Shadow-based component finite element analysis

Abstract

Illustrative embodiments operate in a computer-aided design environment to facilitate finite element analysis of a multi-component system that includes a master component coupled to a slave component. An example embodiment projects a shadow of an end of the slave component and obtains mesh nodes on a surface of the master component from the shadow. An example embodiment then forms a mesh from the mesh nodes, which is input to a finite element analysis engine.

Description

[0001] Related applications

[0002] This application claims priority to U.S. Patent Application No. 18 / 414,274 [Attorney No. 37402-20801], filed January 16, 2024, entitled “Shadow-Based Component FiniteElement Analysis”, inventor: Ravintra Ozarker.

[0003] The public information of each of the foregoing is incorporated herein by reference in its entirety. Technical Field

[0004] The illustrative embodiments of the present invention generally relate to the computer-aided design of physical systems, and more specifically, various embodiments relate to the finite element analysis of physical systems. Background Technology

[0005] Finite element analysis (“FEA”) is a computer-implemented process that uses models and simulations to analyze physical objects in order to evaluate how the objects will behave under various physical conditions.

[0006] For example, engineers designing new (i.e., structures that have not yet been built) structures typically perform finite element analysis on a model of the structure before finalizing the design to determine whether the design is structurally sound.

[0007] For pre-existing structures, engineers may wish to perform finite element analysis (FEM) and quickly obtain a rough assessment. Performing FEM on a pre-existing structure is more difficult than on a structure under design but not yet built, because the pre-existing structure may have been designed by older engineers using older design codes and principles, and this can become even more challenging if an accurate and up-to-date model of the pre-existing structure is unavailable. Typically, before performing FEM, engineers must first create one or more models of the existing structure, or at least a subset of its components.

[0008] Many design engineers use computer-aided design systems (CADS) to design new structures. Some CAS have finite element analysis capabilities. In the past, engineers would use complex and difficult-to-use software separate from CAD systems to perform finite element analyses. These products would use three-node plate elements or six-node wedge elements with different local axes. For the average practical engineer, understanding the stress direction and results to make their designs acceptable is very difficult.

[0009] One challenge of these FEA-based processes is the complexity of requiring proper connections between components. This task requires engineers to examine the boundaries of parts and identify common points, which can be extremely difficult, even with seemingly simple issues like piping connections to a ship. Summary of the Invention

[0010] The illustrative embodiments operate in a computer-aided design environment to facilitate finite element analysis of a multi-component system, which includes a master component connected to subordinate components.

[0011] Performing finite element analysis on an object or system typically requires the user to have considerable experience in preparing the model of the object or system before performing the finite element analysis. Such a user must be experienced in preparing the model and inputs used for the finite element analysis.

[0012] Conversely, exemplary embodiments enable CAD operators to perform finite element analysis on multi-component systems, even when the CAD operator has no experience in preparing models and inputs for finite element analysis.

[0013] Furthermore, performing finite element analysis on existing structures is more difficult than performing it on structures that have not yet been built but exist in CAD models. This is because, at least in part, a model of the existing structure must be created to serve as input for the finite element analysis. The illustrative examples enable CAD operators to perform finite element analysis on pre-existing structures by more easily creating models of those structures, even when a CAD model of the pre-existing structure is unavailable.

[0014] An exemplary embodiment projects a shadow on the end of the subordinate component and obtains mesh nodes on the surface of the main component from the shadow. The exemplary embodiment then forms a mesh from the mesh nodes, which is input into the finite element analysis engine.

[0015] The first embodiment includes a method for performing finite element analysis on a digital model of the interface between a primary component and a secondary component of a physical device in a computer. The method includes: A first digital model of the main component is obtained, the main component having a main surface; Obtain a second digital model of the subordinate component, which has a longitudinal axis and a cross-section defining the connecting plane; Orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; then The shadow of the cross-section of the subordinate component is projected onto the surface where the subordinate component intersects the surface, and the shadow defines a contour at its outer edge, the contour being the intersection curve between the main component and the subordinate component.

[0016] The method further includes identifying a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points on the surface of the main component that form the outline of the shadow; Identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; and A mesh is defined by comprising multiple mesh elements, each mesh element being defined by a set of points from a first set of principal surface points and a second set of principal surface points.

[0017] The method also includes submitting the mesh to the finite element analysis system and performing finite element analysis on the mesh.

[0018] In some embodiments, the surface is the surface of the main component.

[0019] In some embodiments, casting the shadow of the cross-section of the dependent component onto the surface includes: An intermediate shadow of the cross-section of the subordinate component is created on a two-dimensional shadow plane, the shadow plane being parallel to a tangent plane that is tangent to the main surface at the intersection point where the subordinate component intersects the main surface. The shadow has an outer edge and defines a contour at the outer edge of the shadow, the contour being the intersection curve between the shadow plane and the subordinate component. Select the midpoint on the intersecting curves; and The midpoint is translated onto the main surface to generate the first set of main surface points.

[0020] In some such embodiments, the shadow plane is coplanar with the tangent plane.

[0021] In some such embodiments, the main surface includes a flat surface defining a two-dimensional plane, and said flat surface includes a two-dimensional shadow plane.

[0022] In some such embodiments, the surface is a primary surface, and the primary surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the primary component, the floating surface being perpendicular to the line perpendicular to the primary surface at the intersection.

[0023] In some embodiments, the second set of points is located radially outside the first set of points relative to the intersection point.

[0024] In some such embodiments, shadows are cast by parallel light rays.

[0025] Another embodiment includes a system for performing finite element analysis on a digital model of an interface between a master component specified by a first digital model and a slave component specified by a second digital model, the slave component having a longitudinal axis and a cross-section defining a connection plane. In such an embodiment, the system includes: A CAD module configured to provide the first digital model and the second digital model; An orientation module configured to orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; A shadow module configured to project the shadow of the cross-section of the subordinate component onto a surface where the subordinate component intersects the surface, the shadow defining a contour at the outer edge of the shadow, the contour being an intersection curve between the main component and the subordinate component; A dot module configured to identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points forming the outline of the shadow on the surface of the main component; The point module is also configured to identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh module configured to define a mesh comprising multiple mesh elements, each mesh element being defined by a set of points from the first set of principal surface points and the second set of principal surface points; and The finite element analysis module is configured to submit the mesh to the finite element analysis system and perform finite element analysis on the mesh.

