Application of fuzzy logic for thin region detection in mesh generation

Abstract

A computer-implemented method of generating a thin volume grid in a computer-aided technology (CAx) model of an object is described. A volume region located between a first surface grid having a first set of grid parameters and a second surface grid having a second set of grid parameters is selected. The volume region has a thickness t corresponding to a distance between the first surface mesh and the second surface mesh. If the volume region is thin, a prismatic unit volume grid is generated to fill the entire volume region. Whether the volume region is thin or not is given from explicit values calculated using a fuzzy logical reasoning mechanism including fuzzy set thin and non-thin, and wherein the relationship between the first set of grid parameters and the second set of grid parameters and the thickness t determine the thin and non-thin membership of the fuzzy set.

Description

Technical Field

[0001] The present disclosure relates to a computer-implemented method for generating a thin volume mesh in a model of an object. Background Art

[0002] Computational Fluid Dynamics (CFD) simulations may rely on meshing techniques as part of finite element analysis or finite volume methods in order to be able to compute the transport of physical quantities on a discrete mesh. For example, Simcenter STAR-CCM+ available from Siemens AG (www.siemens.com) integrates meshing techniques as well as CAD (Computer-Aided Design), multi-physics CFD, and design exploration as part of the design process. Meshing is particularly advantageous for CFD modeling because it requires less computational investment than other surface and volume generation modeling techniques. The meshing process itself is the result of many different combinations of algorithms and data, all of which can be effective. Accepting a mesh modification or performing a particular action among a set of specific choices can be the result of a comparison between a stored value and a hard-coded threshold. Any complex meshing algorithm is full of such comparisons, each of which may or may not lead to an optimal result and can be selected based on the user's experience. Alternatively, such a choice can be the result of extensive testing that covers many but not all possible scenarios, where values are adjusted incrementally to find the best possible (or most reasonable) compromise. Additionally, during any given meshing run, variables typically remain very close to threshold values, so if a small perturbation is introduced in any upstream processing, it may lead to completely different decisions. As a result of the code evolving over time, such perturbations may occur easily.

[0003] One way to address these issues is to introduce human decisions into the process. However, this is not compatible with hard-coded constant thresholds and is difficult to implement in complex downstream computations such as CFD. Therefore, there is a need to overcome such problems in order to be able to improve the overall performance of meshing techniques and thus improve the modeling of physical quantities and the quality in product design. Summary of the Invention

[0004] The present disclosure aims to solve this problem by providing, in a first aspect, a computer-implemented method for generating a thin volume mesh in a computer-aided technology (CAx) model of an object, the method comprising: selecting a volume region located between a first surface mesh having a first set of mesh parameters and a second surface mesh having a second set of mesh parameters, the volume region having a thickness t corresponding to the distance between the first surface mesh and the second surface mesh; and generating a prismatic cell volume mesh to fill the entire volume region if the volume region is thin; wherein it is given by an explicit value calculated using a fuzzy logic inference mechanism including fuzzy sets thin and non-thin whether the volume region is thin, and wherein the relationship between the first set of mesh parameters and the second set of mesh parameters and the thickness t determine the membership degrees of the fuzzy sets thin and non-thin.

[0005] By using fuzzy logic means to determine the nature of the volume within the object in the CAx model, there is no longer a need for human decision-making to quantify "thin" or "non-thin", and thus no longer a need for human decision-making to determine whether a prismatic volume mesh can be used to fill the volume. Due to the improved quality of the generated mesh volume, this results in higher accuracy in subsequent CFD modeling.

[0006] Determining the fuzzy membership degrees of the fuzzy sets can include: selecting a source point S on the first surface mesh where a volume mesh is required, and measuring the surface mesh size SS at the source point, and calculating the deviation ρ of the triangle of the surface mesh at the source point S from a reference equilateral triangle S ; and by extending a ray along the local normal from the source point, selecting a target point T on the second surface mesh, measuring the surface mesh size TS at the target point, and calculating the deviation ρ of the triangle of the surface mesh at the target point T from the reference equilateral triangle T ; wherein if the ratios SS / t and TS / t are higher than a first reference value and a second reference value, the volume region is in the fuzzy set of thin, and wherein if the deviation ρ S or the deviation ρ T is higher than a third reference value, the volume region is in the fuzzy set of non-thin.

