Constant radius rolling-ball blend on graphics processing unit (GPU)

Abstract

Current approaches to generating rolling-ball bend faces are computationally inefficient, or result in defects, among other technical issues. A computing system can be configured to generate rolling-ball blend faces on a graphics processing unit (GPU) via multiple passes.

Description

Docket No. 202413055CONSTANT RADIUS ROLLING-BALL BLEND ON GRAPHICS PROCESSING UNIT (GPU)BACKGROUND

[0001] Blending, or creating a smooth transition face (blend face) between two input faces, is a common operation in computer-aided design (CAD) operations. One of the techniques to produce a blend face can be referred to as a rolling-ball blend. To generate a rolling-ball blend between two input faces, a spherical ball having a blend radius is rolled such that it remains in contact with the two input faces. Circular cross sections can be computed as the ball rolls, and then a blend surface can be computed that passes through the cross-sections. The new blend face can be computed from the blend surface that represents the underlying geometry of the blend face. It is recognized herein, however, that current approaches to generating rolling-ball bend faces are computationally inefficient, or result in defects, among other technical issues.BRIEF SUMMARY

[0002] Embodiments of the invention address and overcome one or more of the described- herein shortcomings or technical problems by providing methods, systems, and apparatuses for generating rolling-ball blend faces on a graphics processing unit (GPU) via multiple passes.

[0003] In an example aspect, a computing system is configured to generate a model representative of a part capable of being manufactured. The system can obtain a first mesh model and a second mesh model. The first mesh model includes a first body that defines a first face, and the second mesh model includes a second body that defines a second face. The system can transfer the first and second mesh models to a graphics processing unit (GPU). The system can generate a first signed distance field (SDF) representation on the GPU, from the first mesh model. The system can also generate a second SDF representation on the GPU, from the second mesh model. Based on the first SDF and the second SDF, the system can perform first rolling-ball blend operations so as to generate a blend surface SDF. The first rolling-ball blend operations define a constant radius blend. The system can convert the blend surface SDF to a blend surface mesh. The blend surface mesh is representative of a blend face between the first face and the second face, such that the blend face defines the constant radius blend. Thus, the model representative of the part capable of being manufactured includes the first face, the second face, and the blend face.Docket No. 202413055

[0004] In another example aspect, the system can, on the GPU, determine third and fourth SDF representations of first and second bound tubes, respectively, wherein the first bound tube defines a first boundary along the first face, and the second bound tube defines a second boundary along the second face. The system can perform second rolling-ball blend operations using the third SDF and the fourth SDF, as to generate a first bound curve and a second bound curve. The first bound curve defines a first edge of the blend face along the first face, and the second bound curve defines a second edge of the blend face along the second face. In an example, before converting the blend surface SDF to the blend surface mesh, the system transfers the blend surface SDF from the GPU to a central processing unit (CPU) of the computing system, and then computes the blend surface mesh from the SDF, on the CPU. In another example, the system can compute the mesh directly from the SDF on the GPU, and then transfer the mesh from the GPU to the CPU. The system can generate the first SDF and the second SDF during multiple passes on the GPU, such that a pass corresponds to each of the first and second mesh models. Furthermore, the system can generate the third SDF and the fourth SDF during multiple passes on the GPU, such that a pass corresponds to each of the first and second bound tubes.

[0005] In another example aspect, the first mesh model can define a first plurality or set of faces including the first face, and the second mesh model can define a second plurality or set of faces including the second face. In such an example, the system can convert the blend surface SDF to the blend surface mesh representative of the bend face, such that the blend face is defined between the first plurality of faces and the second plurality of faces.BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0006] The foregoing and other aspects of the present invention are best understood from the following detailed description when read in connection with the accompanying drawings. For the purpose of illustrating the invention, there is shown in the drawings embodiments that are presently preferred, it being understood, however, that the invention is not limited to the specific instrumentalities disclosed. Included in the drawings are the following Figures:

[0007] FIG. 1 is a perspective view of an example model that defines two faces that can be blended in accordance with an example embodiment.Docket No. 202413055

[0008] FIG. 2 is a perspective view of another example model that depicts a blend face that blends the two faces of the model shown in FIG. 1, wherein the blend face can be generated according to various embodiments.

[0009] FIG. 3 is another view of the model shown in FIG 1, illustrating a ball that can be used in a rolling-ball blend operation to generate the blend face.

[0010] FIG. 4 is another view of the model shown in FIG. 2, illustrating bound curves that can be generated according to various example embodiments. room FIG. 5 is a view of an example model generated using previous approaches, which results in an example defect in the blend face.

