Quadric Rendering via Parameter Space Transformation
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Solution Overview
Problem
Current rendering techniques for quadrics in computer graphics, such as ray casting, face inefficiencies when dealing with large numbers of quadrics, particularly in rendering high-resolution electroanatomical maps of heart surfaces, where many quadrics need to be quickly and accurately rendered.
Innovation Solution
The processor transforms virtual rays passing through pixels into parameter space to determine intersection points with quadrics, using a diagonal matrix representation to speed up computations, and marks silhouettes by estimating distances, allowing for rapid rendering of quadrics over electroanatomical maps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional ray casting techniques are used to render quadrics in view space, then rendering accuracy is maintained, but rendering speed and efficiency deteriorate due to the large number of operations required
Solution Approach 1:
The patent transforms the rendering problem from view space to parameter space by changing the coordinate system parameters. Quadrics are represented in their canonical form in parameter space, which simplifies the mathematical operations. The transformation involves computing a change-of-basis matrix that maps points from parameter space to view space, allowing efficient rendering while maintaining accuracy.
Solution Approach 2:
The patent introduces parameter space as an intermediary coordinate system between the object definition space and the view space. Instead of directly transforming quadrics from their canonical form to view space for each rendering operation, the parameter space serves as a中间 representation that simplifies intersection calculations and reduces computational complexity.
2Measurement precision
If high-resolution electroanatomical maps with many quadrics are rendered, then mapping precision is improved, but rendering time increases significantly
Solution Approach 1:
By representing quadrics in parameter space with canonical forms, the patent enables efficient processing of large numbers of quadrics. The parameter space representation allows for simplified intersection tests and distance calculations, which are performed repeatedly when rendering high-resolution maps with many quadrics, thus reducing overall rendering time while maintaining precision.
Solution Approach 2:
The patent performs preliminary transformation of quadrics to parameter space representation before rendering. This pre-processing step establishes the canonical form and change-of-basis matrices in advance, so that during the actual rendering of high-resolution maps, the system can efficiently process many quadrics without repeating complex transformation calculations, thereby reducing rendering time for high-precision maps.
Data Source
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AI summary
Described embodiments include an apparatus that includes a display, including a screen, and a processor. The processor is configured to define a bounding region on the screen. The processor is further configured to render a quadric, which is defined in a parameter space, over a three-dimensional electroanatomical map of a surface of a heart that is displayed on the screen, by, for each pixel in the bounding region, transforming, to the parameter space, a virtual ray that passes through the pixel, and ascertaining whether a point of intersection between the transformed virtual ray and the quadric exists in the parameter space, and, for each pixel in the bounding region for which the point of intersection exists, rendering the pixel on the screen, based on properties of the point of intersection. Other embodiments are also described.