[0026] In some embodiments of the system, the surface is the surface of the main component, and the shadow module is configured to project the shadow of the cross-section of the subordinate component onto the surface of the main component.

[0027] In some embodiments, the CAD module is further configured to provide a two-dimensional shadow plane parallel to a tangent plane at the intersection point of the subordinate component and the main surface on the main surface, and...

[0028] The shadow module is configured to create an intermediate shadow of the cross-section of the subordinate component on a shadow plane, the intermediate shadow having an outer edge and defining a contour at the outer edge of the intermediate shadow, the contour being an intersecting curve between the main component and the subordinate component; The point module is configured to select the midpoint on intersecting curves; and The intermediate point is translated onto the main surface to generate the first set of main surface points.

[0029] In some such embodiments, the tangent planes are coplanar.

[0030] In some embodiments, the surface is the main surface of the main component, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

[0031] Another embodiment includes a non-transitory computer-readable medium having computer-executable code stored thereon. When executed by a computer processor, the computer-executable code causes the computer to perform a method comprising: A first digital model of the main component is provided, the main component having a main surface; A second digital model of the dependent component is provided, the dependent component having a longitudinal axis and a cross-section defining the connection plane; Orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; The shadow of the cross-section of the subordinate component is projected onto the surface where the subordinate component intersects the surface, and the shadow defines a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points on the surface of the main component that form the outline of the shadow; Identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh is defined comprising multiple mesh elements, each mesh element being defined by a set of points from the first set of principal surface points and the second set of principal surface points; and Submit the mesh to the finite element analysis system and perform finite element analysis on the mesh.

[0032] In some embodiments, the surface is the surface of the main component.

[0033] In some embodiments, casting the shadow of the cross-section of the dependent component onto the surface includes: A mid-shading of the cross-section of the subordinate component is created on a two-dimensional shadow plane, the shadow plane being parallel to a tangent plane that is tangent to the main surface at the intersection point where the subordinate component intersects the main surface, the shadow having an outer edge and defining a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Select the midpoint on the intersecting curves; and The midpoint is translated onto the main surface to generate the first set of main surface points.

[0034] In some such embodiments, the tangent plane and the shadow plane are coplanar.

[0035] In some such embodiments, the main surface includes a flat surface defining a two-dimensional plane, and said flat surface includes a two-dimensional shadow plane.

[0036] In some embodiments, the surface is a primary surface, and the primary surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the primary component, the floating surface being perpendicular to a line perpendicular to the primary surface at the intersection.

[0037] In some embodiments, shadows are cast by parallel light rays. Attached Figure Description

[0038] Those skilled in the art will more fully appreciate the advantages of various embodiments of the invention from the “Description of Illustrative Embodiments” discussed below with reference to the accompanying drawings, which will be summarized immediately below.

[0039] Figure 1A An embodiment of a system for finite element analysis of a digital model of the interface between the main and subordinate components of a physical device is schematically illustrated. Figure 1B A block diagram schematically illustrates an embodiment of a system for performing finite element analysis on a digital model of the interface between the main and subordinate components of a physical device. Figure 2A This is a flowchart of an embodiment of a method for finite element analysis of a digital model used to perform interface between the main and subordinate components of a physical device; Figure 2B The user interface is illustrated schematically; Figure 3 This is a flowchart of an embodiment of a method for projecting simulated shadows in a computer system; Figure 4 This is a flowchart of an embodiment of a method for modeling existing structures; Figure 5A An embodiment of a cylindrical multi-component system is schematically illustrated; Figure 5B An embodiment of a cylindrical multi-component system is schematically illustrated; Figure 5C An embodiment of a subordinate component of a cylindrical multi-component system is schematically illustrated; Figure 5DAn embodiment of a rectangular multi-component system is schematically illustrated; Figure 5E An embodiment of the components of a rectangular multi-component system is schematically illustrated; Figure 6A An embodiment of an example of projecting a direct shadow on the main component is illustrated schematically; Figure 6B : An embodiment of a shadow cast on the main component is illustrated schematically; Figure 7A An embodiment of projecting an intermediate shadow on a shadow plane is schematically illustrated; Figure 7B An embodiment of projecting an intermediate shadow on a shadow plane is schematically illustrated; Figure 7C An embodiment of projecting an intermediate shadow on a shadow plane is schematically illustrated; Figure 8A An embodiment of points obtained from shadows is schematically shown; Figure 8B An embodiment of points obtained from shadows is schematically shown; Figure 8C An embodiment of concentric rings of points obtained from shadows is schematically shown; Figure 8D An embodiment of a mesh defined by concentric rings of points obtained from shadows is schematically shown; Figure 8E An embodiment of a grid defined by multiple points is illustrated schematically. Detailed Implementation

[0040] Exemplary embodiments provide improvements to methods and systems for performing finite element analysis on multi-component systems (i.e., systems comprising multiple physically connected components), even if the engineer does not possess the expertise typically held by those skilled in the art of finite element analysis. Typical computer-aided design system operators lack the skills or experience to perform finite element analysis on finite element analysis systems.

[0041] Some implementations enable engineers using computer-aided design systems to perform finite element analysis on multi-component systems designed by engineers.

[0042] Some embodiments enable engineers using computer-aided design systems to perform finite element analysis on pre-existing (i.e., already constructed) multi-component systems. For example, in some embodiments, measurements from a pre-existing multi-component system can be translated onto a model on the computer-aided design system, and finite element analysis can be performed on that model. Some embodiments may use scanning modalities (e.g., scanning devices that generate point clouds of the system) to scan the pre-existing multi-component system. For example, some embodiments may use a scanner mounted on a target to scan the pre-existing multi-component system.