[0012] FIG. 6 is a flow diagram that illustrates example operations that can be performed by a computing system on a graphics processing unit (GPU) in accordance with an example embodiment.

[0013] FIG. 7 is a flow diagram that illustrates example operations performed in multiple passes on the GPU, as to generate a blend surface for a rolling-ball blend face in accordance with an example embodiment.

[0014] FIG. 8 is an example illustration that depicts operations shown in FIG. 7.

[0015] FIG. 9 is a flow diagram and associated illustrations that depict example operations performed in multiple passes on the GPU, so as to generate bound tubes for generating a rolling-ball blend face in accordance with an example embodiment.

[0016] FIG. 10 is a flow diagram that depicts example operations performed on a central processing unit (CPU) of the computing system, so as to extract bound curves that define a rolling-ball blend face in accordance with an example embodiment.

[0017] FIG. 11 illustrates a computing environment within which embodiments of the disclosure may be implemented.DETAILED DESCRIPTION

[0018] Referring initially to FIGs. 1 and 2, an example first model 100a includes a first body 102 and a second body 104 connected to the first body 102. The first body 102 defines a first face 103 and the second body 104 defines a second face 105 that supports the first body 102. A computer-aided design (CAD) operation, in particular a blending operation, can be performed on the model 100a so as to generate a second model 100b that includes a blend face 106 between the first face 103 and the second face 105. The models described herein can representDocket No. 202413055 any physical part or object, or portion thereof, for instance power train parts, machined parts, or objects designed for topology optimization, among others. By way of further example, and without limitation, blending operations such as those described herein can be critical in designing automotive or aerospace structures, performing topology optimizations, or in integrating lattice structures into part models. Further example implementations include any situation where two or more faces have a sharp edge between them and blending is used to reduce or avoid stress concentration or to improve aesthetics. For example, and without limitation, such situations can occur when modeling machined parts using Boolean operations, or when generating mesh models using topology optimization, or when infilling the volume of a part with lattice structures and those lattices connect to its outer shell in sharp edges.

[0019] Referring also to FIGs. 3 and 4, for example, a spherical ball 108 can be rolled around the first body 102 while the ball 108 maintains contact with the first face 103 and the second face 105, so as to define a path or spine curve 110 that surrounds first body 102. The faces can be defined as respective topological entities, such that each face can define a respective blend surface that represents the underlying geometry of the face. For example, the blend face 106 can be generated by computing circular cross-sections as the ball 108 rolls along the spine curve 110. In some cases, a user defines the radius of the ball 108. The ball 108 can roll such that its center moves along the spine curve 110. The blend surface can be topologically connected in a boundary representation (B-rep) of the part or object that is represented by the models 100a and 100b, so as to form the blend face 106. The blend face 106 can connect with the input faces 103 and 105 so as to define a first bound curve or boundary 112 along the first face 103, and a second boundary or bound curve 114 along the second input face 105. The boundaries 112 and 114 of the blend face 106 can be referred to as bound curves of the blend.

[0020] Referring now to FIG. 5, its recognized herein that, in some cases, rolling-ball blend operations can result in defects, for instance a defect 116. For example, and without limitation, the defect can define a self-intersection in the blend surface at regions where the bend radius is large and the curvature of the spine curve 110 is high. In previous approaches, such rolling-ball blends can be addressed in a manner that is computationally burdensome, and often results in blend surfaces that do not define a constant radius rolling ball blend. For example, previous approaches include B-rep modeling in which a local defective area of the blend face is split into multiple faces, and then additional bend faces surfaces are created that might not match the original constant radius rolling-ball blend surface.Docket No. 202413055

[0021] In various example embodiments, a computing system including a graphics processing unit (GPU) is configured to perform multi-pass operations so as to compute a constant radius rolling blend between multiple input faces (or solids) using an implicit signed distance field (SDF) representation of the input faces (or solids). As used herein, unless otherwise specified, faces or solids can be used interchangeably without limitation. Implicit modeling refers to representing three-dimensional (3D) models using implicit functions. For example, in an implicit model, a surface of the model corresponds to an iso-surface of a function field, / (x), which represents the distance of a point x in three-dimensional space from the surface. Thus, the signed distance function or signed distance field (SDF) generally refers to the orthogonal distance of a given point x to the boundary of a set in a metric space. Implicit models often have advantages over models generated using other modelling techniques. For example, implicit models may be combined easily using Boolean operations. By of further background, meshing is a modelling technique that is found in many CAD systems. A mesh representation comprises subdivision of a continuous geometric space into discrete geometric and topological cells called facets. Meshes are often useful in various modelling applications such as finite element analysis, 3D scanning, topology optimization, and 3D printing. Some CAD systems also allow a mixed representation that includes classic geometry and facet data in a single B-rep model without conversion between data types. It is recognized herein, however, that current approaches to rolling-ball blends are often not suited to mesh-based modelling or models that combine B-rep or implicit modelling with mesh-based modelling.

