Curved Surface Moiré via Parametric Mapping
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Solution Overview
Problem
Existing methods for creating moiré patterns are limited to planar surfaces and fail to effectively produce aesthetically pleasing, dynamically evolving moiré shapes on curved surfaces, which are desirable for decoration purposes.
Innovation Solution
A method involving a curved surface with a grating of sampling elements, such as cylindrical or spherical lenses, where the distance between the sampling and base layers is optimized to create a dynamically evolving moiré shape, involving geometric transformations and mappings to ensure a consistent angular field of view and correct positioning of lenses for fabrication using 3D printing or other technologies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If planar moiré methods are applied to curved surfaces, then existing authentication techniques can be used, but the moiré shapes are not aesthetically pleasing and do not dynamically evolve on curved surfaces
Solution Approach 1:
The patent applies curvature by mapping planar moiré patterns onto curved surfaces using parametric equations. The curved surface is defined by parametric coordinates (u,v) that map to 3D space (x,y,z), allowing the moiré pattern to conform to spherical or other curved geometries while maintaining aesthetic appearance and dynamic evolution capabilities
Solution Approach 2:
The patent transitions from 2D planar moiré patterns to 3D curved surface moiré by introducing parametric dimensionality. The mapping process uses parametric equations that add a third spatial dimension, enabling the moiré pattern to evolve dynamically across curved surfaces while preserving the underlying mathematical structure of planar moiré
2Area of moving object
If the distance between sampling and base layers is increased to create larger moiré features, then the moiré shapes become more visible, but the angular field of view consistency deteriorates
Solution Approach 1:
The patent applies local quality by varying the sampling element dimensions and spacing based on their position on the curved surface. The mapping process calculates local scale factors and adjusts the base layer feature sizes accordingly, ensuring that moiré patterns maintain consistent visual appearance and angular field of view across different regions of the curved surface
Solution Approach 2:
The patent uses parameter changes by adjusting the mapping parameters (scale, rotation, distortion) based on position on the curved surface. The base layer parameters are modified locally to compensate for curvature effects, maintaining manufacturing precision while achieving larger visible moiré features through controlled parameter variation
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables the creation of visually appealing, dynamically evolving moiré shapes on curved surfaces, allowing for beating, moving, or rotating patterns that enhance the decorative value of objects like watches, jewelry, and other items by reproducing planar moiré effects on curved surfaces with improved mapping techniques.
Implementation Method 1
A curved surface capable of displaying a dynamically evolving moiré shape comprises on its superior surface a grating of sampling elements. Sampling elements can be embodied by a grating of cylindrical lenses, a grating of spherical lenses
Implementation Method 2
The distance between the curved sampling revealing layer and the curved base layer depends on the sampling period. In case of sampling by cylindrical or spherical lenses, this distance is smaller than the focal length of the lenses.
Data Source
AI summary
The present disclosure describes a method and computerized means for creating dynamically evolving moiré shapes on curved surfaces. The method applies geometrical transformations in order to obtain curvilinear moirés and creates the moirés on curved surfaces by applying mappings from planar space to 3D space. The method relies on the superposition of a base layer with base bands and of a revealing layer with sampling elements. The dimensions of the revealing layer sampling elements such as cylindrical or spherical lenses as well as the distances between the base and revealing layer surfaces are adapted to the space between neighbouring isoparametric lines that define the curved surface. The resulting moiré shapes evolve smoothly on the specified curved surface and show recognizable shapes such as words, letters, numbers, flags, logos, graphic motifs, drawings, clip art, and faces.