Composite Transformation Matrix Decomposition for Rendering Order
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional systems face challenges in properly decomposing composite transformation matrices to match the transformation order of rendering devices, leading to inefficiencies in rendering rasterized data, especially when rotation, scaling, and translation operations are performed in different orders.
Innovation Solution
A method and system that decompose composite transformation matrices using polar decomposition to derive rotation, scaling, and translation matrices, allowing these operations to be performed in any desired order, thereby aligning with the rendering device's operation sequence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional systems use composite transformation matrices for rendering, then transformation operations can be performed, but the systems cannot properly decompose the matrices to match the transformation order of rendering devices
Solution Approach 1:
The patent segments the composite transformation matrix into individual transformation matrices representing rotation, scaling, and translation operations. This segmentation allows each transformation to be independently applied in the correct order matching the rendering device's operation sequence, resolving the incompatibility between composite matrix usage and device-specific transformation orders.
Solution Approach 2:
The patent performs preliminary decomposition of the composite transformation matrix into individual transformation components before rendering. By pre-calculating and separating the transformation operations, the system can then apply them in the correct sequence that matches the rendering device's expected operation order, avoiding the need for complex real-time decomposition during rendering.
2Manufacturing precision
If transformation matrices are decomposed to match rendering device order, then accurate rendering is achieved, but processing time increases
Solution Approach 1:
The patent performs matrix decomposition as a preliminary action before the rendering process. By decomposing the composite transformation matrix into individual transformation matrices in advance, the system ensures accurate rendering while minimizing processing time during the actual rendering operation, as the decomposition work is completed beforehand.
3Productivity
If conventional systems abandon composite transformation matrix after rasterization, then processing is simplified, but transformation information is lost
Solution Approach 1:
The patent makes the transformation matrix decomposition and application process universal by implementing it as a standardized procedure that works with both rasterized and non-rasterized data. This multi-functional approach allows the system to maintain transformation information throughout the rendering pipeline while efficiently processing different data types, eliminating the need to abandon composite transformation matrices after rasterization.
Data Source
AI summary
A method and system render rasterized data by receiving non-rasterized page description language data and a corresponding transformation matrix representing transformation operations to be performed. The non-rasterized page description language data is rasterizing to create rasterized data. The corresponding transformation matrix is decomposed into a plurality of individual transformation operation matrices and a discrete transformation operation value, from each corresponding individual transformation operation matrix, is generated for each transformation operation to be performed upon the rasterized data. The transformation operations are performed upon the rasterized data based upon the generated discrete transformation operation values.