Swept Volume Determination Using Voxel Subsets
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Solution Overview
Problem
Existing techniques for determining the swept volume of objects in 3D space are limited to specific shapes and trajectories, are computationally intensive, and require processing the entire 3D space, leading to inefficiencies and artifacts in computation.
Innovation Solution
The techniques evaluate a subset of voxels near the surface of the swept volume using a signed distance field representation and a local growth algorithm, reducing computational complexity by only processing voxels through which the surface passes and those close to it.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional swept volume determination techniques are used to ensure accuracy, then measurement precision is improved, but computational complexity increases significantly
Solution Approach 1:
The 3D space is segmented into a voxel grid structure, dividing the continuous space into discrete volumetric elements. This segmentation allows the algorithm to process only relevant voxels rather than the entire continuous space, reducing computational complexity while maintaining accuracy in swept volume determination
Solution Approach 2:
The patent introduces a temporal dimension to the voxel grid, creating a 4D representation (x, y, z, t) where time is the fourth dimension. This dimensional extension allows the algorithm to track object positions through time and accurately determine swept volumes by examining voxel states across multiple time steps, improving precision without proportionally increasing computational complexity
2Measurement precision
If the entire 3D space is processed to ensure complete coverage, then productivity is reduced, but measurement precision is improved
Solution Approach 1:
The algorithm applies local quality by focusing computational resources only on voxels that are relevant to the swept volume calculation. Instead of uniformly processing all voxels in the 3D space, the method identifies and processes only those voxels that intersect with the object's trajectory or are adjacent to it, significantly improving computation speed while maintaining accuracy
Solution Approach 2:
The patent implements partial action by evaluating only a subset of voxels rather than the complete voxel grid. The algorithm determines which voxels need to be processed based on the object's position and trajectory, evaluating only those voxels that are necessary for accurate swept volume determination, thus improving productivity without sacrificing measurement precision
3Ease of manufacture
If existing techniques are used for specific object shapes, then ease of manufacture is improved, but adaptability deteriorates
Solution Approach 1:
The voxel-based algorithm provides universality by being applicable to objects of any shape and trajectory type. The method does not require specialized handling for different object geometries, as the voxel grid approach naturally accommodates any form factor. This single unified algorithm can process spheres, cubes, irregular shapes, and complex structures equally effectively, greatly enhancing adaptability while maintaining implementation simplicity
Data Source
AI summary
Techniques for determining a swept volume of an object moving along a trajectory in a 3D space are disclosed. In some examples, a computer graphics application accesses a representation of the object, such as the signed distance field (SDF), and the trajectory information describing the movement path in the 3D space over a time period. The 3D space is represented using a grid of voxels each having multiple vertices. The computer graphics application determines the swept volume of the object in the 3D space by evaluating a subset of the grid of voxels (e.g., the voxels surrounding the surface of the swept volume). The number of voxels in the subset of voxels is less than the number of voxels in the grid of voxels. The computer graphics application further generates a representation of the swept volume surface for output.