Multi-zone quadrilateral mesh generator for high mesh quality and isotropy

Abstract

A method and corresponding system (2100) for CAD operation and a computer readable medium (2126) are disclosed herein. A method (2000) includes: receiving model data (2002) of a surface (210) of a part (200) to be manufactured. The method includes: performing a loop laying process (2004) on a first portion of the surface (210) to generate a first set of elements (302, 304, 306). The method includes: performing a Cartesian meshing process (2010) on a second portion of the surface (210) to generate a second set of elements (704). The method includes: performing a subdivision meshing process (2016) on a third portion of the surface (210) to generate a third set of elements (1002). The method includes combining (2020) a first set of elements (302, 304, 306), a second set of elements (704), and a third set of elements (1002) to produce a final mesh (1202) for a surface (210) of a part (200) to be manufactured.

Description

Technical Field

[0001] The present disclosure relates generally to computer-aided design, visualization, engineering, and manufacturing systems ("CAD systems"), product lifecycle management ("PLM") systems, and similar systems (collectively, "product data management" systems or PDM systems) that manage data for products and other items. Background Art

[0002] CAD systems are useful for designing and visualizing two-dimensional (2D) and three-dimensional (3D) models and drawings for manufacture into physical products. Improved systems are desired. Summary of the invention

[0003] Various disclosed embodiments include methods and corresponding systems for CAD operations and computer readable media disclosed herein. A method includes: receiving model data of a surface of a part to be manufactured. The method includes: performing a loop laying process for a first portion of the surface to generate a first set of elements. The method includes: performing a Cartesian meshing process for a second portion of the surface to generate a second set of elements. The method includes: performing a subdivision meshing process for a third portion of the surface to generate a third set of elements. The method includes: combining the first set of elements, the second set of elements, and the third set of elements to generate a final mesh for the surface of the part to be manufactured.

[0004] Various disclosed embodiments also include a data processing system including a processor. The data processing system also includes an accessible memory. The data processing system is specifically configured to perform the process as described herein.

[0005] Various disclosed embodiments also include non-transitory computer-readable media encoded with executable instructions that, when executed, cause one or more data processing systems to perform processes as described herein.

[0006] Some embodiments also include: manufacturing a part based on the final mesh. Some embodiments also include: defining a boundary node ring of the surface based on the first group of elements, connecting the boundary node rings to produce a first single node ring, and constructing a bounding box based on the first single node ring. In some embodiments, a Cartesian meshing process is performed based on the bounding box constructed based on the first group of elements. Some embodiments also include: defining a region node ring of the surface based on the first group of elements and the second group of elements, and connecting the region node rings to produce a single region node ring. In some embodiments, a subdivision meshing process is performed based on a single connected region node ring based on the first group of elements and the second group of elements. Some embodiments also include: performing a smoothing process on a combination of the second group of elements and the third group of elements. Some embodiments also include: transforming the bounding box of the surface to a different 2D or 3D coordinate domain.

[0007] The features and technical advantages of the present disclosure have been summarized quite extensively above so that those skilled in the art can better understand the subsequent detailed description. Additional features and advantages of the present disclosure that form the subject matter of the claims will be described later in this article. Those skilled in the art will understand that they can easily use the disclosed concepts and specific embodiments as a basis for modifying, designing or analyzing other structures to perform the same purpose of the present disclosure. Those skilled in the art will also recognize that such equivalent constructions do not depart from the spirit and scope of the present disclosure in its broadest form.

[0008] Before proceeding to the following detailed description, it may be helpful to set forth definitions of certain words or phrases used throughout this patent document: the terms "include" and "comprising" and their derivatives mean inclusion without limitation; the term "or" is inclusive, meaning and / or; the phrases "associated with" and "associated with" and their derivatives may mean including, included, interconnected with, containing, contained within, connected to or connected with, coupled to or coupled with, communicable with, cooperating with, interlaced, juxtaposed, proximate, bound to or bound with, having, having characteristics thereof, and the like; and the term "controller" means any device, system, or portion thereof that controls at least one operation, whether such device is implemented in hardware, firmware, software, or some combination of at least two thereof. It should be noted that the functionality associated with any particular controller may be centralized or distributed, whether local or remote. Definitions of certain words and phrases are provided throughout this patent document, and those of ordinary skill in the art will understand that such definitions apply in many, if not most, instances to prior and future uses of such defined words and phrases. Although some terms may include various embodiments, the appended claims may expressly limit such terms to specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] For a more complete understanding of the present disclosure and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings, in which like reference numerals designate like objects, and in which:

[0010] Figure 1A An example of a subdivided quad-dominated mesh on a surface is illustrated;

[0011] Figure 1B An example of a quad-dominated paving grid on a surface is illustrated;

[0012] Figure 2 illustrates a plurality of meshes on a surface of a part to be manufactured according to the disclosed embodiments;

[0013] Figure 3 illustrates a model having one layer of ring paving elements around all face rings in accordance with the disclosed embodiments;

[0014] Figure 4 illustrates a ring of border nodes joined into a single connected ring in accordance with the disclosed embodiments;

[0015] Figure 5 A Cartesian grid is illustrated in accordance with disclosed embodiments.

