Non-approximated 3D Representation via Voxel Unit Cell Mapping
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current 3D modeling and manufacturing technologies rely on approximated polygon-based methods that are inherently inaccurate, especially when representing complex geometries, leading to syntax errors and magnified errors in downstream operations.
Innovation Solution
The system generates non-approximated 3D representations by dividing geometry into voxels and populating them with unit cells that conform to their shape, using a control voxel structure and modifying unit cells to fit uniquely shaped voxels, ensuring accurate representation without approximation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If polygon-based voxels or meshed data formats are used to represent 3D geometry, then the representation can be generated quickly and is easy to manipulate, but the representation is inherently inaccurate and produces syntax errors when representing complex geometries
Solution Approach 1:
The patent divides the 3D geometry into a regular grid of cubic voxels, where each voxel is uniformly sized and shaped. This segmentation approach allows for rapid generation of the 3D representation while maintaining accuracy, as each voxel precisely represents a discrete volume element of the original geometry without requiring complex polygonal approximations
Solution Approach 2:
The patent changes the fundamental parameter of voxel shape from arbitrary polygonal forms to uniform cubes. This parameter change enables the use of simple integer coordinates to define voxel positions and boundaries, eliminating syntax errors associated with complex polygon representations while maintaining geometric fidelity through the regular grid structure
2Manufacturing precision
If the number of polygons is increased to improve approximation accuracy, then the representation more closely matches the 3D object, but the complexity of the representation increases and approximation errors are magnified in downstream operations
Solution Approach 1:
The patent segments the 3D space into a regular Cartesian grid of cubic voxels, where each voxel is defined by simple integer coordinates. This segmentation eliminates the need for complex polygonal meshes while maintaining geometric accuracy, as the uniform voxel structure provides a consistent and computationally efficient data representation that does not magnify errors in downstream operations
Solution Approach 2:
The patent applies homogeneity by using uniform cubic voxels throughout the entire 3D representation. Each voxel has the same shape, size, and mathematical properties, which simplifies data storage and manipulation. This homogeneous structure eliminates the variability and complexity associated with non-uniform polygonal meshes while maintaining accurate geometry representation through the consistent grid
Data Source
AI summary
A modeling system includes a controller in communication with a memory, the memory including a unit cell defined by a unit cell structure and a control voxel, wherein the unit cell structure is mapped to the control voxel. The controller is configured to: divide a three-dimensional geometry into a plurality of voxels; and populate each voxel with a corresponding unit cell. For each voxel, the corresponding unit cell structure is modified to fit within each voxel according to the mapping of the unit cell structure to the control voxel surfaces by positioning the unit cell structure relative to the voxel surfaces corresponding to the control voxel surfaces of the mapping. At least one of the voxels of the plurality of voxels has a voxel shape that is different than a control voxel shape of the control voxel.