[0007] The first reference value and the second reference value can be given respectively by the following formulas:

[0008]

[0009] and

[0010]

[0011] The third reference value is given by the following formula:

[0012]

[0013] In these equations: S is the local mesh size of the first surface mesh, t is the thickness of the volume region, and σ is the standard deviation of the S / t ratio on the surface of the first surface mesh. is where ε = 10 -4 and PF is the percentage of vertices that are locally thin on the first mesh surface and p is the penalty factor.

[0014] The method may further include: combining, on an image, a plot representing the membership degree of the fuzzy set of thin with a plot representing the membership degree of the fuzzy set of non - thin using an OR operator; calculating the centroid of the area under the curve of the combined plot; and taking the centroid as a crisp value.

[0015] The object may include thin plates or thin walls.

[0016] The model may be a computational fluid dynamics (CFD) model.

[0017] The fuzzy - logic inference mechanism may be a Mamdani inference mechanism.

[0018] In some examples, the thin volume mesh may not contain any volume cells.

[0019] The present disclosure also provides, in a second aspect, a computer program including instructions that, when executed by a computer processor, cause the computer to perform the steps of the above - described method.

[0020] The present disclosure also provides, in a third aspect, a data - processing system including: an input device adapted to receive a selection of a volume region located between a first surface mesh having a first set of mesh parameters and a second surface mesh having a second set of mesh parameters, the volume region having a thickness t corresponding to the distance between the first surface mesh and the second surface mesh; and a processor adapted to generate a prismatic - cell volume mesh to fill the entire volume region; wherein a crisp value calculated by the processor using a fuzzy - logic inference mechanism including the fuzzy sets of thin and non - thin gives whether the volume region is thin, and wherein the relationship between the first set of mesh parameters and the second set of mesh parameters and the thickness t determine the membership degrees of the fuzzy sets of thin and non - thin. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present disclosure is now described only by way of example and with reference to the drawings, in which:

[0022] Figure 1 shows the value with respect to a plot;

[0023] Figure 2 is an example of a mesh portion for which thinness needs to be determined.

[0024] Figure 3 is a plot of the first membership function for the "thin" attribute according to an embodiment of the present disclosure;

[0025] Figure 4 is a plot of the second membership function for the "thin" attribute according to an embodiment of the present disclosure;

[0026] Figure 5 is a plot of the membership function for the "not thin" attribute according to an embodiment of the present disclosure;

[0027] Figure 6 a is a plot of not thin vs. thin based on values of the membership function for not thin;

[0028] Figure 6 b is a plot of not thin vs. thin based on values of the membership function for thin;

[0029] Figure 6 c is a combined plot of not thin and thin for the position under analysis;

[0030] Figure 7 is a flowchart of a method according to an embodiment of the present disclosure;

[0031] Figure 8 a is a perspective view of a three-dimensional curved thin plate having a meshed surface modeled with hard-coded tolerances;

[0032] Figure 8 b is a perspective view of a three-dimensional curved thin plate having a meshed surface modeled with an embodiment of the present disclosure;

[0033] Figure 8 c is Figure 8 an alternative perspective view of a portion of the thin plate shown in a;

[0034] Figure 8 d is Figure 8 an alternative perspective view of a portion of the thin plate shown in b;

[0035] Figure 8 e is Figure 8 an alternative perspective view of a portion of the thin plate shown in a;

[0036] Figure 8 f is Figure 8 an alternative perspective view of a portion of the thin plate shown in b;

[0037] Figure 9 a is a perspective view of a three-dimensional complex component having a meshed surface modeled with hard-coded tolerances;