[0016] Figure 6 illustrates an example of the results of a Boolean action that generates a model according to the disclosed embodiments;

[0017] Figure 7 illustrates an example of a model having a combination of elements from region one and region two according to the disclosed embodiments;

[0018] Figure 8 illustrates a ring of nodes in a model according to the disclosed embodiments;

[0019] Fig. 9 illustrates a third region formed by a ring of connected nodes in accordance with the disclosed embodiments;

[0020] Fig.10 illustrates a subdivided grid in a zone 3 region of a model according to the disclosed embodiments;

[0021] Fig.11 illustrates a model with dual combined grids on zones two and three according to the disclosed embodiments;

[0022] Fig.12 illustrates a three-combination final mesh according to the disclosed embodiment;

[0023] Fig.13 illustrates an example of a surface having an axis at an angle to an XY plane in accordance with the disclosed embodiments;

[0024] Fig.14 illustrates a Booleanized Cartesian grid according to the disclosed embodiments;

[0025] Fig.15 illustrates a final mesh Cartesian tiler mesh generated on a surface according to the disclosed embodiments;

[0026] Fig.16 illustrates a portion of an outer ring of a dominant linear surface according to a disclosed embodiment;

[0027] Fig.17 An example of a surface having an axis transformed to be aligned with the XY plane is illustrated in accordance with the disclosed embodiments.

[0028] Fig.18An example of a surface mesh having axes transformed to align with the XY plane is illustrated in accordance with the disclosed embodiments.

[0029] Fig.19 illustrates an example of a final mesh after an inverse transformation of a Cartesian portion according to the disclosed embodiments;

[0030] Fig. 20 illustrates a process according to the disclosed embodiments; and

[0031] Fig.21 Illustrated is a block diagram of a data processing system in which embodiments may be implemented. DETAILED DESCRIPTION

[0032] Figures 1 to 2 discussed below Fig.21 The various embodiments used to describe the principles of the present disclosure in this patent document are merely illustrative and should not be construed in any way to limit the scope of the present disclosure. It will be appreciated by those skilled in the art that the principles of the present disclosure can be implemented in any appropriately arranged device. Many innovative teachings of the present application will be described with reference to exemplary non-limiting embodiments.

[0033] CAD systems are used to design, model, visualize, engineer and ultimately manufacture parts for manufacturing. To model and analyze parts, in particular, finite element analysis (FEA) techniques are used to create, analyze, manipulate and simulate the surfaces, representative meshes, features, interactions and behavioral properties of parts. In a large number of industrial finite element analysis problems, especially in the automotive and aerospace industries, structural designers and analysts require quadrilateral-dominated meshes with very high fidelity and mesh quality. Many component areas in the automotive industry, such as fillets, beads, annular surfaces, flanges, and large flat body panel areas near these features, are of particular interest, especially for crash simulations. High-quality quadrilateral meshes can be valuable for computer-aided engineering design and analysis.

[0034] The accuracy of many finite element analyses, especially collision and multi-physics analyses, required depends on the quality of the mesh being solved. Quadrilateral meshes are typically used in these applications. In contrast to triangles (linear) which are planar, quadrilateral elements or quadrilaterals, which are usually non-planar, are susceptible to error accumulation. Triangular meshes may not be suitable for modeling many parts to be manufactured (e.g., plate parts) because triangular meshes tend to make the structure too rigid, which leads to erroneous designs. A common defect of even the most well-established surface meshing algorithms is the appearance of poorly formed, distorted quadrilaterals. The disadvantages of these defects, for example, are undesirable because they can significantly affect the accuracy of the finite element solution. The disadvantages can also reduce the computational efficiency of the solution process.

[0035] The disclosed embodiments include a surface mesh generator that can satisfy quadrilateral element quality requirements and strictly adhere to mesh size, such as described below.

[0036] Mesh quality requirements are an important factor in the FEA process. Quad element quality is measured by a number of different parameters, including the Jacobian or other distortion measures, aspect ratio, skew, taper, warp, element angle, minimum and maximum element edge lengths, etc. For each of these parameters, the quad elements must be below a certain threshold. These parameters are loosely related, but there is no well-defined mathematical correlation between them.

[0037] All quadrilateral / quad-dominant mesh generation algorithms have limitations or natural imperfections that result in geometrically deformed elements. Limitations or shortcomings at different stages of the meshing process (e.g., boundary discretization, surface flattening, paving, domain subdivision, or others) can result in the formation of poorly formed quadrilateral elements. While element quality-driven mesh post-processing tools can address most shortcomings, these solutions are expensive, induce anisotropic sizing variations in the mesh, and cannot repair all shortcomings.

[0038] The mesh isotropy requirement is also an important factor in the FEA process. Uniform mesh size or isotropic mesh, especially in non-featured flat areas of the surface, is the main requirement. However, for a predefined element size, which is usually specified by the user, there are often scenarios where the actual mesh size deviates greatly from this target size. This results in elements that are too small or too large. Smaller elements affect the solver convergence rate, while coarser meshes affect solution accuracy. Mesh size variations also make it more difficult for quadrilateral elements to pass the specified quality threshold. In certain critical areas of interest, such as in automotive body panel flanges, beads, holes, annuli, dimples, and areas around these features, a very well-structured hierarchical mesh is important to improve solution accuracy.

