Volumetric Kernel Modeling for 3D Material Property Control
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Solution Overview
Problem
Current CAD modeling systems are limited in representing and manipulating volumetric properties within three-dimensional objects, particularly in controlling the interior volume and material variations, which is crucial for advanced manufacturing techniques like additive manufacturing.
Innovation Solution
A volumetric kernel representation (VKR) approach that uses tensor fields to parameterize volumetric properties, enabling unified geometry manipulation and composition, allowing for discrete and continuous material representations, and facilitating seamless integration with existing CAD environments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional boundary representation (B-Rep) format is used to store 3D geometry, then smooth and precise mathematical surfaces are achieved, but the ability to represent and manipulate volumetric properties like porosity and material mixing is limited
Solution Approach 1:
The patent merges B-Rep surface representation with volumetric property fields into a unified model structure. The volumetric kernel representation integrates both boundary geometry and internal volumetric characteristics (porosity, material mixing, density) into a single coherent framework, allowing simultaneous access to surface precision and volume properties.
Solution Approach 2:
The patent transitions from purely surface-based 2D boundary definitions to 3D volumetric property distributions. By introducing scalar and vector fields that define properties throughout the entire volume rather than just at boundaries, the system adds a dimensional aspect that enables control over internal material characteristics while maintaining surface precision.
2Manufacturing precision
If volumetric properties like porosity and material mixing are represented using traditional methods, then manufacturing control is limited, but computational complexity increases significantly
Solution Approach 1:
The patent segments volumetric properties into distinct field types (scalar fields for porosity and density, vector fields for material mixing ratios). This segmentation allows each property to be represented and manipulated independently using appropriate mathematical structures, reducing overall computational complexity while maintaining manufacturing precision.
Solution Approach 2:
The patent changes the parameterization approach by using continuous field representations with controlled resolution. Instead of discrete volumetric meshes, the system uses parameterized fields that can be evaluated at any point, allowing manufacturing precision to be controlled by field sampling density rather than fixed mesh granularity, thus reducing computational complexity.
3Adaptability or versatility
If discrete volumetric representations (voxels) are used to represent 3D objects, then inherently volumetric properties are well-described, but the smooth surface quality and CAD manipulation capabilities are lost
Solution Approach 1:
The patent creates a composite representation that combines the advantages of both voxel-based volumetric data and surface-based CAD models. The hybrid structure uses volumetric fields to describe internal properties while maintaining smooth B-Rep surfaces for external geometry, effectively creating a composite model that exhibits both discrete volumetric characterization and continuous surface quality.
Data Source
AI summary
Methods, systems, and apparatus, including medium-encoded computer program products, for volumetric kernel representation of three dimensional models include: modeling a three dimensional object using a volumetric representation including fields that determine volumetric properties, each of the fields being parameterized by an input and output tensor structure, and at least one of the fields mapping tensor output of a first of the fields to tensor input of a second of the fields to provide a unified framework for geometry manipulation and composition that encompasses both discrete and continuous representations of materials in the three dimensional space; evaluating the fields including using coverage values that determine compositing behavior to generate output data corresponding to the volumetric properties; and providing the output data for the three dimensional object having physical characteristics that vary from point to point within a volume of the three dimensional object in accordance with the volumetric properties.