[0038] Figure 9 Figure b is a perspective view of a three-dimensional complex component having a meshed surface modeled using an embodiment of the present disclosure;

[0039] Figure 9 Figure c is Figure 9 an alternative perspective view of a portion of the component shown in Figure a;

[0040] Figure 9 Figure d is Figure 9 an alternative perspective view of a portion of the component shown in Figure b;

[0041] Figure 9 Figure e is Figure 9 an alternative perspective view of a portion of the component shown in Figure a;

[0042] Figure 9 Figure f is Figure 9 an alternative perspective view of a portion of the component shown in Figure b; and

[0043] Figure 10 An example of a data processing system in which embodiments of the present disclosure may be implemented is shown, such as a CAx system configured to perform the processes described in this application. DETAILED DESCRIPTION

[0044] In addition to human intervention, techniques for making decisions include fuzzy logic, which introduces flexibility by intelligently relaxing fixed metric boundaries. Fuzzy logic is a more human-like means of determining the truth value of a given statement while maintaining the rules behind classical "sharp" logic, such as commutativity, associativity, distributivity, and transitivity. Since the development of fuzzy logic in the 1960s, it has been explored and extended to many different fields, including facial recognition, weather forecasting, and subway control, to name just a few. However, such techniques have not been widely applied to fields such as meshing. The embodiments utilize the advantages of fuzzy logic and apply them to the decision-making process in a dedicated mesher within a CAx (computer-aided technology) model, which is designed to appropriately identify and handle arbitrarily complex geometries within local thin regions. Local thin regions occur in objects such as thin plates and thin walls, particularly those used in fluid flow applications, including pipes, airfoils, and cooling devices, to name just a few. This is done by initially selecting a volume region located between a first surface mesh having a first set of mesh parameters and a second surface mesh having a second set of mesh parameters. The volume region has a thickness t corresponding to the distance between the first surface mesh and the second surface mesh. If the volume region is thin, a prismatic cell volume mesh will be generated to fill the entire volume region. Whether the volume region is thin is given by a crisp value calculated using a fuzzy logic inference mechanism that includes the fuzzy sets thin and non-thin, and wherein the relationship between the first set of mesh parameters and the second set of mesh parameters and the thickness t determine the membership degrees of the fuzzy sets thin and non-thin. This methodology is described in more detail below.

[0045] Fuzzy Logic

[0046] By way of background, the fuzzy logic concepts employed by the embodiments are now described. Consider a crisp set X containing three entries:

[0047] X = {x1, x2, x3}

[0048] A subset Y = {x2} can be expressed through the concept of membership degrees associated with each entry of X. In strict or Boolean logic, this is a value that can be either 0 (the entry is not within the subset) or 1 (the entry is included within the subset):

[0049] Y = {(x1, 0), (x2, 1), (x3, 0)}

[0050] When processed in fuzzy logic, this subset becomes:

[0051] Y = {(x1, μ Y (x1)), (x2, μ Y (x2)), (x3, μY (x3))}

[0052] where 0 ≤ μ Y (x) ≤ 1 is the membership function. An entry can belong to subset Y only partially, which is a completely new property compared to strict logic. All standard properties (such as commutativity, associativity, distributivity, idempotency, transitivity) are still maintained, and all known operations on sets can be generalized appropriately. Three examples are given below.

[0053] (Example 1) Complement:

[0054] · Boolean logic: Who does not belong to the set?

[0055] · Fuzzy logic: To what extent does an element not belong to the set?

[0056] Thus, if A is defined as:

[0057] A = {(x1, μ A (x1)), (x2, μ A (x2)), (x3, μ A (x3))}

[0058] The complementary set is then defined as:

[0059] not(A) = {(x1, 1 - μ A (x1)), (x2, 1 - μ A (x2)), (x3, 1 - μ A (x3))}

[0060] (Example 2) Intersection:

[0061] · Boolean logic: Which elements belong to both sets?

[0062] · Fuzzy logic: To what extent does an element lie in both sets?