[0043] Some implementations allow engineers to easily connect two or more components without having to deal with complex functions to represent the intersections of curves or make any assumptions. This feature can be easily implemented in software to create four-node meshes, thereby simplifying the interpretation of the results.

[0044] Some embodiments are implemented as computer program products having computer-readable program code on a computer-usable medium. This computer-readable code can be read and used by a computer system for conventional processing.

[0045] The illustrative embodiments operate within a computer-aided design environment to facilitate finite element analysis of a multi-component system, including a master component connected to subordinate components. An exemplary embodiment projects shadows on the ends of the subordinate components and obtains mesh nodes on the surface of the master component from these shadows. The exemplary embodiment then forms a mesh from the mesh nodes, which is input into a finite element analysis engine.

[0046] Figure 1A An embodiment of a CAD system 100 is schematically illustrated for finite element analysis of digital models of interfaces between primary and secondary components of a physical device. The system includes a central processing unit 102 that communicates data with a computer monitor having a display screen 104, a keyboard 106, and a computer mouse 108. A system operator can provide input to the system using the keyboard 106 and / or the mouse 108, and the central processing unit 103 can display images (e.g., CAD images and finite element analysis images) on the screen 104.

[0047] Figure 1BA block diagram schematically illustrates an embodiment of a system 100 for performing finite element analysis on a digital model of an interface between a master component and slave components of a physical device. System 100 includes a set of modules interconnected in data communication via a communication bus 121. These modules include a communication interface 120 configured to communicate with other computers or systems (e.g., a network; a component cloud; a remote database 131). The system also includes a memory 130, in which CAD designs and executable software can be stored. The system further includes a CAD module 140 configured to render an image of a CAD drawing for display on a screen 104; an orientation module 150 configured to orient slave components relative to a master component as described herein; a shading module 160 configured to display CAD-projected shadows of components in the CAD drawing; a point module 170 configured to select points from the shadows; a mesh module 180 configured to generate a finite element analysis mechanism from a plurality of selected points; and a finite element analysis module 190 configured to perform finite element analysis using the mesh.

[0048] Figure 2A This is a flowchart of an embodiment of a method 200 for performing finite element analysis on a digital model of the interface between the main and subordinate components of a physical device. It can be considered that... Figure 2A In this embodiment, the shadow 610 is projected directly onto the surface 512 of the main component 510.

[0049] Step 210 includes obtaining the CAD model of the main component.

[0050] exist Figure 5A , Figure 5B and Figure 5C An illustrative example of a main component 510 and a subordinate component 520 is schematically shown. Figure 5D , Figure 5E The diagram illustrates an illustrative example of another main component 510 and another subordinate component 520.

[0051] In an illustrative embodiment, the main component 510 has a main surface 512 and an intersection 540, at which the subordinate component 520 meets the main component 510. In such an embodiment, the subordinate component 520 has an interface region (or interface end) 521, at which the subordinate component 520 meets the surface 512 of the main component 510. In an illustrative embodiment, the interface region 521 defines an interface plane 525. The interface plane 525 defines a longitudinal axis 530 perpendicular to the interface plane 525. In some embodiments, the system 100 displays the longitudinal axis on a computer screen 104.

[0052] Step 230 includes orienting the model of the subordinate component 520 relative to the model of the master component 510 in the CAD environment. This orientation may be referred to as orienting the subordinate component 520 relative to the master component 510. In an illustrative embodiment, orienting the subordinate component 520 relative to the master component 510 includes showing the intersection point 540 where the longitudinal axis 530 of the subordinate component 520 meets the surface 512 of the master component 510.

[0053] Step 240 includes projecting the shadow 610 of the interface plane 525 onto the surface 512 of the main component 510 in the CAD environment. The shadow 610 has a profile at its outer edge 611, which is partially dependent on the shape of the interface plane 525 and the shape (or profile) of the surface 512 of the main component 510.

[0054] Typical CAD systems have the ability, for example, to project shadows of elements in a CAD drawing from a virtual light source 550. In a preferred embodiment, shadow 610 is projected using parallel rays (e.g., from virtual light source 500). In some embodiments, shadow 610 is projected using rays that are not parallel but preferably have a small angle relative to each other (e.g., from virtual light source 500). In some such embodiments, the angle between such non-parallel rays can be 1 degree, between 1 and 2 degrees, 2 degrees, between 2 and 3 degrees, 3 degrees, between 4 and 5 degrees, or 5 degrees. In some embodiments, this angle between virtual rays can depend on, for example, how the virtual light source 550 generates the light. In some embodiments, this angle between virtual rays can depend on, for example, how far the virtual light source is from the interface plane 525 of the dependent component 520 in the CAD drawing. Generally, a larger distance between the virtual light source 500 and the interface plane 525 is preferred over a smaller distance, because at a larger distance, the virtual rays incident on the interface plane 525 of the dependent component tend to be closer to each other (i.e., have a smaller angle relative to each other).

[0055] Step 250 involves selecting points 899 from the shaded area 610, which will form the basis of the mesh used for finite element analysis.

[0056] In an illustrative embodiment, step 250 includes identifying a first set of points on the edge 611 of the shadow 610, for example, such as Figure 6A and Figure 6B As shown schematically. The first set of points includes multiple points that form the outline of the shadow 610.

[0057] exist Figure 8A An embodiment of point 899 in the first set of points 800 is schematically shown. Figure 8AThe outline of the first set of points 800 forms a circle, for example, a circle can be obtained from a circular shadow (e.g., a shadow surrounded on a planar surface by a subordinate part 520 having a circular cross-section).

[0058] exist Figure 8B Another embodiment of the first set of points 800 is schematically shown in the figure. Figure 8B The outline of the first set of points 800 forms an ellipse, for example, which can be obtained from an elliptical shadow, such as the shadow cast onto a plane by a subordinate member 520 having a circular cross-section and a longitudinal axis 530, the longitudinal axis 530 intersecting the flat surface 512 of the main member 510 at an angle that is not a right angle.

