METHODS OF HIGH-DEFINITION CELLULAR LEVEL SET IN B-SPLINES FOR MODELING AND TOPOLOGY OPTIMIZATION OF THREE-DIMENSIONAL CELLULAR STRUCTURES

• US 20200134918A1
• Filed: 10/28/2019
• Published: 04/30/2020
• Est. Priority Date: 10/31/2018
• Status: Active Grant

• Current Assignee: Hong Kong University of Science and Technology
• Original Assignee: Hong Kong University of Science and Technology
• Inventors: Wang, Michael Yu
• Granted Patent: US 10,984,593 B2
• Time in Patent Office: Days
• CPC Class Codes: G06T 15/08 Volume rendering
• CPC Class Codes: G06T 17/30 Polynomial surface description
• CPC Class Codes: G06T 19/20 Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
• CPC Class Codes: G06T 2219/2021 Shape modification
• CPC Class Codes: G06T 5/30 Erosion or dilatation, e.g. thinning

Abstract

Techniques for designing and optimization of solid/cellular structures are described using a modeling process referred to as high-definition cellular level set in B-splines (HD-CUBS). With this process, the entire design domain for the solid/cellular structure in question is subdivided into a set of connected volumetric cells in three dimensions. An implicit trivariate B-spline function is defined on each subdomain cell. With this parameterization scheme, constraints can be imposed on the relevant B-spline coefficients to naturally maintain geometric continuities at the connection faces between neighboring cells. The method offers several useful properties and powerful functionalities to build and modify a solid/cellular structure in the modeling process and to conduct topology optimization by directly adjusting the B-spline coefficients. The model construction can be carried out using a fast B-spline interpolation, and the topology optimization can involve a sequence of discrete B-spline convolutions.

Claims

1. A system comprising,

a processor;

and

a memory that stores executable instructions that, when executed by the processor, facilitate performance of operations, comprising;

receiving volumetric data defining a structure; and

generating a three-dimensional model of the structure based on the volumetric data, comprising;

partitioning a global design domain for the structure into subdomain cells in three-dimensions;

defining cellular level set functions for respective subdomain cells of the subdomain cells; and

defining parameters of the cellular level set functions using B-spline basis functions for the respective subdomain cells.

2. The system of claim 1, wherein the generating further comprises:

initializing the cellular level set functions using a fast B-spline interpolation method or a fast discrete B-spline convolution method to determine B-spline coefficients for the B-spline basis functions based on the volumetric data, resulting in initialized cellular level set functions.

3. The system of claim 2, wherein the generating further comprises:

assembling the initialized cellular level set functions into a global level set function for the structure; and

reconstructing the volumetric data based on the global level set function, resulting in a transformation of the volumetric data into the three-dimensional model.

4. The system of claim 2, wherein the generating further comprises:

determining B-spline coefficients for the B-spline basis functions based on the volumetric data using a fast B-spline interpolation method or a fast discrete B-spline convolution method, resulting in defining internal geometric properties of the subdomain cells;

determining values of the cellular level set functions using the B-spline coefficients, resulting in defining level set representations of the subdomain cells; and

assembling the level set representations in accordance with a global level set function for the structures, resulting in a transformation of the volumetric data into the three-dimensional model.

5. The system of claim 1, wherein the operations further comprise:

controlling properties of the three-dimensional model by adjusting B-spline coefficients and knot vectors of the B-spline basis functions.

6. The system of claim 1, wherein the generating further comprises, for the respective subdomain cells:

defining a rectilinear grid with regular spacing in respective directions of the three-dimensions;

locating knot vectors of the B-spline basis functions on the rectilinear grid; and

setting first and last knots in the respective directions to be fully repeated with highest multiplicity.

7. The system of claim 1, wherein the three-dimensional model comprises a first high-definition cellular level set in B-splines (HD-CLIBS) model, and wherein operations further comprise:

connecting the first HD-CLIBS model with a second HD-CLIBS model; and

constraining boundary B-spline coefficients associated with boundary faces between neighboring subdomain cells of the first HD-CLIBS model and the second HD-CLIBS model to achieve a defined order differentiable of continuity between the first HD-CLIBS model and the second HD-CLIBS model.

8. The system of claim 1, wherein the operations further comprise:

dividing a subdomain cell of the subdomain cells into two or more cells by inserting a repeating knot into a knot sequence of a B-spline basis function of the B-spline basis functions defined for the subdomain cell.

9. The system of claim 1, wherein the operations further comprise:

adjusting geometric properties of the three-dimensional model by adjusting B-spline coefficients of the B-spline basis functions.

10. The system of claim 9, wherein the adjusting comprises independently adjusting geometric properties of the subdomain cells by independently adjusting subsets of B-spline coefficients respectively associated with the subdomain cells.

11. The system of claim 9, wherein the adjusting comprises performing adjustment operations comprising dilation, erosion, grading, and blending operations.

12. The system of claim 1, wherein the operations further comprise:

optimizing a topology of the three-dimensional model in accordance with a defined optimization function by independently adjusting the B-spline coefficients for the respective subdomain cells using as a sequence of discrete convolution operations.

13. The system of claim 12, wherein the optimizing comprises determining a solution to the optimization function without applying the Hamilton-Jacobi equation or a linear system with an interpolation matrix.

14. The system of claim 12, wherein the optimizing comprises applying a re-normalization scheme to bound a gradient norm of the cellular level set functions by a defined value.

15. A method, comprising:

obtaining, by a system operatively coupled to at least one processor, volumetric data defining a structure; and

generating, by the system, a three-dimensional model of the structure based on the volumetric data, comprising;

partitioning, by the system, a global design domain for the structure into subdomain cells in three-dimensions;

defining, by the system, cellular level set functions for respective subdomain cells of the subdomain cells; and

defining, by the system, parameters of the cellular level set functions using B-spline basis functions for the respective subdomain cells.

16. The method of claim 15, wherein the generating further comprises:

initializing, by the system, the cellular level set functions using a fast B-spline interpolation method or a fast discrete B-spline convolution method to determine B-spline coefficients for the B-spline basis functions based on the volumetric data, resulting in initialized cellular level set functions.

17. The method of claim 16, wherein the generating further comprises:

building, by the system, the global level set function by assembling the initialized cellular level set functions; and

reconstructing, by the system, the volumetric data based on the global level set function, resulting in a transformation of the volumetric data into the three-dimensional model.

18. The method of claim 15, further comprising:

optimizing, by the system, a topology of the three-dimensional model in accordance with a defined optimization function by independently adjusting the B-spline coefficients for the respective subdomain cells using as a sequence of discrete convolution operations.

19. A machine-readable storage medium, comprising executable instructions that, when executed by one or more processors, facilitate performance of operations, comprising:

defining a three-dimensional model for a structure, comprising;

partitioning a global design domain for the structure subdomain cells in three-dimensions;

defining cellular level set functions for respective subdomain cells of the subdomain cells; and

defining parameters of the cellular level set functions using B-spline basis functions for the respective subdomain cells; and

generating the three-dimensional model based on volumetric data corresponding to the structure.

20. The machine-readable storage medium of claim 19, wherein the generating comprises:

initializing the cellular level set functions using a fast B-spline interpolation method or a fast discrete B-spline convolution method to determine B-spline coefficients for the B-spline basis functions based on the volumetric data, resulting in initialized cellular level set functions;

assembling the initialized cellular level set functions into a global level set function for the structure; and

reconstructing the volumetric data based on the global level set function, resulting in a transformation of the volumetric data into the three-dimensional model.