Dental Object BSP Trees for Faster 3D Geometry Processing
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Solution Overview
Problem
Binary space partitioning methods are computationally intensive and memory-intensive for complex dental objects, leading to slow computation speeds and high memory usage.
Innovation Solution
A method of representing dental objects using binary space partitioning that employs parallel processing and a working stealing algorithm to generate internal and leaf trees, reducing memory requirements and improving computation speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If binary space partitioning is performed on complex dental objects with large number of geometric elements, then accurate representation of the object shape is achieved, but computation time increases significantly
Solution Approach 1:
The patent divides the complex dental object into multiple geometric elements (triangles, quads) and organizes them into a hierarchical binary space partitioning structure with internal trees and leaf trees. This segmentation allows the computation to be distributed across multiple levels of the hierarchy, reducing the time complexity from O(n) to O(log n) for certain operations while maintaining accurate shape representation.
Solution Approach 2:
The patent introduces a hierarchical dimension to the binary space partitioning structure by creating multiple levels of trees (internal trees and leaf trees). This dimensional transformation allows operations to be performed at different levels of abstraction, enabling faster computation by operating on aggregated representations at higher levels rather than individual geometric elements.
2Reliability
If binary space partitioning is performed on complex dental objects, then complete space partitioning is achieved, but memory space requirements increase
Solution Approach 1:
The patent implements a nested hierarchical structure where leaf trees are contained within internal trees, which are in turn contained within higher-level internal trees. This nesting allows the data structure to represent the complete space partitioning while sharing common nodes and boundaries across multiple levels, reducing redundant storage and overall memory consumption.
Solution Approach 2:
The patent designs the binary space partitioning structure to serve multiple functions: shape representation, collision detection, and spatial queries. By making the data structure multi-functional, the same hierarchical structure is used for various operations, eliminating the need for separate data structures and reducing overall memory requirements.
3Ease of manufacture
If sequential binary space partitioning is used, then simple implementation is maintained, but computation speed is slow
Solution Approach 1:
The patent segments the binary space partitioning computation into independent parallel tasks that can be executed simultaneously. Each internal tree and leaf tree can be constructed and processed independently, allowing the use of multi-threading or distributed computing to accelerate the overall computation while maintaining the logical simplicity of the sequential algorithm.
Solution Approach 2:
The patent performs preliminary organization of geometric elements into hierarchical structures before executing specific operations. By pre-computing the binary space partitioning hierarchy and storing it in an optimized data structure, subsequent operations such as collision detection or rendering can be performed much faster without re-computing the entire partitioning structure.
Data Source
AI summary
A method of representing a dental object using a binary space partitioning for performing a binary space partitioning according to the present inventive concept, the method includes generating internal trees for partitioning a space including the dental object represented as a polygon mesh, and generating leaf trees for representing a shape of the dental object in spaces generated based on the internal trees. Each of the internal trees and the leaf trees includes internal nodes and leaf nodes.