Automated Image Warping for Conical Surfaces
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Solution Overview
Problem
The complex process of designing and applying graphics to conical surfaces, such as paper cups, requires significant effort and expertise due to their non-cylindrical shape, leading to distorted images and high costs, making it difficult for novice designers and limiting production to large orders.
Innovation Solution
An automated process and system that transforms two-dimensional images into a warped representation suitable for conical shapes using a transformation formula, allowing for efficient alignment and printing on conical objects without manual intervention, enabling the production of low-order quantities and simplifying the graphic design process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If manual warping and stretching of images is used to fit conical surfaces, then images can be applied to conical shapes, but design time increases to 30-40 minutes and requires skilled designers
Solution Approach 1:
The patent replaces manual mechanical warping and stretching operations with an automated computational system. The processor automatically performs the image transformation using a mathematical model of the conical surface, eliminating the need for skilled designers to manually manipulate images and removing the time-consuming iterative adjustment process.
Solution Approach 2:
The patent changes the parameters of the image (coordinates, distortion factors) automatically based on the conical surface geometry. By using a mathematical model that incorporates the cone's apex angle and diameter, the system dynamically adjusts image parameters to achieve proper alignment and undistorted appearance on the conical surface.
2Manufacturing precision
If expensive offline software is used for warping and curving images, then images can be transformed to match conical templates, but costs increase and skilled designers are required
Solution Approach 1:
The patent extracts the essential geometric parameters (apex angle, diameter) from the conical surface and uses only these critical elements to perform the image transformation. This simplifies the process by removing the need for complex pre-defined templates and expensive specialized software, achieving precise alignment through a streamlined mathematical approach.
Solution Approach 2:
The patent creates a mathematical model (copy) of the conical surface geometry that can be used repeatedly for different images and cup sizes. This model replaces the need for expensive proprietary software and complex templates, providing a reusable framework that maintains precision while reducing complexity and cost.
3Adaptability or versatility
If graphics are designed in rectangular format and manually warped, then images can be applied to conical cups, but logos and certain images become distorted (circles become ovals)
Solution Approach 1:
The patent performs preliminary calculation of the transformation parameters based on the conical geometry before applying the image. By pre-computing the distortion factors and coordinate mappings using the apex angle and diameter, the system ensures that logos and other shape-sensitive graphics maintain their intended geometry throughout the warping process, preventing circles from becoming ovals.
4Productivity
If automated transformation formula is used, then design time is reduced and small orders become viable, but complex mathematical transformation is required
Solution Approach 1:
The patent segments the image transformation process into distinct computational steps: calculating transformation parameters from geometric data, applying coordinate mapping, and rendering the final image. This segmentation allows the complex transformation to be broken down into manageable operations that can be efficiently executed by a processor, improving speed while managing complexity.
Data Source
AI summary
Provided are an automated process and system for rendering an image on a conical surface, the process comprising: transforming a two-dimensional (2D) planar representation of an image to a 2D planar representation of the image configured for a conical shape; applying the 2D transformed representation onto a planar template; and manufacturing a conically-shaped object from the planar template on which the 2D transformed representation has been applied.