[0059] Step 250 also includes identifying at least one second set of points for the shadow, each such second set of points comprising a plurality of points 899 surrounding the first set of points 800. In an illustrative embodiment, step 250 includes identifying a plurality of second sets of points, each such set forming a path around the first set of points. In an exemplary embodiment, each second set of points is concentric with the first set of points. In some embodiments where the shadow 610 is directly projected onto the surface 512 of the first component 510, the first set of points and the second set of points may be considered to coincide with corresponding points on the surface 512 of the first component 510.

[0060] exist Figure 8C An exemplary embodiment of the second set of points 810 is schematically shown. In this embodiment, the second set of points 810 forms an ellipse and is concentric with the first set of points 810 (i.e., has the same center point as the first set of points 810).

[0061] Figure 8C Additional second group points 812 and third second group points 814 are also schematically shown.

[0062] In some embodiments, the system operator may base their actions on user experience, for example via a user interface 299 generated by and presented on the computer monitor of the CAD system 100 (e.g., ...). Figure 2B(Illustrated schematically) to identify points. In some embodiments, the system operator can identify a portion of the CAD drawing and specify how points should be identified within that portion, and the CAD system 100 (e.g., point module 170) automatically identifies points based on this operator input. In some embodiments, the system operator can specify the distance between adjacent points, and the CAD system 100 (e.g., point module 170) automatically identifies these points based on this operator input. In some embodiments, the method and system begin with a default number of points in each set of points and then automatically evaluate the corresponding aspect ratio of the resulting mesh elements 892 (described below) to determine whether to repeat step 250 to identify additional points. In the illustrative embodiment, the default number of points may be, for example, 12 points. In some embodiments, the default number of points can be: 20 points, with a number of points not less than 20 but less than 30 points; 30 points, with a number of points not less than 30 but less than 40 points; 40 points, with a number of points not less than 40 but less than 50 points; 50 points, with a number of points not less than 50 but less than 50 points; 100 points, with a number of points not less than 100 but less than 200 points, and so on. These are just a few examples.

[0063] As described below, these points are used to form multiple grid elements 892, such as Figure 8D and Figure 8E This is illustrated schematically. In some embodiments, the number of points is selected, specified, or determined such that each grid element 892 has an aspect ratio equal to or less than 4:1, wherein the aspect ratio of the grid element is defined as the ratio of the length of the grid element to the width of the grid element. For example, in Figure 8EIn this example, a grid element 892 has a first side 895 representing the length of the grid element 892 and a second side 896 representing the width of the grid element 892, wherein the first side 895 is adjacent to the second side, and the length of the first side 895 is equal to or greater than the length of the second side 896. For example, if the first side 895 has a length of 1.7 mm and the second side 896 has a length of 0.8 mm, the aspect ratio of the grid element will be 1.7 divided by 0.8, which equals a ratio of 2.125, which is less than 4:1. As another example, if the first side 895 has a length of 4.0 mm and the second side 896 has a length of 1.7 mm, the aspect ratio of the grid element will be 4.0 divided by 1.7, which equals a ratio of 2.35, which is also less than 4:1. In the illustrative embodiment, if the aspect ratio of any grid element among the plurality of grid elements is greater than 4:1, the number of points is insufficient, and the operator or system may increase the number of points until the aspect ratio of each grid element 892 is equal to or less than 4.0. Generally, the more mesh elements used in a finite element analysis, the more accurate the results. Although the examples in this document are described with reference to an aspect ratio of 4:1 or less, other embodiments may use different aspect ratios. For example, depending on the structure and system being analyzed and the experience level of the operator, some embodiments may specify or require different pre-specified aspect ratios, such as 1:1 or less; 2:1 or less; 3:1 or less; 5:1 or less; 6:1 or less; 7:1 or less; or 8:1 or less.

[0064] Step 260 includes forming a mesh 890 from the identified points (i.e., the points identified at step 250), the mesh comprising a plurality of mesh elements 892. This can be done automatically by the CAD system 100 (e.g., by the mesh module 180). In an illustrative embodiment, each mesh element is defined by four of the identified points and may be referred to as a four-node mesh element or a “quadrilateral” mesh element. A mesh of four-node mesh elements may be referred to as a four-node mesh. For example, in Figure 8D The diagram schematically illustrates a four-node mesh 890.

[0065] In a preferred embodiment, each mesh cell shares at least one node common to its neighboring mesh cells (i.e., a node if a point is identified), and no node is part of a single mesh cell. Note that meshes generated for image generation, such as those used in computer animation, video games, and even conventional CAD drawing, are insufficient as meshes generated in step 260 and are insufficient as input for finite element analysis, because in those applications, gaps between mesh elements are acceptable, and any lack of fidelity in the rendered image will not degrade the image (relative to an image rendered from a mesh with no gaps between adjacent mesh elements) to a degree that would be noticeable to the human eye.

[0066] In the illustrative embodiment, the aspect ratio of each grid element 892 is less than or equal to 4:1, as described above. Some embodiments determine which of the plurality of grid elements 892 has the largest aspect ratio, and if the aspect ratio of that grid element is greater than 4:1, the method loops back to step 250 (step 261), increases the number of identified points, and repeats step 260 until the aspect ratio of each grid element 892 is less than or equal to 4:1 (i.e., an aspect ratio not greater than 4:1).

[0067] Step 270 includes performing a finite element analysis of the multi-part object 500 based on the mesh 890 generated in step 260. The mesh 890 is input into the finite element analysis engine (e.g., finite element analysis module 190) and used by the finite element analysis engine.

[0068] Figure 3 This is a flowchart of an embodiment of a method 300 for performing finite element analysis on a digital model of the interface between the main and subordinate components of a physical device. It can be considered that... Figure 3 The embodiment projects the shadow 610 indirectly onto the surface 512 of the main component 510 because method 300 includes projecting the intermediate shadow 630 onto the shadow plane (instead of projecting the shadow directly onto the surface 512 of the main component 510) 260, and then translating the point from the intermediate shadow 630 onto the surface 512 of the main component 510.

