Vector Graphic Pixelation via Manhattan Approximation and Convolution
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Solution Overview
Problem
Existing methods for converting vector graphics into images are complex and slow, especially when dealing with graphics of large size and high resolution, due to the need for extensive pixel-by-pixel operations and high memory requirements.
Innovation Solution
A method that approximates a vector graphic with an arbitrary curve boundary as a Manhattan structure, using convolution with Dirac pulse functions and fast Fourier transform to simplify the pixelation process, reducing the need for repeated superimposition of quadrant planes and improving computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If pixel-by-pixel operations are used to determine whether a pixel is inside a given graphic, then the pixelation can be completed, but the computational time becomes considerable
Solution Approach 1:
The patent segments the graphic into multiple quadrant planes (first, second, third, and fourth quadrant planes) based on the position of vertices relative to pixel centers. This segmentation allows parallel processing of different regions, significantly reducing computational time while maintaining pixelation accuracy through systematic coverage of the entire graphic area.
Solution Approach 2:
The patent performs preliminary classification of vertices into different quadrant planes before pixelation. By pre-organizing vertex data and determining which quadrant plane each vertex belongs to, the system prepares the data structure in advance, enabling faster pixelation processing without sacrificing accuracy in determining pixel inclusion.
2Measurement precision
If the size of the graphic becomes larger and the resolution of the image becomes higher, then the image quality improves, but the number of pixels to be accessed and modified increases, consuming considerable runtime
Solution Approach 1:
The patent divides large high-resolution graphics into multiple quadrant planes, each processed independently and in parallel. This segmentation strategy allows the system to handle large graphics with high resolution by breaking down the computational burden into manageable chunks, reducing overall runtime while maintaining image quality.
Solution Approach 2:
The patent introduces a quadrant plane dimension to organize and process pixels. By mapping pixels to specific quadrant planes based on vertex positions, the system adds a dimensional organization layer that enables more efficient access and processing of large numbers of pixels in high-resolution images.
3Productivity
If a large graphic is divided into many small graphic sets for separate processing, then the computation process is accelerated, but the complexity and memory requirements of the method increase
Solution Approach 1:
The patent segments the graphic into quadrant planes based on vertex positions rather than arbitrary divisions. This vertex-based segmentation naturally organizes the graphic into manageable sets while maintaining spatial coherence, accelerating computation through parallel processing of quadrant planes without excessively increasing method complexity.
Solution Approach 2:
Instead of dividing the graphic arbitrarily and then mapping vertices, the patent inverts the approach by first classifying vertices into quadrant planes and then processing pixels accordingly. This inversion simplifies the overall method by establishing a clear hierarchical structure from vertices to quadrant planes to pixels.
4Loss of time
If tree code-type strategy is employed to pixelate only a logarithmic number of graphics, then runtime is significantly improved, but the complexity in polygon boundary detection and processing becomes very high
Solution Approach 1:
The patent segments polygon boundaries into quadrant planes based on vertex positions, creating a simplified hierarchical structure. This segmentation approach achieves logarithmic-level efficiency in processing by organizing boundary detection into manageable quadrant sections, reducing overall complexity while maintaining fast runtime performance.
Solution Approach 2:
The patent performs preliminary classification of polygon vertices into quadrant planes before boundary detection and processing. This pre-organization of vertex data simplifies subsequent boundary detection operations by providing a structured framework, reducing the complexity of polygon processing while maintaining efficient runtime.
Data Source
AI summary
The present invention provides a method and a system for pixelating a vector graphic into an image. First, a vector graphic defined by an arbitrary curve boundary is approximated as a vector graphic of a Manhattan structure, and then a fast algorithm is used to pixelate the approximate Manhattan vector graphic into a two-dimensional image. A process of moving quadrant planes to superimpose on vertices of the vector graphic is replaced with convolution of an image resulting from a template rectangle image and Dirac pulse functions of the vertices of the vector graphic, and a pixelated image of this vector graphic is obtained through convolution of the template rectangle and a sparse image composed of Dirac pulses located at the positions of the vertices of the vector graphic.