Flexible Hierarchical N-Tree Spatial Storage
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Solution Overview
Problem
Existing spatial partitioning methods, such as binary trees, trees of quadrants, and trees of octants, face inefficiencies in handling objects whose boundaries intersect with partitioning boundaries, leading to significant resource costs and suboptimal storage and retrieval processes.
Innovation Solution
A flexible hierarchical structure using an n-tree is employed, where objects are placed in the most suitable element, and if their boundaries exceed the element's boundaries, the element's size is artificially increased by adding a zone of presence, allowing for efficient storage and retrieval by considering neighboring elements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If objects are placed in fixed partitioning elements (binary tree, tree of quadrants, tree of octants), then spatial storage structure is simplified, but resource consumption increases when object boundaries intersect with partitioning boundaries
Solution Approach 1:
The partitioning elements are made dynamic by allowing their boundaries to expand when objects intersect with them. Instead of fixed partitioning boundaries, the system adapts the element boundaries to contain entire objects, transforming the static spatial structure into a dynamic one that responds to object placement requirements.
Solution Approach 2:
The system changes the size parameter of partitioning elements based on object boundaries. When an object boundary intersects with a partitioning element boundary, the element's size parameter is modified to expand and fully contain the object, thereby eliminating intersection problems and reducing the computational resources needed for handling partial overlaps.
2Ease of manufacture
If partitioning boundaries are fixed, then data structure creation is simplified, but storage efficiency decreases when objects span multiple elements
Solution Approach 1:
The data structure transitions from static fixed boundaries to dynamic adaptive boundaries. Partitioning elements automatically adjust their extent to match object boundaries, ensuring that each object is contained within a single element. This dynamic adaptation improves storage efficiency by eliminating the need to store and manage objects that span multiple partitioning elements.
3Area of stationary object
If objects are allowed to span multiple partitioning elements, then spatial coverage is improved, but retrieval complexity increases due to intersection handling
Solution Approach 1:
Instead of allowing objects to span multiple elements and then managing the complexity of retrieval across boundaries, the system inverts the approach by making the partitioning elements adapt to objects. The elements expand to contain entire objects, ensuring that each object resides in exactly one element. This inversion eliminates the need for complex intersection handling during retrieval operations.
Data Source
AI summary
Method of determining the spatial storage of an object by means of a flexible hierarchical structure containing a set of elements of an n-tree. Method comprises: Obtaining an object for placement in one of the set of elements of the n-tree. Determining if the boundary of the object goes beyond the boundaries of the most suitable element that is intersected by a portion of the object when the object is placed in this most appropriate element. Increasing the size of the most suitable element by adding to it a zone of presence of the object, the boundary of the zone of presence of the object being distant from the boundary of the most suitable element by the maximum value of the projection of the object beyond the boundaries of the most suitable element.