Interactive Labyrinth Curve Generation on 3D Surfaces
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Solution Overview
Problem
Existing computer graphics methods for generating maze and labyrinth patterns are limited by their reliance on grid-based systems, which distort when projected onto 3D objects, and lack the ability to evolve geometric complexity interactively.
Innovation Solution
A computer-implemented method for generating labyrinth curves through an iterative process that includes resampling and spatial modulation using curve evolution parameters, allowing user interaction and spatial modulation by image or texture maps, with displacement calculations based on geodesic distance metrics in a non-Euclidean evolution space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If grid-based systems are used to generate maze patterns, then the generation process is simplified and standardized, but the patterns become distorted when projected onto 3D objects
Solution Approach 1:
The patent transitions from 2D grid-based maze generation to 3D surface-based generation. By defining mazes on the actual 3D surface geometry rather than flattening to 2D grids, the invention eliminates projection distortion while maintaining generability through iterative evolution algorithms that operate directly on surface coordinates.
Solution Approach 2:
The invention changes the fundamental parameters of maze generation from discrete grid cell coordinates to continuous surface geometry parameters. By using surface normal vectors, curvature information, and geodesic distances as control parameters, the system adapts maze patterns to complex 3D surfaces without the distortion inherent in grid-based approaches.
2Adaptability or versatility
If manual creation methods are used for maze patterns, then artistic control and customization are maximized, but the time required to produce large and intricate patterns increases significantly
Solution Approach 1:
The patent implements dynamic, iterative evolution algorithms that allow maze patterns to adapt and evolve automatically on 3D surfaces. Users can guide the evolution process through interactive parameter adjustment while the system autonomously generates complex patterns, combining artistic control with computational efficiency to produce intricate designs rapidly.
Solution Approach 2:
The invention enables the maze generation system to automatically adapt patterns to complex 3D geometries without requiring manual tracing or adjustment. The iterative evolution algorithm self-corrects and self-optimizes the maze configuration based on surface properties, eliminating the time-consuming manual adaptation process while preserving artistic intent through user-defined parameters.
3Device complexity
If fractal techniques are used to generate decorative curves, then geometric complexity is increased through iterative processes, but the methods lack the ability to evolve patterns interactively and adapt to 3D surfaces
Solution Approach 1:
The patent incorporates feedback mechanisms where the evolving maze patterns continuously adapt to 3D surface geometry through iterative evaluation. Surface properties such as curvature and normal vectors provide feedback that guides the evolution process, allowing the system to maintain geometric complexity while adapting to complex surface forms and responding to user interactions in real-time.
Solution Approach 2:
The invention creates a universal maze generation framework that can operate on any 3D surface geometry, unlike traditional fractal techniques limited to 2D planes. The system integrates multiple functions including surface analysis, iterative evolution, user interaction handling, and adaptive pattern generation into a single versatile platform that handles both geometric complexity and surface adaptability.
Data Source
AI summary
Complex labyrinth curves are interactively generated by an iterative process that spatially modulates curve evolution by an image or other function defined on the evolution space. After curves and evolution parameters are initialized [100], the iterative process resamples the curves [104], and spatially modulates the curves according to the evolution parameters [106]. The spatial modulation includes computing sample point displacements by calculating distances between each of the sample points and neighboring points using a surface distance metric that estimates a geodesic distance metric in a two-dimensional non-Euclidean evolution space. The evolved labyrinth curves are may be processed [110] for use in various applications. The evolved curves can also be triangulated and projected to a plane to create patterns for manufacturing developable surfaces.