Systems and methods for quadrilateral mesh generation

1. A processor-implemented system for generating quadrilateral mesh elements to represent a physical object, the system comprising:

one or more data processors configured to:

receive a geometric structure representing a physical object;

determine a directional field;

determine a size field;

select one or more locations associated with local data from a region of the geometric structure; and

generate one or more quadrilateral mesh elements based at least in part on the directional field, the size field, and the local data to represent the physical object; and

a non-transitory computer-readable storage medium configured to:

store a first data structure for the geometric structure;

store data related to the directional field, data related to the size field, and the local data; and

store a second data structure for the one or more quadrilateral mesh elements;

wherein the one or more data processors are further configured to update the second data structure based at least in part on the first data structure, the data related to the directional field, the data related to the size field and the local data;

wherein the one or more locations correspond to non-singular locations; and

wherein the one or more data processors are further configured to:

generate the one or more quadrilateral mesh elements based on a weighted combination of the size field and the directional field;

determine an angle weight based at least in part on an angle between the directional field and a front growth direction;

determine a length weight based at least in part on a ratio between the size field and a front length; and

generate the one or more quadrilateral mesh elements based at last in part on a linear combination of the angle weight and the length weight.

2. The system of claim 1 , wherein the one or more data processors are further configured to generate the quadrilateral mesh elements using an advanced front approach.

3. The system of claim 2 , wherein the one or more data processors are further configured to generate the quadrilateral mesh elements using a paving approach.

4. The system of claim 2 , wherein the one or more data processors are further configured to generate the quadrilateral mesh elements using a Q-Morph approach.

5. The system of claim 1 , wherein the local data includes one or more of the following: sizes of local fronts, interaction between local fronts, interactions between features, and front directions.

6. The system of claim 1 , wherein the one or more data processors are further configured to generate the quadrilateral mesh elements using a weighted combination of the directional field, the size field, and the local data.

7. The system of claim 1 , wherein the one or more data processors are further configured to select the front growth direction from two orthogonal directions.

8. The system of claim 7 , wherein:

the two orthogonal directions include a first direction and a second direction, where the first direction aligns better with an initial growth direction than the second direction; and

the one or more data processors are further configured to select the first direction as the front growth direction.

9. The system of claim 7 , wherein:

the two orthogonal directions include a first direction and a second direction, where a first angle between the first direction and an initial growth direction and a second angle between the second direction and the initial growth direction are both larger than a threshold;

the first direction aligns better with a growth direction of a neighboring front than the second direction; and

the one or more data processors are further configured to select the first direction as the front growth direction.

10. The system of claim 1 , wherein:

the one or more locations include a singular location; and

the one or more data processors are further configured to generate the one or more quadrilateral mesh elements for the singular location using a predetermined direction and a predetermined size associated with the singular location.

11. The system of claim 1 , wherein:

the one or more locations include a singular location; and

the one or more data processors are further configured to generate the one or more quadrilateral mesh elements for the singular location in a predetermined pattern.

12. The system of claim 11 , wherein the one or more data processors are further configured to:

in response to the singular location corresponds to a negative singularity, generate three quadrilateral elements around the singular location; and

in response to the singular location corresponds to a positive singularity, generate five quadrilateral elements around the singular location.

13. The system of claim 1 , wherein:

the one or more data processors are further configured to:

generate one or more initial meshes for the geometric structure;

determine one or more first constraints related to one or more curvature directions of the geometric structure based at least in part on the one or more initial meshes;

determine one or more second constraints related to the local data of the geometric structure based at least in part on the one or more initial meshes;

determine the directional field based at least in part on the one or more first constraints and the one or more second constraints; and

generate the one or more quadrilateral mesh elements based at least in part on the directional field, the size field, the one or more first constraints and the one or more second constraints; and

the non-transitory computer-readable storage medium is further configured to store data related to the one or more first constraints and data related to the one or more second constraints;

wherein the one or more data processors are further configured to update the second data structure based at least in part on the first data structure, the data related to the directional field, the data related to the size field, the data related to the one or more first constraints and the data related to the one or more second constraints.

14. The system of claim 13 , wherein the one or more data processors are further configured to perform edge meshing and triangle meshing on one or more initial regions of the geometric structure to generate the one or more initial meshes.

15. The system of claim 13 , wherein the one or more second constraints are related to one or more of the following: interior boundaries of the geometric structure, exterior boundaries of the geometric structure, sharp features of the geometric structure, prominent features of the geometric structure, and user-specified directions.

16. The system of claim 13 , wherein the one or more data processors configured to determine the directional field at a body level, on a group of regions of the geometric structure, or on an individual region of the geometric structure.

17. A method for generating quadrilateral mesh elements to represent a physical object, the method comprising:

receiving a geometric structure representing a physical object, a first data structure for the geometric structure being stored in a non-transitory computer-readable storage medium;

determining a directional field using one or more data processors, data related to the directional field being stored in the non-transitory computer-readable storage medium;

determining a size field using the one or more data processors, data related to the size field being stored in the non-transitory computer-readable storage medium;

selecting one or more locations from a region of the geometric structure, local data associated with the locations being stored in the non-transitory computer-readable storage medium; and

generating one or more quadrilateral mesh elements based at least in part on the directional field, the size field, and the local data using the one or more data processors, a second data structure for the one or more quadrilateral elements being stored in the non-transitory computer-readable storage medium;

wherein the second data structure is updated based at least in part on the first data structure, the data related to the directional field, the data related to the size field and the local data;

wherein the one or more locations correspond to non-singular locations; and

wherein the method further includes:

generating the one or more quadrilateral mesh elements based on a weighted combination of the size field and the directional field;

determining an angle weight based at least in part on an angle between the directional field and a front growth direction;

determining a length weight based at least in part on a ratio between the size field and a front length; and

generating the one or more quadrilateral mesh elements based at last in part on a linear combination of the angle weight and the length weight.

18. A non-transitory machine-readable medium encoded with instructions for commanding one or more data processors to execute operations of a method for generating quadrilateral mesh elements to represent a physical object, the method comprising:

receiving a geometric structure representing a physical object, a first data structure for the geometric structure being stored in a non-transitory computer-readable storage medium;

determining a directional field using one or more data processors, data related to the directional field being stored in the non-transitory computer-readable storage medium;

determining a size field using the one or more data processors, data related to the size field being stored being stored in the non-transitory computer-readable storage medium;

selecting one or more locations from a region of the geometric structure, local data associated with the locations being stored in the non-transitory computer-readable storage medium; and

generating one or more quadrilateral mesh elements based at least in part on the directional field, the size field, and the local data using the one or more data processors, a second data structure for the one or more quadrilateral elements being stored in the non-transitory computer-readable storage medium;

wherein the second data structure is updated based at least in part on the first data structure, the data related to the directional field, the data related to the size field and the local data;

wherein the one or more locations correspond to non-singular locations: and wherein the method further includes:

generating the one or more quadrilateral mesh elements based on a weighted combination of the size field and the directional field;

determining an angle weight based at least in part on an angle between the directional field and a front growth direction;

determining a length weight based at least in part on a ratio between the size field and a front length: and

generating the one or more quadrilateral mesh elements based at last in part on a linear combination of the angle weight and the length weight.