[0069] In method 300, steps 210, 220, 230, 260 and 270 are the same as those described above for method 200.

[0070] However, method 300 (after steps 210, 220 and 230) provides a shadow plane 620 in step 310 instead of projecting the shadow 610 directly onto the surface 512 of the main component 510.

[0071] In an illustrative embodiment, the shadow plane is parallel to the tangent plane 622, which is tangent to the main surface 512 at the intersection point 540 where the subordinate member 520 intersects with the main surface 512. In some embodiments, the shadow plane 620 and the tangent plane 622 are coplanar, such as... Figure 7B It is shown schematically in the diagram.

[0072] In some embodiments, the shadow plane 620 is not coplanar with the tangent plane 622 and is arranged between the tangent plane 622 (e.g., between intersections 540) and the dependent component 520, such as... Figure 7C The shadow plane is schematically shown (such a shadow plane may be referred to as a "floating" plane). In some embodiments, the main surface 512 includes a flat surface defining a two-dimensional plane, and the flat surface is a two-dimensional shadow plane.

[0073] Then, in step 320, method 300 projects the intermediate shadow 630 onto the shadow plane 620. Figure 7A The diagram schematically illustrates embodiments of a shadow plane 620 and an intermediate shadow 630. In a preferred embodiment, the intermediate shadow 630 is projected using parallel rays (e.g., rays from a virtual light source 500). In some embodiments, the intermediate shadow 630 is projected using rays that are not parallel but preferably have a small angle between them (e.g., rays from a virtual light source 500). In some such embodiments, the angle between such non-parallel rays can be 1 degree, between 1 and 2 degrees, 2 degrees, between 2 and 3 degrees, 3 degrees, between 4 and 5 degrees, or 5 degrees. In some embodiments, this angle between virtual rays can depend on, for example, how the virtual light source 550 generates light. In some embodiments, this angle between virtual rays can depend on, for example, how far the virtual light source is from the interface plane 525 of the subordinate component 520 in a CAD drawing. Generally, a larger distance between the virtual light source and the interface plane 525 is preferred over a smaller distance, because at a larger distance, the virtual rays incident on the interface plane 525 of the subordinate component tend to be closer to each other parallel (i.e., have a smaller angle relative to each other).

[0074] In step 330, following step 320, method 300 selects points on the shadow plane 620 from the intermediate shadow 630. In an illustrative embodiment, step 330 includes identifying a first set of points on the edge 611 of the intermediate shadow 630. This first set of points includes a plurality of points forming the contour of the intermediate shadow 630. In an illustrative embodiment, the points in the first set of points are selected to be spaced apart from each other such that the first set of points does not form a continuous curve. In some exemplary embodiments, the spacing between the points in the first set of points is specified by the CAD operator. In some illustrative embodiments, the spacing between the points in the first set of points is determined to be a portion of the perimeter of the dependent component 520, where "perimeter" is the total distance around the outer surface of the dependent component 520. For example, in some embodiments, the spacing between the points in the first set of points is set to one percent (1%) of the perimeter of the dependent component 520. In some embodiments, the spacing between the points in the first set of points is set to half (0.5%), one-quarter (0.25%), or 2% of the perimeter of the dependent component 520.

[0075] Step 330 further includes identifying at least one second set of points of the intermediate shading 630 (and in some embodiments, including identifying multiple such second sets of points), each such second set of points comprising multiple points surrounding the first set of points. In an illustrative embodiment, step 330 includes identifying multiple second sets of points, each such set forming a path around the first set of points. In an exemplary embodiment, each second set of points is concentric with the first set of points.

[0076] In some embodiments, one or more of such a second set of points are selected such that these points are arranged within the first set of points (i.e., surrounded by the first set of points).

[0077] Each point identified in step 330 can be referred to as a shaded point.

[0078] After step 330, step 340 translates the shadow point identified in step 330 from the shadow plane 620 to the surface 512 of the main component 510.

[0079] When the main surface 512 is flat, the action of translating the shadow point from the shadow plane 620 to the surface 512 of the main component 510 involves simply projecting each point from the shadow plane 620 onto the main surface 512 along a line perpendicular to the shadow plane 620.

[0080] In cases where the main component 510 has a curved surface 512 (e.g., with a constant radius, such as when the main component 510 has a circular cross-section), step 340 translates the point identified in step 330 from the intermediate shade 630 to the surface 512 of the main component 510 by identifying a reference point 515 inside the main component 510. In an illustrative embodiment, the reference point 515 is located at the geometric center of the cross-section of the main component 510. For example, in Figure 7B In the middle, the main component 510 has a circular cross-section, and the reference point 515 is located at the center of the circular cross-section.

[0081] Then, for each shaded point identified in step 330, step 340 identifies the corresponding mesh node on the surface 512 of the main component 510 as a point on the surface 512 of the main component 510, at which the line segment between the shaded point identified in step 330 and the reference point intersects the surface 512 of the main component.

[0082] For example, in Figure 7B In this process, method 300 and system 100 define a line segment 750 extending from reference point 515 to a shadow point 752 on the shadow plane. The corresponding mesh node 754 is located at the intersection. Step 340 thereby identifies a mesh node on the surface 512 of the main component 510 for (and corresponding to) each shadow point on the shadow plane 620.

[0083] The mesh nodes on the surface 512 of component 510 form a contour similar to, but different from, that of intermediate shadow 630 in the illustrative embodiment. For example, if the surface 512 of the main component 510 is curved, the curve of the surface will result in the contour of the mesh nodes being a distorted (different shape) version of intermediate shadow 630.

[0084] Furthermore, in step 340, each mesh node is offset towards the longitudinal axis 530 relative to its corresponding median shaded point. As a result, the profile of the mesh nodes on the surface 512 of the main component 510 is smaller than the median shaded point 630. The profile of the mesh nodes on the surface 512 of the main component 510 can be beneficial because it identifies mesh nodes closer to the longitudinal axis 530, and therefore closer to the center of the subordinate component 520. This can be advantageous, for example, when the subordinate component 520 is a conduit, pipe, or cylinder with walls of unknown thickness, or when the subordinate component 520 is a solid cylinder. In this case, at least some mesh nodes represent points within the conduit wall, pipe wall, and / or cylinder interior that would otherwise have been omitted from the mesh and finite element analysis, as described herein.