[0063] Thus, if A = {(x, μ A (x))} and B = {(x, μ B (x))}, then their intersection is defined as:

[0064] A ∩ B = {(x, μ A∩B (x))} = min[μ A (x), μ B (x)] = μ A (x) ∩ μ B (x)

[0065] (Example 3) Union

[0066] · Boolean logic: Which elements belong to either set?

[0067] · Fuzzy logic: To what extent does an element belong to any set?

[0068] · Thus, if A = {(x, μ A (x))} and B = {(x, μ B (x))}, then their union is defined as:

[0069] A ∪ B = {(x, μ A∪B (x))} = max[μ A (x), μ B (x)] = μ A (x) ∪ μ B (x)

[0070] The most commonly used fuzzy inference technique is the so-called Mamdani method, which can be summarized as follows:

[0071]

[0072] Now describe the application of these techniques to "thin meshing" in the embodiments. Thin meshing is the process of finding the locally thin (below a threshold determined by the mesh geometry) parts in a mesh and generating a well-shaped prismatic mesh in that thin part, which also requires the mesh faces in the thin part to be well-aligned to create such well-shaped elements. Filling the regions of the model with prismatic elements produces better results than using only arbitrary volume elements. However, doing so can be computationally expensive, so it is very important to find an ideal compromise between the numerical accuracy of determining what is and what is not a thin mesh part and the required computational cost.

[0073] Fuzzy Parameters, Definitions and Rules for Thin Meshing

[0074] The following definitions are used in the specification:

[0075] · SS (Source Size): The local surface mesh size at a specific location (source) where the thinness of the model is examined;

[0076] · TS (Target Size): The size of the surface mesh near the intersection point (target) between the mesh surface and the ray emitted from the source point along its local normal direction;

[0077] · t (Thickness): The length of the line segment between the source point and the target point;

[0078] · A measure of the deviation of a triangular mesh face from a reference equilateral triangle, where R circum and r inscr are the circumradius and inradius respectively. 1 ≤ ρ ≤ ∞, where the larger the value, the greater the deviation;

[0079] · PF (Projection Factor): The percentage of mesh vertices on a given mesh surface that are clearly locally very thin. 1 ≤ PF ≤ ∞, where 0 means no mesh surface vertices belong to any thin part, and 1 means all mesh surface vertices are thin.

[0080] This gives rise to two definitions for what is thin and what is non-thin in a vague sense for a part of the mesh surface:

[0081] 1. If ( large and large) - the part is thin; and

[0082] 2. If (ρ source large and ρ target large) - the part is non-thin.

[0083] Statement 1 identifies parts with decreasing thickness as thin, and statement 2 assumes that highly stretched triangles can correspond to mesh faces on the model surface located on the sides of the defined thin parts. For and both, "large" can mean giving a standard lower bound of 2. However, in the method of the embodiment, two variables and independent reference values are applied (where S is the local mesh size):

[0084]

[0085] and

[0086]

[0087] where σ is defined as the standard deviation of the ratio on the mesh surface, and where ε has a small value set to 10 －4 .

[0088] This results in:

[0089]

[0090] Thus:

[0091] [0, ∞] → [1, 2] and [0, 1] → [2, 1]

[0092] In this way, as long as the standard deviation of such a ratio is small (assuming a given mesh surface size, the thickness is almost constant), or almost all vertices have been successfully projected (the part is almost completely marked as thin), the lower bound is reduced to account for and The value is large towards the orientation value 1. These conditions should enhance the thinness of this part; otherwise, the lower bound of the large ratio tends to the default value j. Initially, this default value was set to 2. and The value indicates whether this part is to be considered "thin" when it reaches a "reasonably large" value. However, it may be desirable to represent the default value j as changing over time to make sense for the particular surface being modeled. For a part with a constant thickness, it is more likely that such a part can be considered "thin", and thus the default value j tends to the value 1. This adds a further "fuzziness" variable to the model. Similarly, The value can be regarded as another fuzzy variable. Returning to Figure 1 , The value may change due to a change in the value, where for a zero value, for this part to be considered thin, the value should be greater than 1, and when the value is around 6, for this part to be considered thin, the value should be greater than 2.5. The projection factor PF initially has a value of 0 because at each vertex, no adjacent vertices are projected to new positions as part of determining the thinness of the part. However, as the exploration of this thinness continues, if the part is determined to be thin, then ultimately all adjacent vertices have been projected such that the projection factor PF = 1.