[0039] Figure 1A An example of a subdivided quad-dominant mesh 100 on a surface is illustrated. Note that this example is "quad-dominant" because it consists primarily of quadrilateral elements, but also includes some triangles.

[0040] Figure 1BAn example of a quadrilateral-dominated paving grid 110 on a surface is illustrated. The paving method (or "paving") is an attractive quadrilateral mesh generation method that can create very high-quality structured grids near surface boundaries. Surface boundaries are locations where features appear and key components align. Stress and displacement are critically studied in these regions. Therefore, any mesher that creates high-fidelity, high-quality grids in these zones becomes the first choice. The main disadvantage of paving is that it loses its elegance in the deep portion of the surface, where the mesher cannot maintain mesh size isotropy due to wedging, pleating, and stitching, and creates diamond-shaped quadrilaterals that interrupt the well-formed mesh line flow.

[0041] The subdivision mesher also includes super-finite meshing, and helps the mesher create the best possible quadrilateral mesh over a 3- or 4-sided mesh area.

[0042] Other quadrilateral mesh generation techniques have been reported, such as Cartesian or block decomposition methods, circle filling, etc., but they all suffer from severe limitations and have not found adaptors in industry.

[0043] Known meshers have areas of strength, but none of them have the flexibility to holistically meet the quad meshing needs of industries and applications that require high quad element quality and strict adherence to mesh size, such as, but not limited to, the automotive and aerospace industries. The disclosed embodiments include a quad mesher that can create a finer-sized structured map-like mesh on surface features, but a uniform but boundary-structured mesh on larger, flatter faces in the neighborhood of the features, while ensuring that the final quad mesh meets or exceeds a mesh quality threshold.

[0044] Hybrid methods include super-finite or mapped meshers, subdivision meshers, and ring pavers. These meshers have different strengths. For example, for regular 4-sided rectangular surfaces, super-finite meshing produces high-quality results, ring pavers perform well for boundary structured grids, and subdivision meshing algorithms have the efficiency and robustness to operate on narrow areas and harsh constraints, which can add high fidelity and mileage to quadrilateral meshers. Cartesian or block decomposition methods have the unique ability to create perfectly shaped quadrilateral elements in the interior of any surface, which is a desirable property especially for processing large faces with large widths.

[0045] The disclosed embodiments include a Cartesian tiler hybrid meshing process that overcomes weaknesses in other mesher technologies and provides significant improvements in the functionality and operation of systems and devices that employ the disclosed process.

[0046] The disclosed mesher is a hybrid method that combines multiple meshing strategies in a unique and innovative way. The disclosed embodiments can use an improved ring paving algorithm on the surface boundary to produce a structured grid of up to two layers. The disclosed embodiments can use a Cartesian meshing method for the main part of the surface interior. The disclosed embodiments can use a subdivision meshing strategy to fill the narrow cracks between the boundary structured paving area and the Cartesian interior area. Finally, the disclosed embodiments can use a transfinite (or mapped) meshing process with a subdivision mesher, wherein, if the surface or a sub-region thereof is rectangular, a regularly structured quadrilateral mesh is generated.

[0047] Figure 2 The surface 210 of the part 200 to be manufactured is illustrated, which is meshed by a subdivision mesher used with the multi-block strategy described in US Patent Publication US20170061037A1, which is hereby incorporated by reference. Topologically, this surface of the part 200 has two inner rings (at the openings 202 and 204) bounded by a concave outer ring (outer boundary 206, included in the concave portion 208 of the outer ring). Figure 2 Multiple subdivided grids (as opposed to multiple zones) are shown on the surface of part 200 .

[0048] The ring pavers (also known as "combined subdivision and ring front quads" or "CSALF-Q") are an improved ring front-based paving process that advances a row of quadrilateral elements created on an input ring. The output of the algorithm is a row of well-formed quadrilateral elements and another ring formed by the outer edges of the row of elements (which may be referred to herein as the "second ring"). A drawback or limitation of the ring pavers is that if a paved ring self-intersects or intersects with other face rings, the paved ring will be completely discarded. This is an intentional limitation of the typical ring pavers process because it allows the ring pavers process to fully interact with the subdivision mesher. It is often advantageous to discard a paved ring in its entirety due to a discovered intersection of a paved ring with some of its fronts because the resulting domain is split again to produce more "paved" boundaries.

[0049] In accordance with the disclosed embodiments, the system performs a modified loop laying process for a first zone (Zone 1).

[0050] However, in a Cartesian tiler mesher as disclosed herein, discarding the laid rings is not preferred. The disclosed embodiment creates only one or two layers on the border in order to create a border structured mesh and no longer intrude on the surface. The inner core is handled by a Cartesian algorithm. Therefore, the disclosed ring tiler process is modified to avoid dropping a complete layer when an intersection is found. Instead, only the intersecting elements are erased.