[0022] In various example embodiments, the computing system that defines the GPU instantiates grids of voxels around the input faces, stores the input faces as SDFs in these grids, and then computes the SDF of the blend surface and the SDF of the bound tubes (tubular shapes along the bound curves), through a series of operations, executed as multiple passes through these voxel grids on the GPU. In some examples, the SDFs of the blend surface and of the bound tubes are transferred from the GPU to a CPU of the computing system. The CPU can convert the blend surface SDF to a blend surface mesh using marching cubes. Furthermore, bound curves can be extracted as central polylines from the SDFs of the bound tubes. A CAD kernel (e.g., Siemens Parasolid that has existing API’s such as PK FACE change) can be used to take the blend surface mesh and the bound curves as inputs, and generate the corresponding blend face in the B-rep of the overall part of the two input faces (or solids).Docket No. 202413055

[0023] Referring to FIG. 6, the computing system including at least one GPU can perform example operations 600. At 602, the system can obtain mesh models or triangle meshes, for instance two triangle meshes. The triangle meshes can define a 3D surface representation or polygon mesh, in which a collection of triangles in three dimensions that are connected by their common edges or vertices, so as to form a network of triangles that define a shape or object. The triangle meshes can each represent a respective face (or a solid) in a pair of faces (or solids) that arc to be blended. In some examples, the system can blend more than two faces together by first blending two faces together to define a blended face, and the blending the blended face with a third face. For example, a first triangle mesh can represent the first face 103, and a second triangle mesh can represent the second face 105. In some cases, a user of the system specifies a blend radius, or the radius of the ball 108. While an example is described in which the inputs are triangle meshes, it would be understood that that the input faces 103 and 105 can vary in form as desired, assuming their SDF representations can be computed as described herein, and all such input faces are contemplated as being within the scope of this disclosure. Additionally, in the examples it is assumed the inputs are meshes from two faces lying on either side of their intersection edge, but it will be understood that the inputs may define a chain of edges, such that multiple adjacent face pairs lying on either side of this chain can be combined into respective meshes to create two meshes. Thus, the system can blend two sets of multiple faces, such that the system is not restricted to blending a single pair of faces.

[0024] With continuing reference to FIG. 6, at 604, the system can transfer the two meshes to a compute shader on the GPU using Shader Storage Buffer Objects (SSBOs). The blend radius can also be passed to the computer shader, at 604, as a uniform variable. In some examples, OpenGL APIs can be used to write GPU specific code, although it will be understood that embodiments can be implemented in other platforms, (e.g., NVIDIA CUDA, Web-GPU, Vulkan, or Metal that utilizes different GPU language variants), and all such platforms are contemplated as being within the scope of this disclosure. At 606, two 3D textures are generated or created on the GPU. The 3D textures can act as voxel grids to store the SDFs of the two input meshes. At 608, the SDF of the blend surface is computed on the GPU. To do so, in accordance with various embodiments, as series of passes are run through the compute shader on the GPU, as further described herein.

[0025] Referring also to FIG. 7, to perform the operations at 608, a series of passes through the compute shader on the GPU can include example operations 700. At 702, the computeDocket No. 202413055 shader on the GPU receives the input meshes, for instance a first mesh that represents the first face 103, and a second mesh that represents the second face 105. At 704, SDF computation passes are performed, for example, so as to convert the first and second meshes to first and second SDFs, respectively. In various examples, a pass corresponds to each of the input meshes. In particular, for example, the system can launch parallel invocations though multiple voxels to compute and store the SDF of the respective input meshes in the voxel grids. At 706, the system can perform a union pass, in which a union of the first SDF and the second SDF is computed, as to define a union SDF. At 708, an outward offset pass is performed, in which the outward offset of the union SDF is computed. At 710, an inward offset pass is performed, in which an inward offset of the outward pass from 708 is computed. The pass at 710 can generate a blend surface, at 712.