[0093] Modify each of the above expressions for the ratio to increase the calculated fuzziness:

[0094]

[0095] and

[0096]

[0097] where p is a penalty factor for large values of σ and is set to a value of 0.2. Its effect is shown in Figure 1 which is a plot showing the value of versus . The purpose of the parameter p is to increase the asymptotic value of the lower bound such that parts with very irregular thickness (large σ) or with very few thin regions (large → small FP) are penalized in terms of the thin condition.

[0098] This leads to the adoption of the last three statements in the embodiment:

[0099] 1a If ( and ), then this part is thin in the fuzzy sense;

[0100] 1b If ( and ), then this part is thin in the fuzzy sense;

[0101] 2 If ( or ), where serves as the lower bound of the large value of ρ, then this part is non - thin in the fuzzy sense.

[0102] Mamdani Mechanism for Thin Meshing

[0103] Figure 2 Shows an example of an embodiment according to the described method. Figure 2 Is an example of a mesh part for which thinness needs to be determined. Mesh part 1 includes a first mesh surface 2 and a second mesh surface 3 separated from each other. The first mesh surface 2 includes a plurality of mesh vertices 4a, 4b, 4c, 4d, 4e, 4f, 4g separated from each other by a plurality of mesh faces 5a, 5b, 5c, 5d, 5e, 5f. The second mesh surface 3 includes a plurality of mesh vertices 6a, 6b, 6c, 6d separated from each other by a plurality of mesh faces 7a, 7b, 7c. The size of the local mesh at the source point S is given by the source size SS of 0.045 size units. The size of the local mesh at the target point T is given by the target size TS of 0.18 size units. The thickness t of part 1 is 0.09 size units, which is equal to the spacing between the first mesh surface 2 and the second mesh surface 3. Using the equations above, the following values are provided:

[0104] ρ source = 1.3, ρ target = 1.5

[0105] Depending on the value of σ (which is related to the geometry of the mesh and its discretization) and the value of PF (which is related to the extent to which this part has been detected as thin when the check is performed), different situations may occur. For this example, consider the following values:

[0106] p = 0.2, σ = 0.01, such that

[0107]

[0108] Figure 3 Is a plot of the first membership function for the "thin" attribute according to an embodiment of the present disclosure. The value of is plotted along the x - axis, so that the value 1.006 on the x - axis is plotted at 1 on the y - axis. Reading the value of on the x - axis provides a y - axis value of 0.497, and The value provides a y-axis value of 1.

[0109] Figure 4 It is a plot of the second membership function for the "thin" attribute according to an embodiment of the present disclosure. The values are plotted along the x-axis, so that the value 2.5 on the x-axis is plotted at the value 1 on the y-axis. Reading the values provides a y-axis value of 0.2, and the value provides a y-axis value of 0.8.

[0110] Applying the "AND" operator of fuzzy logic to determine whether the part is thin provides the following:

[0111] 1a If is thin and is thin, then the part is 49.7% thin;

[0112] 1b If is thin and is thin, then the part is 20% thin.

[0113] For the second statement, the values of ρ source and ρ target (1.3 and 1.5 respectively) can be plotted in a similar manner.

[0114] Figure 5 It is a plot of the membership function for the "not thin" attribute according to an embodiment of the present disclosure. ρ is plotted on the x-axis, where the upper bound of ρ is given as 1.8, equal to the value 1 on the y-axis, the ρ source value of 1.3 gives a value of 0.375 on the y-axis, and the ρ target value of 1.5 gives a value of 0.625 on the y-axis. The second statement then gives:

[0115] 2(ρ source is 37.5% not thin or ρ target is 62.5% not thin) - the part is 62.5% not thin.