[0051] Figure 3A model 300 is illustrated having one layer of ring tiling elements around all face rings in accordance with the disclosed embodiments. The figure shows outer ring boundary elements 302 and inner ring boundary elements 304 and 306. These tiling rows of one or more elements form a meshed region 1 as referred to herein.

[0052] Assume that the pavers create m quadrilateral elements and q p nodes. Then, the paver grid P can be expressed as:

[0053] P=∪(m,q p ) (1.1)

[0054] In this particular example, no elements are dropped from the first paved layer because no ring-ring intersections are found. However, a second layer cannot be created as there are too many elements for all three ring intersections. Partial ring paving is performed only when the new ring intersection is minimal.

[0055] According to the disclosed embodiment, the system performs a Cartesian gridding process in the second zone (Zone 2). Figure 4 Model 400 is depicted with boundary node rings 402 (illustrated by lines) of laid layers. These lines define the inner and outer boundaries of zone 2 - the area where the system will perform a Cartesian meshing process for most or all of the defined area. A conventional ring joining process is used to join the three rings into a single ring with some foldable portions. Such ring joining processes are known to those skilled in the art.

[0056] exist Figure 4 In the figure, the "Zone 2" node ring 402 in the model 400 formed by the laid layers is connected into a single ring with a foldable portion according to the disclosed embodiment.

[0057] The system then constructs the bounding box of the resulting single ring. The bounding box of the domain is expressed as:

[0058]

[0059] Where N(x, y) represents the coordinates of the 2D node ring. Note that although specific examples may refer to 2D or 3D elements herein, the techniques and processes described herein may be applied to 2D or 3D parts, surfaces, elements, etc.

[0060] Next, the system generates a Cartesian grid over the bounding box. The Cartesian grid C is similar to the voxel grid and can be expressed as a component of n elements and qc nodes as:

[0061] C=∪(n,q c ) (1.3)

[0062] Figure 5A Cartesian grid 504 is illustrated over a resulting bounding box 506 of a single ring 502 in the model 500 in accordance with the disclosed embodiments.

[0063] The number of n elements generated is carefully calculated to reflect the user driven size of the area that needs to be meshed. The individual elements of the Cartesian grid are perfect squares. The coordinates of the m nodes are based on the extremes (a,b) or corner boundaries (0,0), (0,a), (a,b), (0,b) of the box.

[0064] In the resulting single ring ( Figure 4 ) and the Cartesian grid ( Figure 5 A Boolean operation is performed between the single ring (502) and the quadrilateral elements intersecting the single ring (502) and the quadrilateral elements intersecting the single ring (502) are deleted.

[0065] Figure 6 The diagram shows a schematic diagram of a system according to the disclosed embodiment. Figure 4 Ring 402 and Figure 5 An example of the result of such a Boolean action performed between a single ring and a Cartesian grid of Cartesian grid 504 to produce model 600. All elements in grid 604 that intersect ring 602 and fall outside of it are removed.

[0066] Figure 7 An example of a model 700 having a combination of elements in region 1 (eg, element 702 ) and elements in region 2 (eg, element 704 ) is illustrated in accordance with the disclosed embodiments.

[0067] The system then extracts the free element edges of the two detached meshes to form two separate node rings (these node rings may be referred to herein as region node rings).

[0068] Figure 8 The region node rings 802 and 804 in the model 800 are illustrated, and the region node rings 802 and 804 correspond to the free element edges of the region 1 and region 2 elements ( Fig. 9 ).

[0069] Then, the system uses a node ring joining process known to those skilled in the art to connect the two separate node rings. Once these node rings are joined, a single node ring ("single zone node ring") is created. This ring forms the area of ​​zone 3.

[0070] Fig. 9A third region 902 ("Region 3") is illustrated, in accordance with the disclosed embodiments, formed by connected node rings (single region node ring 904) in the model 900. Notably, Region 3 represents the long strip of space between Regions 1 and 2, both of which are regions having a very regular structured mesh with high quality and isotropic quadrilateral elements.

[0071] The system performs fine meshing in region 3. This narrow area in region 3 is meshed by the fine mesher process.

[0072] Fig.10 Illustrated is a subdivided mesh in a zone 3 area 1002 of a model 1000 in accordance with disclosed embodiments.

[0073] Fig.11 Model 1100 with a combination of grids in zone 2 and zone 3 for a dual combined grid 1102 is illustrated.

[0074] The system may perform a smoothing process on the combined mesh 1102 using a smoothing process such as that described in US Pat. No. 9,082,220, which is hereby incorporated by reference.

[0075] The system combines the two combined meshes (zone 2 and zone 3) with the mesh in zone 1 to produce a three combined mesh. Note that all three zones can be combined together to produce a three combined final mesh, or they can be combined in a different order to produce a three combined final mesh.

[0076] Fig.12 A three-combination final mesh 1202 is illustrated in the model 1200 as a combination of zones 1, 2, and 3 in accordance with the disclosed embodiments. Fig.12 The final grid of the three combinations in Figure 2 The multi-block meshes shown are compared. Sub-regions of the multi-block face are actively mapped for meshing.