[0026] Referring to FIG. 8, the offset passes at 708 and 710 are further described by way of a two dimensional (2D) illustrative example using an example input shape 800 in a voxel grid 802 that defines a plurality of voxels. To compute the offsets at 708 and 710, a ball 804 can be placed on each voxel, so as to create a plurality of sample points on the surface of the ball 804. The ball 804 can define a radius that is equal to the offset distance. The offset distance refers to the distance by which the SDF is offset. For example, the offset distance values can be subtracted from the distance field so as to move the surface toward the surface normal, or added to the distance field so a to move the surface away from the surface normal. In some cases, the offset distance is equivalent to the blend radius. The system can compute a minimum SDF value across the sample points, so as to define the outward offset 808. The system can compute a maximum SDF value across the sample points, so as to define the inward offset 810. A blend shape or blended edges 812 can be determined by the order of computing the outward and inward offsets. When the outward offset 808 is first computed and then the inward offset 810 is computed, a rounded blend is defined on the concave edge. When the inward offset 810 is first computed and then the outward offset 808 is computed, rounded blends are defined on the convex edges. The ball sampling operations described above for computing SDF offsets can be performed efficiently via parallel processing on the GPU. The system can then perform a smoothing pass on the bend surface SDF, for instance the blend surface SDF 812, so as to generate a smooth blend surface SDF representative of the blend face 106.

[0027] Referring now to FIG. 9, to perform the operations at 608, further passes can be performed through the compute shader on the GPU. For example, operations 900 can beDocket No. 202413055 performed to compute bound tubes, for instance a first bound tube 901 and a second bound tube 903. Bound curves corresponding to the bound tubes, for instance bound curves 112 and 114, define the respective central axis of the corresponding bound tubes. The central axis can vary in direction so as to define an axis that is not straight. For example, voxel representations on the GPU can create mesh models, such that a tube mesh can be generated first and then the corresponding curve can be determined from the tube mesh. Thus, bound tubes can define tubular shapes around bound curves. Bound tubes can be represented as an SDF or triangle mesh. In an example described herein, the system first computes the SDF of a given bound tube, and then the corresponding bound curve is extracted as a curve that passes approximately through the center of the corresponding tube. In an example, at 902, a gradient pass is performed for each input mesh, for instance the first mesh that represents the first face 103, and the second mesh that represents the second face 105. In an example, a Sobel gradient operator is used, so as generate a first gradient of the first SDF, and a second gradient 1003 of the second SDF (at 904), though it will be understood that the system can use alternative gradient operators, and all such gradient operators are contemplated as being within the scope of this disclosure.

[0028] With continuing reference to FIG. 9, at 906, the system, in particular the GPU, can perform a spine tube pass, so as to compute or generate the SDF of a tubular shape (at 908), for instance an SDF of a spine tube 905, around the spine curve of the input faces, for instance the input faces 103 and 105. Given the SDF of the input meshes d- nd d2, blend radius rbiendand spine tube radius rspine, the system can compute the spine tube SDF dspinein accordance with Equation (1):

[0029] In accordance with the example illustrated by Equation (1), the system generates a circular cross-section tube along the spine, though it will be understood that alternatively shaped cross-sections can be generated along the spine, and all such cross-sections are contemplated as being within the scope of this disclosure. For example, the system can perform operations that can be represented by Equations (2), which generates a substantially rectangular cross-section tube along the spine:Docket No. 202413055

[0030] Still referring to FIG. 9, the system, in particular the GPU, can perform bound tube passes, so as to compute bound tube SDFs, for instance SDFs of the first bound tube 901 and the second bound tube 903. In particular, at 910, the system can use the respective gradients to project the spine tube 905 on the first and second input meshes, so to compute or generate the bound tubes 901 and 903, at 912. Referring again to FIG. 6, at 610, the system can transfer the blend surface SDF from the GPU to the central processing unit (CPU) defined by the system. The blend surface mesh can be computed from the blend surface SDF, on the CPU. In another example, the system can directly compute the blend surface mesh on the GPU, and then transfer the blend surface mesh to the CPU from the GPU. The system can run marching cubes operations on the CPU to generate a blend surface mesh. In particular, for example, at 610, the system can transfer the bound tube SDFs 901 and 903, which define a 3D array of voxels, from the GPU to the CPU. At 612, the system, for instance on the CPU, can perform moving ball operations to compute or generate two bound curves, for instance the first bound curve 112 and the second bound curve 114.

