Projective Hash Maps for 3D Spatial Search
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Solution Overview
Problem
Conventional spatial hash maps require exhaustive searches in three-dimensional space, leading to cubic complexity, making them impractical for large regions or after perspective projection, and inefficient for locating spatially neighboring data in computer graphics applications.
Innovation Solution
Projective hash maps are generated by projecting N-dimensional points onto a projection surface, reducing the dimensionality to facilitate faster searches by using projected coordinates to generate hash keys, allowing for efficient querying of neighboring data in a two-dimensional space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exhaustive search is performed over all non-empty neighboring cells in 3D space, then spatially neighboring data can be located, but the search complexity becomes cubic O(N^3) making it impractical for large regions
Solution Approach 1:
The patent projects 3D spatial coordinates onto a 2D projection surface (such as a view plane or image plane) to create 2D hash keys. This dimensionality reduction transforms the search space from three dimensions to two dimensions, changing the complexity from O(N^3) to O(N^2) while preserving the ability to locate spatially neighboring data through the projection relationship between 3D world space and 2D screen space
2Productivity
If spatial hash map is used to store rendering information, then data access can be accelerated, but the method breaks down after perspective projection when data is inserted
Solution Approach 1:
The patent changes the parameter used for hashing from 3D world coordinates to 2D projected coordinates on the view plane. By using the projected 2D coordinates as hash keys, the system becomes compatible with perspective projection and can efficiently handle data insertion and retrieval in the projected space, maintaining accelerated access speeds while adapting to the projected coordinate system
3Device complexity
If search is restricted to local surface tangent plane for small-curvature surfaces, then complexity reduces from O(N^3) to O(N^2), but this optimization breaks down for large search areas and non-planar surfaces
Solution Approach 1:
The patent creates a universal solution by using 2D projection-based hashing that works for all surface types (planar, non-planar, small-curvature, large-search-area) without requiring special case optimizations. The projection method naturally handles diverse surface geometries and search areas, providing a single versatile approach that maintains O(N^2) complexity across different scenarios
Data Source
AI summary
This application discloses techniques for generating and querying projective hash maps. More specifically, projective hash maps can be used for spatial hashing of data related to N-dimensional points. Each point is projected onto a projection surface to convert the three-dimensional (3D) coordinates for the point to two-dimensional (2D) coordinates associated with the projection surface. Hash values based on the 2D coordinates are then used as an index to store data in the projective hash map. Utilizing the 2D coordinates rather than the 3D coordinates allows for more efficient searches to be performed to locate points in the 3D space. In particular, projective hash maps can be utilized by graphics applications for generating images, and the improved efficiency can, for example, enable a game streaming application on a server to render images transmitted to a user device via a network at faster frame rates.