Digital Shape Approximation via Sample Circle Selection
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Solution Overview
Problem
Conventional shape representation systems are inflexible and inefficient in generating approximating representations for digital shapes, relying heavily on user input for primitive placement and connection, leading to sub-optimal representations that require significant computational resources.
Innovation Solution
The system generates efficient approximating representations using tunable sample circles, employing medial/scale axis polar balls and k-means clustering to select a subset of circles that overlap no more than a user-selected threshold, and computes the smallest enclosing circles to accurately model digital shapes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If conventional systems rely on user input to place and connect graphics primitives, then the system can generate approximating representations for digital shapes, but the system becomes inflexible and requires significant user involvement
Solution Approach 1:
The system automatically determines the placement and connection of graphics primitives by analyzing the digital shape's geometric properties and generating an optimized representation without requiring user input for primitive placement, allowing the system to serve itself in the representation generation process
Solution Approach 2:
The system transforms the digital shape into an approximating representation by changing parameters such as the number, size, and position of graphics primitives based on computational analysis rather than user specification, enabling flexible automation while maintaining representation quality
2Productivity
If conventional systems use sub-optimal number of graphics primitives, then the system can generate approximating representations, but the computational resources (memory, processing power, time) required increase significantly
Solution Approach 1:
The system optimizes the number of graphics primitives by analyzing the digital shape's complexity and adjusting the representation parameters dynamically, using the minimum necessary number of primitives to achieve accurate approximation, thereby improving computational efficiency
Solution Approach 2:
The system generates an approximating representation using a partial set of graphics primitives that are most critical for representing the digital shape's essential features, avoiding the use of excessive primitives while maintaining adequate representation quality
3Extent of automation
If conventional systems use complex models or algorithms for automatic determination of primitive placement, then the system can operate automatically, but the implementation becomes too complex for practical and efficient operation
Solution Approach 1:
The system segments the digital shape analysis into distinct computational steps (e.g., shape characterization, primitive selection, placement optimization, connection determination), allowing each step to be implemented with simpler, more manageable algorithms while maintaining overall automation
Solution Approach 2:
The system uses parameter-based control to manage the complexity of automatic determination, adjusting representation parameters based on the digital shape's properties rather than requiring complex decision-making algorithms, making the implementation more practical and efficient
Data Source
AI summary
The present disclosure relates to systems, methods, and non-transitory computer-readable media that generate sample circle representations for digital shapes. For example, the disclosed systems can generate a sample circle representation for a digital shape by selecting a subset of sample circles generated using a medial axis corresponding to the digital shape. In some embodiments, the disclosed systems generate the sample circle representation for the digital shape by generating one or more enclosing circles based on one or more sampled boundary points of the digital shape. In some embodiments, the disclosed systems generate the sample circle representation for the digital shape by further connecting the sample circles generated for the digital shape.