Signed Distance Function Representation Using Raster Scan Line Intervals
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Solution Overview
Problem
The existing methods for representing signed distance functions in computer graphics require large amounts of memory, especially at higher resolutions, leading to a tradeoff between memory usage and accuracy.
Innovation Solution
Storing only two values per raster scan line, representing intersection intervals between grid lines and the surface, which allows for the determination of signed distance values using parameterization and trilinear interpolation, reducing the need to compute and store values at each grid point.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the grid resolution is increased to improve approximation accuracy, then the measurement precision is improved, but the memory usage increases significantly
Solution Approach 1:
The patent extracts only the essential information needed to represent the signed distance function - specifically storing minimum and maximum values along each raster scan line - rather than storing complete distance values for every grid point. This selective extraction maintains approximation accuracy while dramatically reducing memory requirements from O(N³) to O(N²) where N is the grid dimension.
Solution Approach 2:
The patent segments the grid representation by processing it along raster scan lines and further segmenting each scan line into intervals defined by minimum and maximum values. This segmentation allows the representation to be stored in a compressed format that scales more favorably with resolution, enabling higher grid resolutions without proportional increases in memory usage.
2Manufacturing precision
If the grid resolution is increased to improve approximation accuracy, then the manufacturing precision is improved, but the device complexity increases
Solution Approach 1:
The patent extracts only the critical boundary information (minimum and maximum values) from each raster scan line, discarding redundant distance values. This extraction simplifies the data structure from a complete distance field to a compressed interval representation, reducing computational complexity while preserving shape approximation accuracy.
Solution Approach 2:
Instead of storing complete distance values and deriving intervals, the patent inverts the approach by directly storing only the minimum and maximum values that define the intervals. This inversion simplifies the data structure and computational operations, making the system more efficient while maintaining the same level of precision.
Data Source
AI summary
A system and method for implicitly computing signed distance values in a graphics application. In one embodiment, rather than storing numerous distance values along a given raster scan line, only two values are stored for each interval defining the intersection of the raster scan line with the shape. These two values represent the interior of the object to be rendered along a given grid line. In another embodiment each grid line may be parameterized (e.g., from 0 to 1). Each intersection interval may then be represented by the parameter value at an entry point of the surface and an exit point of the surface, along the given grid line.