Polycube Segmentation with Monotone Boundaries
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Solution Overview
Problem
Current methods for generating polycube representations of input objects face challenges in balancing parameterization distortion and compactness, often requiring manual or semi-manual construction and resulting in non-monotone chart boundaries, which introduce significant distortion.
Innovation Solution
A computational method that generates an initial polycube labeling by assigning Cartesian axis labels to surface faces, followed by an optimization process to create an updated segmentation with monotonic boundaries, using cost functions to balance compactness and fidelity to the input object's geometry.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If manual or semi-manual construction methods are used to generate polycube representations, then parameterization distortion can be controlled, but the process complexity and time consumption increase significantly
Solution Approach 1:
The system performs automatic polycube segmentation through computational algorithms that self-adjust and optimize the segmentation without human intervention. The cost function automatically balances compactness and fidelity metrics, eliminating the need for manual parameter tuning while achieving high-quality results.
Solution Approach 2:
The invention transforms the manual construction process into an automated optimization process by defining a cost function with adjustable parameters (compactness weight λ and fidelity weight μ). These parameters allow flexible control over the trade-off between compactness and geometric fidelity without requiring manual segmentation expertise.
2Quantity of substance
If compact polycube representations are generated with fewer faces and singularities, then storage efficiency improves, but parameterization distortion increases
Solution Approach 1:
The cost function uses adjustable weights (λ for compactness, μ for fidelity) to control the trade-off between polycube compactness and parameterization quality. By tuning these parameters, users can generate polycubes with different face counts while maintaining acceptable distortion levels according to application requirements.
Solution Approach 2:
The optimization process uses feedback from the cost function evaluation to iteratively improve the polycube segmentation. The algorithm continuously adjusts the segmentation to reduce the cost function value, balancing compactness and fidelity metrics until convergence is achieved.
3Ease of manufacture
If non-monotone chart boundaries are used in polycube segmentation, then the segmentation process is simpler, but significant parameterization distortion is introduced
Solution Approach 1:
The algorithm dynamically adjusts chart boundaries during optimization to eliminate non-monotonicity. The segmentation evolves from an initial simple configuration to a refined configuration where boundaries become monotone, improving parameterization quality without requiring complex manual intervention.
Solution Approach 2:
The method performs preliminary automatic segmentation to generate an initial polycube labeling, then applies optimization to correct boundary monotonicity issues. This two-stage approach first establishes a baseline segmentation and then refines it to eliminate distortion-causing non-monotone boundaries.
Data Source
AI summary
A method for generating a polycube segmentation of an input object comprises: providing an input mesh of the object comprising a plurality of surface faces; generating an initial polycube labeling for the faces by assigning, to each face, a label which is one of six directions (±X,±Y,±Z) aligned with a set of Cartesian axes, the initial polycube labeling defining a plurality of charts, and generating the initial polycube labeling comprising effecting a tradeoff between competing objectives of: making the initial polycube labeling relatively compact; and making the initial polycube labeling relatively faithful to the input object. The method further comprises generating an updated polycube segmentation by changing the label assigned to each of one or more surface faces and thereby modifying one or more of the charts to provide the charts with monotonic boundaries.