[0077] If the subdivision mesher process creates p elements and q s nodes, the grid can be expressed as:

[0078] S=∪(p,q s ) (1.4)

[0079] Even without examining the various specific parameters traditionally used to measure the quality of quadrilateral elements (e.g., minimum / maximum element size, element angle, warp, taper, skew, Jacobian, aspect ratio, etc.), it is obvious from ordinary visual inspection that Figure 2 Compared to the illustrated multi-block and sub-region mapped grids, Fig.12How many elements of the Cartesian pavers in the tri-combination mesh are high quality, uniform, isotropic, well-angled, minimally skewed, and tapered.

[0080] The system can also transform the bounding box of the surface of the part (and / or the surface itself). In the above example, the bounding box of the surface is aligned with the global XY axes of the 2D domain where the meshing is performed. This alignment is not always possible.

[0081] Fig.13 An example of a surface 1300 having an axis at an angle to the XY plane represented by a grid 1302 is illustrated. The outer ring of the face to be meshed may be oriented at an angle to the XY axis. In this case, the system may determine the angle between the longest linear extension of the outer ring and the X axis and then determine a transformation matrix based on the angle. The system may use the transformation matrix to transform the node rings of the face so that they are parallel to the XY plane. A Cartesian grid C is generated in this transformed plane and is then used as shown in FIG. Figure 6 After truncation of the illustrated grid, the elements are inversely transformed to the original plane. Figures 13 to 16 This process is illustrated in the figure.

[0082] Fig.14 The diagram shows Fig.13 A Booleanized Cartesian grid 1402 on the surface 1400 in accordance with the disclosed embodiments.

[0083] Fig.15 A final mesh Cartesian tiler mesh 1502 generated on a surface 1500 in accordance with the disclosed embodiments is illustrated. Here, most quadrilateral elements are oriented at an angle relative to the ring axis.

[0084] Fig.16 The longest portion 1602 of the outer ring of the predominantly linear surface 1600 is illustrated, as well as a nodal ring detail 1604 of the portion 1602 .

[0085] like Fig.16 The ring angle deviation between consecutive nodes on the outer ring of the illustrated surface 1600 is given by:

[0086]

[0087] In various embodiments, the ring angle Must be less than the limit (In this example, Spend):

[0088]

[0089] The angle σ collected on the ring segment s It can be expressed as:

[0090]

[0091] In various embodiments, the collected angles σ s must be less than the limit (in this example, σ lim =7 degrees):

[0092] σ s <σ lim (1.8)

[0093] If the condition is met, the vector between points s1 and s2 Specified as the ring axis vector. makes an angle α with the global X axis. If X l represents the position of the node in the node ring in the local coordinate system, then the position vector in the transformed global coordinate system is given by:

[0094] X g =TX l (1.9)

[0095] The transformation matrix T is given by:

[0096]

[0097] Note that although Fig.15 The illustrated mesh is very high quality, structured, isotropic in the core, but the mesh is not oriented along the face boundaries. To address this issue, one or more face node rings can be transformed using the transformation in equation 1.9 above to:

[0098] L new (x,y)=[T]L orig (x,y) (1.11)

[0099] Among them, L orig specifies the original face node ring, and L new is a new ring of nodes in the transformed plane parallel to one of the global axes.

[0100] Figure 17 to Figure 18 The transformed node ring and the resulting Cartesian mesh are shown in .

[0101] Fig.17 An example of a surface 1700 having an axis translated to align with an XY plane 1702 is illustrated in accordance with the disclosed embodiments. One or more surface node rings are transformed so the rings are parallel to the X or Y axis of the meshed 2D domain.

[0102] Fig.18Illustrated is an example of a surface 1800 having axes that have been translated to be aligned with the XY plane, showing a Cartesian grid 1802 in the transformed plane, in accordance with disclosed embodiments.

[0103] The mesh is then truncated; then, it is inverse transformed back to its original plane and the above process is performed to produce the final mesh.

[0104] Fig.19 An example of a final mesh 1900 after an inverse transformation of the Cartesian portion is illustrated. Fig.15 and Fig.19 Comparison of reveals the variation in the orientation of the final grid 1900 along the ring axis.

[0105] The disclosed embodiments employ a unique hybrid meshing algorithm that provides substantial improvements to the ability of CAD systems to produce accurate and consistent quadrilateral meshes, and to model and manufacture corresponding parts. The disclosed mesh generation process uses specific meshing techniques in respective "zones" where each is most effective. The disclosed embodiments are examples of "intelligent meshers" where the system itself decides how to employ the best meshing method for a given meshing zone, and can automatically perform improved, more accurate meshing.

[0106] In some embodiments, a transfinite interpolation process is used as part of the tessellation process to increase its effectiveness in processing rectangular regions.

[0107] In an exemplary implementation of a given model using conventional techniques, 63% of the quadrilateral elements in the final mesh had angle deviations of + / - 10 degrees from the ideal quadrilateral shape (90 degree angle). This means that 64% of the quadrilateral elements had a worst case maximum angle of 100 degrees or less and a minimum angle of 80 degrees or more. Additionally, in this example, the subdivided multiblock mesher created 7.2% of the triangles in the quad-dominated mesh.