[0085] After step 340, method 300 forms a mesh in step 260 and uses the mesh as input to perform a finite element analysis in step 270, as described above in conjunction with method 200.

[0086] In the illustrative embodiment, the aspect ratio of each grid element 892 is less than or equal to 4:1, as described above. Some embodiments determine which of the plurality of grid elements 892 has the largest aspect ratio, and if the aspect ratio of that grid element is greater than 4:1, the method loops back to step 330 (step 261), increases the number of shaded points, and repeats steps 330 and 260 until the aspect ratio of each grid element 892 is less than or equal to 4:1 (i.e., an aspect ratio not greater than 4:1).

[0087] Figure 4 This is a flowchart of an embodiment of a method for modeling existing (i.e., already constructed) multi-component structures.

[0088] Step 410 includes scanning an existing multi-component system using a scanning modality to create an image set of one or more images of the system, such as a scanning device that generates a set of one or more photographs of the system, or a point cloud of the system. In an illustrative embodiment, the set of images includes images of at least a portion of a primary component, images of at least a portion of subordinate components, and images of the intersection of subordinate components and the primary component. In some embodiments, the scanning modality includes a flyable target that can create the set of images under the control of a target operator.

[0089] Step 420 includes generating CAD models of the main component 510 and the subordinate component 520 based on an image set of the system generated by the scanning mode. In some embodiments, such models are created by a CAD operator based on the operator's observation of the image set. In some embodiments, such models are created by an artificial intelligence agent, which may be implemented by the artificial intelligence module 141 of system 100. Such an artificial intelligence agent is trained to identify system components using an image-based training set. Such components may be, for example, pipes, tubes, tanks, supports, and beams, to name a few, and the training set includes images of such components. The CAD models generated in this manner are then used as input to the methods and systems described herein.

[0090] The following is a list of some of the reference figures used in this article: 100: CAD system; 102: CAD system processing unit; 104: Computer monitor; 106: Keyboard; 108: Computer mouse; 120: Communication interface; 121: Bus; 130: Memory; 140: Shadow module; 150: Orientation Module; 160: Shadow module; 170: Point module; 180: Grid module; 190: Finite element analysis module; 510: Main component; 515: The center point of the cross-section of the main component; 520: Subordinate component; 521: Interface terminal of subordinate component; 525: Interface plane of subordinate component; 530: Vertical axis; 540: Intersection point; 550: Light; 610: Shadows on the surface of the main component; 611: The outer edge of the shadow; 620: Shaded plane; 630: Intermediate shadow on the shadow plane; 890: Grid; 892: Grid element; 895: Edges of grid elements; 896: Edges of grid elements; 899: points.

[0091] Features of various embodiments may be listed in the potential claims in the paragraph following this section (and before the actual claims provided at the end of this application). These potential claims form part of the written description of this application. Therefore, the subject matter of the following potential claims may be presented as actual claims in subsequent proceedings relating to this application or any application claiming priority based on this application. The inclusion of such potential claims should not be construed as meaning that the actual claims do not cover the subject matter of the potential claims. Therefore, the decision not to raise these potential claims in subsequent proceedings should not be construed as a donation of subject matter to the public.

[0092] Without limitation, potential subject matter that can be claimed (beginning with the letter "P" to avoid confusion with the actual claims given below) includes: P1. A method for performing finite element analysis on a digital model of the interface between a primary component and a secondary component of a physical device in a computer, the method comprising: A first digital model of the main component is obtained, the main component having a main surface; A second digital model of the subordinate component is obtained, the subordinate component having a longitudinal axis and a cross-section defining a connecting plane; Orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; The shadow of the cross-section of the subordinate component is projected onto the surface where the subordinate component intersects the surface, and the shadow defines a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points on the surface of the main component that form the outline of the shadow; Identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh is defined comprising multiple mesh elements, each mesh element being defined by a set of points from the first set of principal surface points and the second set of principal surface points; and Submit the mesh to the finite element analysis system and perform finite element analysis on the mesh.

[0093] P2. According to the method described in P1, wherein the surface is the surface of the main component.

[0094] P3. The method according to any one of P1 to P2, wherein casting the shadow of the cross-section of the dependent component onto the surface comprises: An intermediate shadow of the cross-section of the subordinate component is created on a two-dimensional shadow plane, the shadow plane being parallel to a tangent plane that is tangent to the main surface at the intersection point where the subordinate component intersects the main surface. The shadow has an outer edge and defines a contour at the outer edge of the shadow, the contour being the intersection curve between the shadow plane and the subordinate component. Select the midpoint on the intersecting curves; and The midpoint is translated onto the main surface to generate the first set of main surface points.

[0095] P4. According to the method described in P3, wherein the shadow plane is coplanar with the tangent plane.

[0096] P5. The method according to P3, wherein the main surface includes a flat surface defining a two-dimensional plane, and wherein the flat surface includes the two-dimensional shadow plane.

[0097] P6. According to the method described in P3, wherein the surface is the main surface, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

[0098] P7. The method according to any one of P1 to P6, wherein the second set of points is located radially outside the first set of points relative to the intersection point, and the aspect ratio of each of the plurality of grid elements is less than or equal to 4:1.

[0099] P8. The method according to any one of P1 to P7, wherein the shadow is cast by parallel light rays.

