3D Geometry Model Simplification Using Morton Codes
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for simplifying complex 3D geometry models are slow, memory-intensive, and may not preserve the original shape, especially when dealing with large models that require near real-time processing and transmission in constrained contexts.
Innovation Solution
An efficient geometry model simplification method using Morton codes and k-d trees, which allows for parallel calculations by determining integral error measures and simplifying points based on shared Morton code prefixes, while considering error measurements and quadric representations to avoid excessive simplification in areas with significant color or geometric changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If iterative simplification algorithms are used to simplify geometry models, then the model complexity is reduced, but the processing time increases and memory consumption increases
Solution Approach 1:
The patent applies segmentation by dividing the geometry model into spatial regions using a k-d tree structure, where each node represents a region with associated points. This segmentation enables parallel processing of different regions simultaneously, reducing overall processing time while maintaining model simplification quality.
Solution Approach 2:
The patent introduces spatial dimensionality through k-d tree structure organization, transforming the simplification problem from a sequential 1D process into a multi-dimensional parallel processing approach. Points are organized in spatial regions (k-d tree nodes) that can be processed independently and concurrently, achieving faster simplification.
2Device complexity
If iterative simplification algorithms are used to simplify geometry models, then the model complexity is reduced, but the memory consumption increases
Solution Approach 1:
The k-d tree segmentation divides the point cloud into hierarchical spatial regions, allowing memory to be allocated and processed in manageable chunks rather than loading entire large models into memory at once. Each node stores only the points within its spatial region, reducing peak memory requirements.
Solution Approach 2:
The patent performs preliminary organization of points into k-d tree structure before simplification, pre-computing spatial relationships and error metrics. This preliminary action enables more efficient memory utilization during the actual simplification process by avoiding repeated computations and data reorganization.
3Device complexity
If partitioning algorithms are used to simplify geometry models, then the model is divided into manageable regions, but the convergence cannot be guaranteed
Solution Approach 1:
The patent implements feedback through error metric calculations at each k-d tree node, where the simplification process continuously evaluates the quality of approximation and adjusts the level of detail accordingly. This feedback mechanism ensures convergence by stopping simplification when error thresholds are met, providing reliable and predictable results.
Solution Approach 2:
The simplification process is made dynamic by allowing different levels of simplification at different k-d tree nodes based on local geometric complexity and error metrics. The algorithm adaptively determines which regions require detailed representation and which can be simplified, ensuring both convergence and quality.
4Productivity
If rapid simplification is performed to achieve near real-time processing, then the processing speed increases, but the quality of the simplified model may deteriorate
Solution Approach 1:
The patent applies local quality by computing error metrics independently for each k-d tree node and applying different simplification levels to different regions based on their local geometric characteristics. Important regions with high curvature or detail are preserved with higher fidelity, while flat regions are simplified more aggressively, maintaining overall quality while enabling fast processing.
Solution Approach 2:
The patent performs preliminary computation of error metrics and quadric approximations for all points before final simplification decisions. This pre-computation enables rapid query and simplification decisions during rendering or transmission without compromising final model quality, achieving both speed and accuracy.
Data Source
Figure 1a~1b
Figure 2
Figure 3
AI summary
The present invention relates to a method of simplifying a geometry model, the method comprises: determination (607) of an integral error measure (Q s i ) defined as being a function of a sum of the error measures associated with the points of the plurality having a lower associated Morton code than the Morton code associated with the current point; determination (614) if a given set of points of the plurality can be simplified by a new point, the points of the given set all being the points of the plurality having a Morton code associated with one and the same prefix of given length, as a function at least of a difference between:- the integral error measure (Qs las) determined for the point of the given set having the largest Morton code (las); and - the integral error measure (Qs ini-1) determined for the point of the plurality having an immediately lower Morton code (ini-1) than the smallest Morton code out of the Morton codes associated with the points of the set.