for Boolean operations, then the operations can be performed on geometric objects, but the system complexity increases and computational efficiency decreases

Engineering Contradiction:

ImproveBoolean operation capabilityVSAvoiddata structure complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent extracts the essential Boolean operation functionality from complex CSG/B-REP frameworks and implements it directly on triangle meshes. Instead of using hierarchical object representations, the invention works directly with facet data structures, taking out only the necessary elements for Boolean operations while eliminating unnecessary complexity.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent segments geometric objects into triangular facets and performs Boolean operations on these discrete elements. By dividing continuous geometric shapes into manageable triangle segments, the system can process complex Boolean operations through systematic triangle-triangle intersection calculations without requiring complex global data structures.

Inventive Principle:

Principle #1Segmentation

2Reliability

If CSG or B-REP data structures are used for Boolean operations, then geometric models can be built, but the computational time and resources increase

Engineering Contradiction:

Improvemodel building capabilityVSAvoidcomputational time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent replaces the mechanical hierarchical construction process of CSG with a direct computational approach working on triangle meshes. Instead of building models through sequential object operations, the system substitutes this with parallelizable triangle-triangle intersection algorithms that operate directly on facet data, significantly reducing computational overhead.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent performs preliminary triangulation of geometric objects before Boolean operations. By pre-converting objects into triangle meshes and organizing their facet data structures in advance, the system eliminates the need for complex real-time geometric computations during Boolean operations, thereby reducing computational time.

Inventive Principle:

Principle #10Preliminary action

3Reliability

If traditional Boolean operation methods are used, then solid modeling can be achieved, but the flexibility for different geometric object types is limited

Engineering Contradiction:

Improvesolid modeling capabilityVSAvoidgeometric object type support

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The patent creates a universal Boolean operation framework that works on triangle meshes regardless of the original geometric object type. By converting all objects to a common triangle-based representation, the system achieves multi-functionality where the same Boolean operation algorithms can handle diverse geometric types including solids, surfaces, and complex shapes uniformly.

Inventive Principle:

Principle #6Universality (Multi-functionality)

4Stability of the object's composition

If CSG or B-REP are used, then hierarchical organization is achieved, but the ease of implementation and user definition of facets is reduced

Engineering Contradiction:

Improvehierarchical structureVSAvoidimplementation simplicity

Core Design Contradiction:

Stability of the object's compositionVSEase of manufacture

Solution Approach 1:

The patent inverts the traditional approach by starting with simple triangle facets and building up to complex models, rather than starting with hierarchical object definitions and decomposing them. This inversion simplifies implementation because users can directly define and manipulate facets without navigating complex hierarchical data structures, making the system easier to implement and use.

Inventive Principle:

Principle #13The other way round (Inversion)

Data Source

PatentUS10120961B2Method for immediate boolean operations using geometric facets

Publication Date: 2018.11.06 NATURE SIMULATION SYST INC

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 facet is visible or obscure, and regrouping the facets 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 flexible. Additionally it is a united method for solid modeling and surface modeling systems, and it is able to generate variant and editable models.