[0100] P9. A system for performing finite element analysis on a digital model of an interface between a master component specified by a first digital model and a subordinate component specified by a second digital model, the subordinate component having a longitudinal axis and a cross-section defining a connection plane, the system comprising: A CAD module configured to provide the first digital model and the second digital model; An orientation module is configured to orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; A shadow module configured to project the shadow of the cross-section of the subordinate component onto a surface where the subordinate component intersects the surface, the shadow defining a contour at the outer edge of the shadow, the contour being an intersection curve between the main component and the subordinate component; A dot module configured to identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points forming the outline of the shadow on the surface of the main component; The point module is also configured to identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh module configured to define a mesh comprising a plurality of mesh elements, each mesh element being defined by a set of points from a first set of principal surface points and a second set of principal surface points; and A finite element analysis module, configured to submit the mesh to a finite element analysis system and perform finite element analysis on the mesh.

[0101] P10. The system according to P9, wherein the surface is the surface of the main component, and the shadow module is configured to project the shadow of the cross-section of the subordinate component onto the surface of the main component.

[0102] P11. The system according to any one of P9 to P10, wherein the system further comprises: The CAD module is also configured to provide a two-dimensional shadow plane, which is parallel to a tangent plane at the intersection point of the subordinate component and the main surface on the main surface, and is tangent to the main surface. The shadow module is configured to create an intermediate shadow of the cross-section of the subordinate component on a shadow plane, the intermediate shadow having an outer edge and defining a contour at the outer edge of the intermediate shadow, the contour being an intersecting curve between the main component and the subordinate component; The point module is configured to select the midpoint on intersecting curves; and The midpoint is translated onto the main surface to generate the first set of main surface points.

[0103] P12. The system according to P11, wherein the tangent plane is coplanar with the tangent plane.

[0104] P13. The system according to P11, wherein the surface is the main surface of the main component, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

[0105] P14. A non-transitory computer-readable medium having computer-executable code stored thereon, the computer-executable code performing a method when executed by a computer processor, the method comprising: A first digital model of the main component is provided, the main component having a main surface; A second digital model of the dependent component is provided, the dependent component having a longitudinal axis and a cross-section defining a connection plane; Orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; The shadow of the cross-section of the subordinate component is projected onto the surface where the subordinate component intersects the surface, and the shadow defines a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points on the surface of the main component that form the outline of the shadow; Identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh is defined comprising multiple mesh elements, each mesh element being defined by a set of points from the first set of principal surface points and the second set of principal surface points; and Submit the mesh to the finite element analysis system and perform finite element analysis on the mesh.

[0106] P15. The non-transient computer-readable medium according to P14, wherein the surface is the surface of the main component.

[0107] P16. A non-transient computer-readable medium according to any one of P14 to P15, wherein the shadow cast on the cross-section of a dependent component projected onto a surface comprises: A mid-shading of the cross-section of the subordinate component is created on a two-dimensional shadow plane, the shadow plane being parallel to a tangent plane that is tangent to the main surface at the intersection point where the subordinate component intersects the main surface, the shadow having an outer edge and defining a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Select the midpoint on the intersecting curves; and The midpoint is translated onto the main surface to generate the first set of main surface points.

[0108] P17. The non-transient computer-readable medium according to P16, wherein the tangent plane and the shadow plane are coplanar.

[0109] P18. The non-transient computer-readable medium according to P16, wherein the main surface includes a flat surface defining a two-dimensional plane, and wherein the flat surface includes the two-dimensional shadow plane.

[0110] P19. A non-transient computer-readable medium according to any one of P14 to P18, wherein the surface is the main surface, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

[0111] P20. The non-transient computer-readable medium according to any one of P14 to P19, wherein the shadow is projected by parallel light rays.

[0112] P30. A non-transient computer-readable medium having computer-executable code stored thereon, the computer-executable code performing a method when executed by a computer processor, the method comprising the method according to any one of P1 to P8.

[0113] Various embodiments of this disclosure can be implemented, at least in part, in any conventional computer programming language. For example, some embodiments may be implemented in a procedural programming language (e.g., "C") or an object-oriented programming language (e.g., "C++") or in Python, R, Java, LISP, or Prolog. Other embodiments of the invention may be implemented as pre-programmed hardware elements (e.g., application-specific integrated circuits, FPGAs, and digital signal processors) or other related components.

[0114] In alternative embodiments, the disclosed apparatus and methods can be implemented as a computer program product for use with a computer system. Such implementations may include a set of computer instructions fixed on a tangible medium such as a non-transitory computer-readable medium (e.g., a disk, CD-ROM, ROM, flash memory, or fixed disk). This set of computer instructions may embody all or part of the functionality previously described herein with respect to the systems.

[0115] Those skilled in the art will understand that such computer instructions can be written in a variety of programming languages ​​to be used with many computer architectures or operating systems. Furthermore, such instructions can be stored in any storage device (e.g., semiconductor, magnetic, optical, or other storage devices) and can be transmitted using any communication technology (e.g., optical, infrared, microwave, or other transmission technologies).

[0116] In other ways, such a computer program product can be distributed as a removable medium along with accompanying printed or electronic documents (e.g., shrink-wrapped software), pre-loaded into a computer system (e.g., on a system ROM or fixed disk), or distributed from a server or electronic bulletin board via a network (e.g., the Internet or the World Wide Web). Of course, some embodiments of this disclosure can be implemented as a combination of software (e.g., a computer program product) and hardware. Other embodiments of this disclosure are implemented as entirely hardware or entirely software.

[0117] The computer program logic that implements all or part of the functionality described earlier in this document can execute on a single processor at different times (e.g., concurrently), or on multiple processors at the same or different times, and can run under a single operating system process / thread or under different operating system processes / threads. Therefore, the term "computer process" generally refers to the execution of a set of computer program instructions, regardless of whether different computer processes execute on the same or different processors, and regardless of whether different computer processes run under the same or different operating system processes / threads.

[0118] The embodiments of the invention described above are intended to be exemplary only; many variations and modifications will be apparent to those skilled in the art. These variations and modifications are all within the scope of the invention as defined by any of the appended claims.

