Orthogonal Interpolation for Graphic Object Resizing
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Solution Overview
Problem
Current methods for resizing graphic objects often result in loss of information content, making it inaccessible, and do not provide sufficient control for graphic designers, especially when scaling or representing dynamic data, as they require extensive calculations and may involve undue constraints.
Innovation Solution
A method for resizing structured graphic objects using orthogonal interpolation of affine transformation matrices, which generates intermediate graphic objects of different sizes by interpolating the matrices along width and height dimensions, preserving geometric characteristics and allowing for local deformations, thus maintaining visual acceptability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If simple rescaling of graphical objects is used, then processing speed is improved, but manufacturing precision deteriorates because information content becomes invisible and deformations are not optimized
Solution Approach 1:
The patent segments the graphical object into multiple primitives (shapes, lines, text elements) and applies separate affine transformation matrices to each primitive rather than uniformly rescaling the entire object. This segmentation allows each element to be transformed independently, preserving information visibility and achieving visually acceptable deformations while maintaining processing efficiency.
Solution Approach 2:
The patent applies local quality by allowing different parts of the graphical object to have different transformation properties. Each primitive can have its own transformation matrix derived through orthogonal interpolation, enabling local deformations that maintain visual acceptability in different regions of the object while processing the entire object efficiently.
2Manufacturing precision
If extensive optimization algorithms are used, then manufacturing precision is improved, but device complexity increases and processing time increases
Solution Approach 1:
The patent replaces complex optimization algorithms with orthogonal interpolation of affine transformation matrices. Instead of using iterative mathematical optimization to determine transformations, the system uses direct orthogonal interpolation between transformation matrices derived from reference reproductions, significantly reducing algorithmic complexity while maintaining visual acceptability.
Solution Approach 2:
The patent performs preliminary action by pre-computing transformation matrices from multiple reference reproductions of the graphical object at different sizes. These pre-computed matrices are then used as input for orthogonal interpolation, eliminating the need for real-time optimization calculations and reducing both device complexity and processing time.
3Manufacturing precision
If multiple reproductions are created for each size, then manufacturing precision is improved, but loss of time increases due to extensive search for invariants
Solution Approach 1:
The patent extracts only the essential transformation information from multiple reproductions by deriving affine transformation matrices that capture the geometric relationships. Instead of performing extensive searches for geometric invariants across multiple reproductions, the system extracts transformation matrices and uses orthogonal interpolation to generate intermediate transformations, significantly reducing processing time.
Solution Approach 2:
The patent uses copying by creating multiple reference reproductions of the graphical object at predetermined sizes and extracting transformation matrices from them. These reproduced transformations are then copied and interpolated to generate transformations for intermediate sizes, eliminating the need for time-consuming invariant searches while maintaining visual acceptability.
4Manufacturing precision
If affine transformation matrices are interpolated orthogonally, then manufacturing precision is improved with local deformations, but device complexity increases
Solution Approach 1:
The patent applies parameter changes by using orthogonal interpolation to vary the transformation matrix parameters (scaling, rotation, shearing components) based on the size parameters of the graphical object. This allows the transformation to adapt to different sizes while maintaining a relatively simple computational approach compared to full optimization algorithms.
Data Source
Figure 1~2
Figure 3a~4
Figure 5~6e
AI summary
The method involves developing a set of reproductions of a graphic object, where the reproductions are copies (1 - 3) of a graphic object. A set of fine transformation matrices (5 - 7) is extracted for each reproduction. An orthogonal interpolation is applied on the matrices to deduce intermediate transformation matrices with size different from that of the reproductions, where the interpolation is separated from first row of matrices along width and from second row of the matrices along height. Geometric characteristics of the intermediate object are deducted from the intermediate matrices.