[0116] By combining the two charts to give the final relationship of thin or not thin, as shown in Figure 6 a, Figure 6 b and Figure 6 c. Figure 6 a is a plot of not thin vs. thin based on the values of the membership function for not thin, while Figure 6 b is a plot of not thin vs. thin based on the values of the membership function for thin. Plotting and combining the charts for the values obtained by analyzing the above first and second statements gives Figure 6 c, i.e., the combined plot of not thin and thin for the analyzed position.Figure 6 c is Figure 6 the union of a and Figure 6 b, and the standard method for determining the clear value of thin or non - thin is to take the centroid of the area under the curve. For the analyzed positions that fall within the non - thin part of the drawing, the grid is considered non - thin at that position.

[0117] Figure 7 is a flowchart of a method according to an embodiment of the present disclosure. Method 700 starts at step 702, where a volume region located between a first surface mesh having a first set of mesh parameters and a second surface mesh having a second set of mesh parameters is selected. The volume region has a thickness t corresponding to the distance between the first surface mesh and the second surface mesh. If the volume region is thin, then at step 704, a prismatic cell volume mesh is generated to fill the entire volume region. As described above, whether the volume region is thin is given by a clear value calculated using a fuzzy logic inference mechanism including the fuzzy sets thin and non - thin. The relationship between the first set of mesh parameters and the second set of mesh parameters and the thickness t determine the membership degrees of the fuzzy sets thin and non - thin. In a first sub - step 704a, a source point S requiring a volume mesh is selected on the first surface mesh, and the surface mesh size SS at the source point is measured. In sub - step 704b, the deviation ρ of the triangle of the surface mesh at the source point S from a reference equilateral triangle is calculated S . Next, in sub - step 704c, a target point T is selected on the second surface mesh by extending a ray along the local normal from the source point, and the surface mesh size TS at the target point is measured. In sub - step 704d, the deviation ρ of the triangle of the surface mesh at the target point T from the reference equilateral triangle is calculated T . If the ratios SS / t and TS / t are higher than a first reference value and a second reference value, then the volume region is in the fuzzy set of thin, and wherein, if the deviation ρ S or the deviation ρ T is higher than a third reference value, then the volume region is in the fuzzy set of non - thin. In sub - step 704e, the plot representing the membership degree of the fuzzy set of thin is combined with the plot representing the membership degree of the fuzzy set of non - thin using the OR operator. In sub - step 704f, the centroid of the area under the resulting curve of the combined plot is calculated. In step 704g, the centroid is taken as the clear value of whether the volume is thin or non - thin.

[0118] The method according to an embodiment of the present disclosure is particularly useful in determining whether a plate or thin - wall of an object in a CAx model is locally thin. This avoids generating arbitrary volumes in locally thin regions, thus obtaining more accurate results when modeling the physical properties of materials and the designed product. In Figure 8 a to Figure 8 f and Figure 9 a to Figure 9Shown in f is a comparison between determining whether a region is locally thin based on hard-coded strict logic and the above method.

[0119] Figure 8 a is a perspective view of a three-dimensional curved thin plate having a meshed surface modeled using hard-coded tolerances. It can be seen that only a small portion of the volume of the thin plate is determined to be locally thin. However, Figure 8 b is a perspective view of a three-dimensional curved thin plate having a meshed surface modeled using the embodiments herein. Here it can be seen that a large portion of the volume of the thin plate in the view is determined to be locally thin. Figure 8 c is Figure 8 an alternative perspective view of a portion of the thin plate shown in a, and Figure 8 d is Figure 8 an alternative perspective view of a portion of the thin plate shown in b. Similarly, Figure 8 e is Figure 8 an alternative perspective view of a portion of the thin plate shown in a, and Figure 8 f is Figure 8 an alternative perspective view of a portion of the thin plate shown in b. In each case, the embodiments herein enable a larger volume of the thin plate to be determined as thin and thus filled with prismatic meshes.