[0108] For the same model, the disclosed multi-zone Cartesian tiler meshing process produces a mesh in which 73% of the quadrilateral elements pass through a 10 degree variation from the ideal quadrilateral shape. Additionally, in this example, the disclosed multi-zone Cartesian tiler meshing process only creates 5.9% of the triangles.

[0109] The disclosed multi-zone Cartesian tiler meshing process is designed to be flexible. It can adjust the use of three meshing methods according to the geometry to be meshed. Each meshing method used produces a given number of elements for a given user-desired global element size. As described above, the tiler process produces m elements, the Cartesian mesher process produces n elements, and the subdivision process creates p elements. The size of the complete mesh generated by the disclosed multi-zone Cartesian tiler meshing process is given by the following formula:

[0110] M=∪(m,n,p) (1.12)

[0111] The ratio between the elements created by each method is expressed as:

[0112] m:n::p=a:b:c (1.13)

[0113] It is important to understand that equation 1.13 is not a constant. The ratios of a, b, and c vary depending on the shape of the surface being meshed. For example, if the surface is rectangular, then a=0, b=0, c=1. This means that the mesher employs basic shape recognition features with the help of which it achieves optimal meshing of this shape through the subdivision process because it has a built-in transfinite or mapped mesher and can generate a perfect all-quad mesh on such a shape. In contrast, if the face is wide and has regular boundaries, b will have a high ratio, followed by a and c decreasing to very small fractions. The disclosed multi-zone Cartesian tiler meshing process is intelligent enough to adjust the unfolding strength of the three meshing methods depending on the shape and complexity of the surface.

[0114] Many design and analysis processes for manufacturing products are performed in batches. Therefore, users do not want too much control and prefer automatic, push-button, batch-driven mesh generation and subsequent finite element analysis. More time is spent checking mesh quality and post-processing analysis results. If the quality of the generated mesh is high, the analysis time as well as the post-processing results are significantly reduced.

[0115] The disclosed multi-zone Cartesian tiler meshing process leverages the strengths of the three most commonly used meshing methods in the industry and invokes them selectively and intelligently to generate a very high quality, boundary structured, isotropic core mesh with weak unstructured transition zones that meet mesh quality requirements.

[0116] The disclosed multi-zone Cartesian pavers meshing process is fully automatic and does not require manual intervention and inspection. Very few meshing options need to be set for the mesher. The user can define the element size, and the system creates the most isotropic, high-quality mesh possible on the surface at the size desired by the user.

[0117] The disclosed multi-zone Cartesian tiler meshing process improves on other techniques in a number of ways. For example, the disclosed process employs a modification of CSALF-Q only on surface boundaries to generate only one or two layers of boundary structured meshes (except for regions where boundary loops self-intersect). Further, the deep portion of the surface is filled with a Cartesian mesh that brings high quadrilateral element quality and isotropy, and the narrow region between two zones is filled by a subdivision mesher that is a proven and robust meshing process.

[0118] Fig. 20 Process 2000 is illustrated in accordance with the disclosed embodiments, which process may be performed by a data processing system as disclosed herein, or by another system configured to perform the processes as described herein, which another system is generally referred to as a "system" hereinafter.

[0119] The system receives model data of a surface of a part to be manufactured (2002). The model data may be 2D model data or 3D solid model data. The data may include the entire model of the part (including the surface) or may include only a subset of elements of the model, the model including the surface. As used herein, receiving may include loading from a storage device, receiving from another device or process, receiving via interaction with a user, or other means. The surface includes at least one face ring (i.e., an outer boundary ring) and may include other rings (inner rings). These face rings may be referred to as "original rings" of the surface. As part of or after receiving the model data of the surface of the part to be manufactured, the system may translate or transform the bounding box of the surface to a different 2D or 3D coordinate domain, as described herein.

[0120] The system performs a loop laying process for a first portion of the surface to produce a first set of elements (2004). According to various embodiments, the first set of elements defines each original loop of the surface and defines a first zone. Note that the labels "first", "second", etc. are intended to distinguish various elements, zones, and processes from each other, and do not imply a required order of operations or that any one label requires elements with different labels. The loop laying process can be a combined subdivision and loop front quadrilateral (CSALF-Q) process. The first set of elements can define a set of second loops. The first set of elements can be in one or two layers. The first set of elements does not include any intersecting elements (i.e., if the process produces intersecting elements, these elements can be removed).

[0121] The system defines boundary node rings of the surface based on the first set of elements and joins the boundary node rings to produce a first single node ring (2006).

[0122] The system constructs a bounding box from the first single node ring (2008).

[0123] The system performs a Cartesian meshing process on a second portion of the surface according to the bounding box to generate a second set of elements (2010). According to various embodiments, the second set of elements defines a second region.

[0124] The system can perform a Boolean operation to remove from the second set of elements any elements in the second set of elements that intersect the first single node ring (2012).

[0125] The system defines region node rings of the surface based on the first set of elements and the second set of elements, and connects the region node rings to produce a single connected region node ring (2014).

