Valence-Based Traversal for Triangular Mesh Compression
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Solution Overview
Problem
Conventional methods for compressing triangular mesh data in three-dimensional objects are inefficient due to arbitrary traversal orders that do not minimize prediction errors, leading to higher entropy and less efficient compression schemes.
Innovation Solution
Generating a traversal order for the vertices of the triangular mesh based on valences, which correlates with similar angles and minimizes prediction errors, resulting in a more efficient compression scheme by using a valence-based penalty function to select the next traversal step.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a deterministic formula is used to generate traversal order, then the traversal order is arbitrary and easy to implement, but prediction errors increase and compression efficiency decreases
Solution Approach 1:
The patent changes the parameter used for traversal order from a fixed deterministic formula to dynamic valence-based ordering. By using the valence (number of adjacent faces) of vertices as the ordering criterion, the system adapts the traversal sequence to the local geometric properties of the mesh, thereby minimizing prediction errors while maintaining implementation feasibility.
2Device complexity
If conventional compression schemes are used, then implementation is simple, but compression ratio is low and more storage resources are required
Solution Approach 1:
The patent performs preliminary ordering of vertices and faces based on valence before the compression process. This preliminary action organizes the data in an optimal sequence that minimizes prediction errors, allowing subsequent compression algorithms to achieve higher compression ratios without increasing operational complexity.
3Speed
If arbitrary traversal order is used, then processing is faster, but entropy of data increases and compression efficiency decreases
Solution Approach 1:
The patent changes the traversal ordering parameter from arbitrary to valence-based, creating a deterministic yet adaptive sequence. This parameter change reduces data entropy by ensuring that vertices are processed in an order that maximizes predictability of geometric properties, thereby improving compression efficiency without significantly impacting processing speed.
Data Source
AI summary
In one general aspect, a method can include receiving, by processing circuitry of a computer configured to represent information related to a three-dimensional object, a plurality of vertices of a triangular mesh representing the three-dimensional object, the triangular mesh including a plurality of faces, each if the plurality of faces including three vertices of the plurality of vertices; generating a traversal order for the vertices of the triangular mesh based on valences of the plurality of vertices; producing an array of errors between predicted vertices and vertices of the plurality of vertices, the array of errors being arranged in a sequence based on the traversal order; and performing a compression operation on the array of differences to produce a compressed error array, the compressed error array producing the plurality of vertices of the triangular mesh in response to a decompression operation.