[0120] Figure 9 a is a perspective view of a three-dimensional complex component having a meshed surface modeled using hard-coded tolerances. Only a small portion of the volume of the highlighted region is determined to be locally thin. However, Figure 9 b is a perspective view of a three-dimensional complex component having a meshed surface modeled using the embodiments herein. Here it can be seen that a large portion of the volume of the highlighted region has been determined to be locally thin. Figure 9 c is Figure 9 an alternative perspective view of a portion of the component shown in a, and Figure 9 d is Figure 9 an alternative perspective view of a portion of the component shown in b. Similarly, Figure 9 e is Figure 9 an alternative perspective view of a portion of the component shown in a, and Figure 9 f is Figure 9 an alternative perspective view of a portion of the component shown in b. In each case, the embodiments herein enable a larger volume of the component in different regions to be determined as thin and thus filled with prismatic meshes.

[0121] Figure 10An example of a data processing system in which embodiments of the present disclosure may be implemented is shown, such as a CAx system configured to perform the processes described in this application. The data processing system 20 includes a processor 21 connected to a local system bus 22. The local system bus connects the processor to a main memory 23 and a graphics display adapter 24, and the display adapter may be connected to a display 25. The data processing system may communicate with other systems via a wireless user interface adapter connected to the local system bus 22 or via a wired network connected to, for example, a local area network. Additional memory 26 may also be connected via the local system bus. Suitable adapters (such as a wireless user interface adapter 27) for other peripheral devices (such as a keyboard 28 and a mouse 29 or other pointing devices) allow a user to provide input to the data processing system. They allow selection of an area of a plate-like or thin-walled object to determine the local thin nature of the volume of the meshed volume. Other peripheral devices may include one or more I / O controllers, such as a USB controller, a Bluetooth controller, and / or a dedicated audio controller (connected to a speaker and / or a microphone). It can also be understood that various peripheral devices may be connected to the USB controller (via various USB ports), and these peripheral devices include input devices (such as a keyboard, a mouse, a touch screen, a trackball, a camera, a microphone, a scanner), output devices (such as a printer, a speaker), or any other type of device operable to provide input to or receive output from the data processing system. Furthermore, it can be understood that many devices referred to as input devices or output devices may both provide input for communicating with the data processing system and receive output for communicating with the data processing system. Additionally, it can be understood that other peripheral hardware connected to the I / O controller may include any type of device, machine, or component configured to communicate with the data processing system.

[0122] The operating system included in the data processing system enables the output from the system to be displayed to the user on the display 25 and enables the user to interact with the system. Examples of operating systems that may be used in the data processing system may include Microsoft Windows TM , Linux TM , UNIX TM , iOS TM and Android TM operating systems.

[0123] Furthermore, it can be understood that the data processing system 20 may be implemented as a networked environment, a distributed system environment, a virtual machine in a virtual machine architecture, and / or a cloud environment. For example, the processor 21 and associated components may correspond to virtual machines executing in a virtual machine environment of one or more servers. Examples of virtual machine architectures include VMware ESCi, Microsoft Hyper-V, Xen, and KVM.

[0124] One of ordinary skill in the art will appreciate that the hardware described with respect to data processing system 20 may vary for a particular implementation. For example, data processing system 20 in this example may correspond to a computer, a workstation, and / or a server. However, it is understood that alternative embodiments of a data processing system may be configured with corresponding or alternative components, such as in the form of a mobile phone, a tablet computer, a controller board, or any other system that is operable to process data and perform the functions and features associated with the operation of the data processing system, computer, processor, and / or controller described in this application. The examples described are provided for illustrative purposes only and are not meant to imply architectural limitations with respect to the present disclosure.