[0126] The system performs a subdivision meshing process on a third portion of the surface according to the single region node ring to produce a third set of elements (2016). According to various embodiments, the third set of elements defines a third region.

[0127] The system may perform a mesh smoothing process (2018) on a combination of the second set of elements and the third set of elements.

[0128] The system combines the first set of elements, the second set of elements, and the third set of elements to produce a final mesh for the surface of the part to be manufactured (2020). As part of this process, the system can perform an inverse transformation of the above-described transformation process.

[0129] The system may store the model data of the surface of the part to be manufactured together with the final mesh (2022).

[0130] In some cases, the system can then manufacture the part based on the final mesh and model data (2024).

[0131] Fig.21 A block diagram of a data processing system in which an embodiment may be implemented is illustrated, for example as a CAD or PDM system, which is particularly configured by software or otherwise to perform a process as described herein, and particularly as each of a plurality of interconnect and communication systems as described herein. The depicted data processing system includes a processor 2102 connected to a secondary cache / bridge 2104, which in turn is connected to a local system bus 2106. The local system bus 2106 may be, for example, a peripheral component interconnect (PCI) architecture bus. In the depicted example, a main memory 2108 and a graphics adapter 2110 are also connected to the local system bus. The graphics adapter 2110 may be connected to a display 2111.

[0132] Other peripheral devices such as a local area network (LAN) / wide area network / wireless (e.g., Wi-Fi) adapter 2112 may also be connected to the local system bus 2106. An expansion bus interface 2114 connects the local system bus 2106 to an input / output (I / O) bus 2116. The I / O bus 2116 connects to a keyboard / mouse adapter 2118, a disk controller 2120, and an I / O adapter 2122. The disk controller 2120 may be connected to a storage device 2126, which may be any suitable machine-usable or machine-readable storage medium, including but not limited to non-volatile, hard-coded type media (such as read-only memory (ROM) or erasable, electrically programmable read-only memory (EEPROM), magnetic tape storage devices) and user-recordable type media (such as floppy disks, hard drives, and compact disk read-only memory (CD-ROM) or digital versatile disk (DVD)), and other known optical, electrical, or magnetic storage devices.

[0133] In the example shown, an audio adapter 2124 is also connected to the I / O bus 2116, to which a speaker (not shown) may be connected for playing sounds. A keyboard / mouse adapter 2118 provides a connection for a pointing device (not shown) such as a mouse, trackball, track pointer, touch screen, etc. The I / O bus 2116 may also be connected directly or via an I / O adapter 2122 to a manufacturing device 2128 for manufacturing parts according to the processes disclosed herein.

[0134] Those of ordinary skill in the art will understand that Fig.21 The depicted hardware may vary for a particular implementation. For example, other peripheral devices such as optical disk drives may be used in addition to or in place of the depicted hardware. The depicted examples are provided for illustration purposes only and are not meant to imply architectural limitations with respect to the present disclosure.

[0135] A data processing system according to an embodiment of the present disclosure includes an operating system that employs a graphical user interface. The operating system allows for the simultaneous presentation of multiple display windows in the graphical user interface, wherein each display window provides an interface to different applications or to different instances of the same application. A cursor in the graphical user interface can be manipulated by a user through a pointing device. The position of the cursor can change and / or generate an event such as clicking a mouse button to actuate a desired response.

[0136] If appropriately modified, one of a variety of commercial operating systems may be used, such as Microsoft Windows TM A version of Microsoft Corp. (a product of Microsoft Corporation located in Redmond, Washington) is provided. As described, the operating system is modified or created according to the present disclosure.

[0137] LAN / WAN / wireless adapter 2112 can be connected to a network 2130 (not part of data processing system 2100), which can be any public or private data processing system network or combination of networks known to those skilled in the art, including the Internet. Data processing system 2100 can communicate with server system 2140 via network 2130, which is also not part of data processing system 2100, but can be implemented as, for example, a separate data processing system 2100.

[0138] Of course, those skilled in the art will recognize that certain steps in the above processes may be omitted, performed simultaneously or sequentially, or performed in a different order unless the order of operations is specifically indicated or required.

[0139] Those skilled in the art will recognize that, for simplicity and clarity, the entire structure and operation of all data processing systems suitable for use with the present disclosure are not depicted or described herein. Instead, only the content of the data processing system that is unique to the present disclosure or necessary to understand the present disclosure is depicted and described. The remaining structure and operation of the data processing system 2100 may conform to any of a variety of current implementations and practices known in the art.

[0140] It is important to note that while the present disclosure includes a description in the context of a fully functional system, those skilled in the art will appreciate that at least portions of the mechanisms of the present disclosure can be distributed in the form of instructions contained within any of a variety of forms of machine-usable, computer-usable, or computer-readable media, and that the present disclosure applies equally regardless of the particular type of instruction or signal-bearing medium or storage medium used to actually perform the distribution. Examples of machine-usable / readable or computer-usable / readable media include non-volatile, hard-coded types of media such as read-only memory (ROM) or erasable, electrically programmable read-only memory (EEPROM) and user-recordable types of media such as floppy disks, hard drives, and compact disk read-only memory (CD-ROM) or digital versatile disks (DVD).

