Interactive Labyrinth Curve Generation for 3D Surface Adaptation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for generating maze and labyrinth patterns are limited by their geometric complexity, requiring extensive manual effort and failing to adapt well to three-dimensional surfaces, with prior techniques either distorting patterns or not increasing geometric complexity effectively.
Innovation Solution
A computer-implemented method that evolves labyrinth curves through an iterative process guided by user interaction and spatially modulated evolution parameters, allowing for increased geometric complexity and adaptability to two-dimensional and three-dimensional spaces, including the use of image texture maps for modulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If manual creation methods are used for maze and labyrinth patterns, then artistic control and design flexibility are maintained, but production time increases significantly and geometric complexity is limited
Solution Approach 1:
The system performs automatic maze generation using computational algorithms that evolve patterns through iterative processes. The computer-implemented method autonomously generates complex labyrinth designs without requiring manual intervention for each pattern element, thereby dramatically increasing productivity while achieving high geometric complexity through algorithmic evolution rather than human craftsmanship.
Solution Approach 2:
The patent employs dynamic evolution processes where maze patterns are generated through iterative refinement and adaptation. The system uses evolving algorithms that can adjust pattern complexity, scale, and design characteristics dynamically, allowing the generation of increasingly complex geometries without proportional increases in production time.
2Ease of manufacture
If grid-based methods are used to generate mazes, then pattern generation is simplified and computational efficiency is improved, but severe distortion occurs when projected to three-dimensional surfaces
Solution Approach 1:
The patent transitions from two-dimensional grid-based maze generation to three-dimensional surface adaptation. The system projects and deforms maze patterns onto curved and three-dimensional surfaces while maintaining pattern integrity. This dimensional extension allows the generated mazes to conform accurately to complex surface geometries without the severe distortion that plagues traditional grid-based projection methods.
Solution Approach 2:
The system dynamically adjusts geometric parameters during the generation and projection process. By modifying scale, curvature, and deformation parameters, the algorithm maintains manufacturing precision when transferring patterns from flat generation spaces to three-dimensional target surfaces, eliminating the distortion issues inherent in fixed-grid approaches.
3Device complexity
If fractal techniques are used to generate decorative curves, then geometric complexity is increased and pattern intricacy is enhanced, but adaptability to user interaction and spatial modulation is limited
Solution Approach 1:
The patent incorporates feedback mechanisms that allow user interaction to influence the maze generation process. Users can provide input during the evolution process, and the system adjusts pattern development based on this feedback. This interactive capability enables users to guide the generation of geometrically complex patterns while maintaining control over design outcomes, bridging the gap between algorithmic complexity and human intent.
Solution Approach 2:
The system employs spatially modulated evolution parameters that can be adjusted during the generation process. These parameters control aspects such as pattern density, curve complexity, and spatial distribution. By allowing dynamic modification of these parameters in response to user input, the system achieves both high geometric complexity and adaptability to user interaction requirements.
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 allows the curve and evolution parameters to be interactively modified by a user [102], resamples the curves [104], and spatially modulates the curves according to the evolution parameters [106]. The evolved labyrinth curves are may be processed [110] for use in various applications including animation, maze creation, intricate artistic patterns, and graphical user interfaces that map linearly ordered data to the evolved curve and allow the data to be navigated using the rendered curve. The evolved curves can also be triangulated and projected to a plane to create patterns for manufacturing developable surfaces.