[0125] Data processing system 20 may be connected to a network (not part of data processing system 20), which may be any public or private data processing system network or combination of networks known to those of skill in the art, including the Internet. Data processing system 20 may communicate with one or more other data processing systems, such as servers (also not part of data processing system 20), via the network. However, alternative data processing systems may correspond to multiple data processing systems implemented as part of a distributed system, where processors associated with several data processing systems may be in communication via one or more network connections and may collectively perform tasks described as being performed by a single data processing system. Thus, it should be understood that when referring to a data processing system, such a system may be implemented across several data processing systems that are organized in a distributed system and communicate with each other via a network.

Claims

1. A computer-implemented method for generating a thin volume mesh in a computer-aided technology (CAx) model of an object, the method comprising: Select a volume region between a first surface mesh having a first set of mesh parameters and a second surface mesh having a second set of mesh parameters, the volume region having a thickness t corresponding to the distance between the first surface mesh and the second surface mesh; And If the volume region is thin, generate a prismatic cell volume mesh to fill the entire volume region; Wherein, the thinness of the volume region is given by a crisp value calculated using a fuzzy logic inference mechanism including the fuzzy sets thin and non - thin, and Wherein, the relationship between the first set of mesh parameters and the second set of mesh parameters and the thickness t determine the membership degrees of the fuzzy sets thin and non - thin.

2. The method according to claim 1, wherein, Determining the membership degrees of the fuzzy sets includes: Select a source point S for which a volume mesh is required on the first surface mesh, measure the surface mesh size SS at the source point, and calculate the deviation ρ of the triangle of the surface mesh at the source point S from a reference equilateral triangle S ; and A target point T is selected on the second surface mesh by extending a ray along the local normal from the source point, the surface mesh size TS at the target point is measured, and the deviation ρ of the triangle of the surface mesh at the target point T from the reference equilateral triangle is calculated T ; Wherein, if the ratios SS / t and TS / t are higher than a first reference value and a second reference value, the volume region is in the fuzzy set of thin, and wherein, if the deviation ρ S or the deviation ρ T is higher than a third reference value, the volume region is in a non-thin fuzzy set.

3. The method according to claim 2, wherein, The first reference value is given by the following formula: Wherein, the second reference value is given by the following formula: Wherein, the third reference value is given by the following formula: Where: S is the local mesh size of the first surface mesh, t is the thickness of the volume region, σ is the standard deviation of the S / t ratio on the surface of the first surface mesh, Yes where ε = 10 -4 and PF is the percentage of vertices that are locally thin on the first grid surface, and p is a penalty factor.

4. The method according to claim 3, further comprising: Combine, on an image, the plot representing the membership degree of the fuzzy set of thin with the plot representing the membership degree of the fuzzy set of non - thin using the OR operator; Calculate the centroid of the area under the curve of the combined plot; And Take the centroid as the crisp value.

5. The method according to claim 1, wherein, The object includes thin plates or thin walls.

6. The method according to claim 1, wherein, The model is a computational fluid dynamics (CFD) model.

7. The method according to claim 1, wherein, The fuzzy logic inference mechanism is a Mamdani inference mechanism.

8. The method according to claim 1, wherein, The thin volume mesh does not contain any volume cells.

9. A computer program comprising instructions which, when executed by a computer processor, cause the computer to perform the steps of the method according to any one of claims 1 to 8.

10. A data processing system adapted to generate a thin volume mesh in a computer-aided technology (CAx) model of an object, the data processing system comprising: An input device, the input device being adapted to receive a selection of a volume region between a first surface mesh having a first set of mesh parameters and a second surface mesh having a second set of mesh parameters, the volume region having a thickness t corresponding to the distance between the first surface mesh and the second surface mesh; And A processor, the processor being adapted to generate a prismatic cell volume mesh to fill the entire volume region; Wherein, the thinness of the volume region is given by a crisp value calculated by the processor using a fuzzy logic inference mechanism including the fuzzy sets thin and non - thin, and wherein the relationship between the first set of mesh parameters and the second set of mesh parameters and the thickness t determine the membership degrees of the fuzzy sets thin and non - thin.

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