[0141] Various publications describe techniques related to the techniques disclosed herein, including the following, each of which is hereby incorporated by reference:

[0142] ·O.C.Zienkiewicz and D.V.Phillips,An automatic mesh generationscheme for plane and curved surfaces by‘isoparametric’co-ordinates,Int.Journal Num.Meth.Engg.,Vol.3,(4),pp.519-528,(1971).

[0143] ·M.L.Sluiter and D.L.Hansen.1982.A general purpose automatic meshgenerator for shell and solid finite elements,ASME Computers in Engg.,29-34.

[0144] ·N.P.Yerry,and M.S.Shephard,A modified quadtree approach to finiteelement mesh generation.IEEE Comp.Graps and Appls.3(1),pp.39-46,(1983).

[0145] ·T.Blacker and M.Stephenson,Paving:A new approach to automatedquadrilateral mesh generation,Int.Journal Num.Meth.Engg.,Vol.32,pp.811-847,(1991).

[0146] ·R.Schneiders,Automatic generation of hexahedral finite elementmeshes,Proc.4th Int.Meshing Roundtable,Albuquerque,NM,pp.130–114(Oct,1995).

[0147] ·M.Bern,D.Eppstein,Quadrilateral Meshing by Circle Packing,Int.J.Comput.Geom.Appl.Vol 10,p.347-360,(2000).

[0148] ·SJ Owen, ML Staten, SA Canann and S. Saigal, Q-MORPH: An Indirect approach to Advancing Front Quad Meshing, Int. J. Numer. Meth. Engng. 44, pp. 1317-1340, (1999).

[0149] ·J.Makem and N.Mukherjee,Mesh generation system and method,patentapplication,WO2017040006A1,Mar 09,2017.

[0150] ·N.Mukherjee, CSALF-Q: A Bricolage Algorithm for Anisotropic Quad MeshGeneration, Proc.XXth International Meshing Roundtable, Paris, France, pp.489-510, Springer, 2011.

[0151] ·J.Cabello, Toward Quality Surface Meshing, Proc.XIIth International Meshing Roundtable, Santa Fe, New Mexico, pp.201-213, (2003).

[0152] ·N.Mukherjee, System, method, and computer program product for smoothing, patent, US 9082220B2, July 14, 2015.

[0153] Although the exemplary embodiments of the present disclosure have been described in detail, those skilled in the art will understand that they may make various changes, substitutions, alterations, and improvements herein disclosed without departing from the spirit and scope of the disclosure in its broadest form.

[0154] The description in this application should not be read as implying that any particular element, step, or function is essential element that must be included in the scope of the claims: the scope of patented subject matter is limited only by the allowed claims. Moreover, none of these claims is intended to invoke 35 USC § 112(f) unless the exact words "means for..." are followed by a participle.

Claims

1. A method for gridding (2000), comprising: Receiving model data (2002) of a surface (210) of a part (200) to be manufactured; performing a loop paving process (2004) on a first portion of the surface (210) to generate a first set of elements (302, 304, 306), wherein the first set of elements (302, 304, 306) are isotropic quadrilateral elements; performing a Cartesian meshing process (2010) on a second portion of the surface (210) to generate a second set of elements (704), wherein the second set of elements (704) are isotropic quadrilateral elements; performing a subdivision meshing process (2016) on a third portion of the surface (210) to produce a third set of elements (1002); and The first group of elements (302, 304, 306), the second group of elements (704), and the third group of elements (1002) are combined (2020) to generate a final mesh (1202) for the surface (210) of the part (200) to be manufactured.

2. The method according to claim 1, further comprising: The part (200) is manufactured (2024) based on the final mesh (1202).

3. The method according to claim 1, further comprising: Defining a boundary node ring (2006) of the surface (210) based on the first set of elements (302, 304, 306); connecting the boundary node ring (2006) to produce a first single node ring (502); and constructing (2008) a bounding box (506) based on the first single node ring (502).

4. The method according to claim 1, wherein: The Cartesian gridding process (2010) is performed based on a bounding box (506) constructed based on the first set of elements (302, 304, 306).

5. The method according to claim 1, further comprising: Defining (2014) a zone node ring (802, 804) for the surface based on the first set of elements (302, 304, 306) and the second set of elements (704); and connecting (2014) the zone node rings (802, 804) to produce a single connected zone node ring (904).

6. The method according to claim 1, wherein: The subdivision meshing process (2016) is performed according to a single region node ring (904) based on the first set of elements (302, 304, 306) and the second set of elements (704).

7. The method according to claim 1, further comprising: A smoothing process (2018) is performed on a combination of the second group of elements (704) and the third group of elements (1002).

8. The method according to claim 1, further comprising: The bounding box of the surface is translated (2002) to a different 2D or 3D coordinate domain.

9. A data processing system (2100), comprising: Processor(2102); and An accessible memory (2108), the data processing system (2100) being particularly configured to execute a process according to any one of claims 1 to 8.

10. A non-transitory computer readable medium (2126) encoded with executable instructions that, when executed, cause one or more data processing systems (2100) to perform a process according to any one of claims 1 to 8.

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