Claims

1. A method for performing finite element analysis on a digital model of the interface between a master component and a slave component of a physical device in a computer, the method comprising: A first digital model of the main component is obtained, the main component having a main surface; A second digital model of the subordinate component is obtained, the subordinate component having a longitudinal axis and a cross-section defining a connecting plane; Orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; The shadow of the cross section of the subordinate component is projected onto the surface where the subordinate component intersects the surface, and the shadow defines a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points on the surface of the main component that form the contour of the shadow; Identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh is defined as comprising multiple mesh elements, each mesh element being defined by a set of points from the first set of principal surface points and the second set of principal surface points; as well as The mesh is submitted to the finite element analysis system, and the finite element analysis of the mesh is performed.

2. The method according to claim 1, wherein, The surface is the surface of the main component.

3. The method according to claim 1, wherein, The step of casting the shadow of the cross-section of the dependent component onto the surface includes: An intermediate shadow of the cross-section of the subordinate component is created on a two-dimensional shadow plane, the shadow plane being parallel to a tangent plane that is tangent to the main surface at the intersection point where the subordinate component intersects the main surface, the shadow having an outer edge and defining a contour at the outer edge of the shadow, the contour being an intersection curve between the shadow plane and the subordinate component; Select the midpoint on the intersecting curves; and The intermediate point is translated onto the main surface to generate the first set of main surface points.

4. The method according to claim 3, wherein, The shadow plane is coplanar with the tangent plane.

5. The method according to claim 3, wherein, The main surface includes a flat surface defining a two-dimensional plane, wherein the flat surface includes the two-dimensional shadow plane.

6. The method according to claim 3, wherein, The surface is the main surface, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

7. The method according to claim 1, wherein, The second set of points is located radially outside the first set of points relative to the intersection point, and the aspect ratio of each of the plurality of grid elements is less than or equal to 4:

1.

8. The method according to claim 1, wherein, The shadow is cast by parallel light rays.

9. A system for performing finite element analysis on a digital model of an interface between a master component specified by a first digital model and a subordinate component specified by a second digital model, the subordinate component having a longitudinal axis and a cross-section defining a connection plane, the system comprising: A CAD module configured to provide the first digital model and the second digital model; An orientation module is configured to orient the second digital model relative to the first digital model, such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; A shadow module configured to project the shadow of the cross section of the subordinate component onto a surface where the subordinate component intersects the surface, the shadow defining a contour at the outer edge of the shadow, the contour being an intersection curve between the main component and the subordinate component; A dot module configured to identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points forming the contour of the shadow on the surface of the main component; The point module is also configured to identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh module configured to define a mesh comprising a plurality of mesh elements, each mesh element being defined by a set of points from a first set of principal surface points and a second set of principal surface points; as well as A finite element analysis module is configured to submit the mesh to a finite element analysis system and perform finite element analysis on the mesh.

10. The system according to claim 9, wherein, The surface is the surface of the main component, and the shadow module is configured to project the shadow of the cross-section of the subordinate component onto the surface of the main component.

11. The system according to claim 9, wherein, The system also includes: The CAD module is also configured to provide a two-dimensional shadow plane, which is parallel to a tangent plane at the intersection point where the subordinate component intersects the main surface on the main surface, and is tangent to the main surface. The shadow module is configured to create an intermediate shadow of the cross-section of the subordinate component on a shadow plane, the intermediate shadow having an outer edge and defining a contour at the outer edge of the intermediate shadow, the contour being an intersecting curve between the main component and the subordinate component; The point module is configured to select an intermediate point on the intersecting curves; and The intermediate point is translated onto the main surface to generate the first set of main surface points.

12. The system according to claim 11, wherein, The tangent plane is coplanar with the tangent plane.

13. The system according to claim 11, wherein, The surface is the main surface of the main component, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

14. A non-transitory computer-readable medium having computer-executable code stored thereon, the computer-executable code executing a method when executed by a computer processor, the method comprising: A first digital model of a main component is provided, the main component having a main surface; A second digital model of a subordinate component is provided, the subordinate component having a longitudinal axis and a cross-section defining a connection plane; Orient the second digital model relative to the first digital model such that the vertical axis of the subordinate component intersects with the intersection point on the first digital model; The shadow of the cross section of the subordinate component is projected onto the surface where the subordinate component intersects the surface, and the shadow defines a contour at the outer edge of the shadow, the contour being the intersection curve between the main component and the subordinate component; Identify a first set of main surface points on the surface of the main component, the first set of main surface points including a plurality of points on the surface of the main component that form the contour of the shadow; Identify a second set of main surface points on the surface of the main component, the second set of main surface points including a plurality of points surrounding the first set of points; A mesh is defined as comprising multiple mesh elements, each mesh element being defined by a set of points from the first set of principal surface points and the second set of principal surface points; as well as The mesh is submitted to the finite element analysis system, and the finite element analysis of the mesh is performed.

15. The non-transient computer-readable medium according to claim 14, wherein, The surface is the surface of the main component.

16. The non-transient computer-readable medium according to claim 14, wherein, Projecting the shadow of the cross-section of the dependent component onto the surface includes: An intermediate shadow of the cross-section of the subordinate component is created on a two-dimensional shadow plane, the shadow plane being parallel to a tangent plane that is tangent to the main surface at the intersection point where the subordinate component intersects the main surface, the shadow having an outer edge and defining a contour at the outer edge of the shadow, the contour being an intersection curve between the main component and the subordinate component; Select the midpoint on the intersecting curves; and The intermediate point is translated onto the main surface to generate the first set of main surface points.

17. The non-transient computer-readable medium according to claim 16, wherein, The tangent plane is coplanar with the shadow plane.

18. The non-transient computer-readable medium according to claim 16, wherein, The main surface includes a flat surface defining a two-dimensional plane, wherein the flat surface includes the two-dimensional shadow plane.

19. The non-transient computer-readable medium according to claim 14, wherein, The surface is the main surface, and the main surface includes a curved surface at the intersection, and the two-dimensional shadow plane includes a floating surface disposed between the subordinate component and the main component, the floating surface being perpendicular to a line perpendicular to the main surface at the intersection.

20. The non-transient computer-readable medium according to claim 14, wherein, The shadow is cast by parallel light rays.

Images