[0031] Referring to FIG. 10, the system can perform example moving ball operations 1000 to compute bound curves, for instance the first bound curve 1 12 and the second bound curve 1 14. At 1002, the system can determine or identify a starting point of a given bound curve. In an example, for a closed loop tube, the system can identify the voxel with the minimum SDF value as the starting point of the bound curve. In such an example, the SDF inside the tube is negative and increases in magnitude as it is moved from the tube surface. This voxel may lie on the centerline of the tube and therefore can be chosen as the starting point of the bound curve. For tubes that do not form a loop, in some examples, the starting point can be identified as the most interior voxel that is closest to one of the ends of the tube. At 1004, the system can instantiate a ball that defines a radius that is larger than the spine tube radius at the starting point determined at 1002. At 1006, the system can sample points on the surface of the instantiated ball. At 1008, for each sample point, the system determines the closest spine tube voxel and evaluates that voxel’s SDF value against the minimum SDF value computed above. While looping through all the sample points on the ball, the system can track and find the voxel whose SDF value is closest to the minimum SDF value computed above. This voxel then gives the next point on the bound curve. Thus, the system can determine points on the bound curve and the current curve direction, at 1008, as each subsequent point defines a new starting point.Docket No. 202413055In some cases, the accuracy of the operations performed at 1008 can be increased by performing trilinear interpolation on the voxel grid to compute an SDF value at the sample point on the ball, instead of using the SDF value of the voxel that is nearest to the sample point.

[0032] With continuing reference to FIG. 10, at 1010, the system moves the ball to the next point computed at 1008. The process can then return to 1008 until the system loops back to the starting point or reaches to the other end of the spine tube, at 1012. In various examples, for every subsequent placement of the ball, the current curve direction can be used to ensure that the next point is chosen in the front facing half of the moving ball, and that the current curve direction is continuously updated. It will be understood that the example moving ball operations 1000 assume that there is no branching in the bound curves, as most blend cases between two meshes do not have branched bound curves. It will further be understood, however, that the system can perform more complex curve extraction routines to extract the bound curves when the bound curves define branches, and such moving ball extraction operations are contemplated as being within the scope of this disclosure.

[0033] Without being bound by theory, it is recognized herein that embodiments described herein can generate smooth blend surfaces that that define constant radius rolling ball blends. Such constant radius rolling ball blends can ensure that CAD operations generate parts or objects that can be manufactured, without bulging and while preserving topology. In various examples, the system generates bend surfaces by performing multiple steps or operations through multiple passes on a GPU. During each pass, the GPU can launch multiple processing threads, for instance one for each voxel, in parallel, thereby enabling the expedited processing of voxels to accurately compute smooth blend surfaces. By way of example, and without limitation, such GPU processing can result in millions of voxels being processed in 1 to 7 seconds.

[0034] Thus, as described herein in accordance with various embodiments, a computing system is configured to generate a model representative of a part capable of being manufactured. The system can obtain a first mesh model and a second mesh model. The first mesh model includes a first body that defines a first face, and the second mesh model includes a second body that defines a second face. The system can transfer the first and second mesh models to a graphics processing unit (GPU). The system can generate a first signed distance field (SDF) representation on the GPU, from the first mesh model. The system can also generate a second SDF representation on the GPU, from the second mesh model. Based on theDocket No. 202413055 first SDF and the second SDF, the system can perform first rolling-ball blend operations so as to generate a blend surface SDF. The first rolling-ball blend operations define a constant radius blend. The system can convert the blend surface SDF to a blend surface mesh. The blend surface mesh is representative of a blend face between the first face and the second face, such that the blend face defines the constant radius blend. Thus, the model representative of the part capable of being manufactured includes the first face, the second face, and the blend face.

[0035] In another example aspect, the system can, on the GPU, determine third and fourth SDF representations of first and second bound tubes, respectively, wherein the first bound tube defines a first boundary along the first face, and the second bound tube defines a second boundary along the second face. The system can perform second rolling-ball blend operations using the third SDF and the fourth SDF, as to generate a first bound curve and a second bound curve. The first bound curve defines a first edge of the blend face along the first face, and the second bound curve defines a second edge of the blend face along the second face. In an example, before converting the blend surface SDF to the blend surface mesh, the system transfers the blend surface SDF from the GPU to a central processing unit (CPU) of the computing system, and then computes the blend surface mesh from the SDF, on the CPU. In another example, the system can compute the mesh directly from the SDF on the GPU, and then transfer the mesh from the GPU to the CPU. The system can generate the first SDF and the second SDF during multiple passes on the GPU, such that a pass corresponds to each of the first and second mesh models. Furthermore, the system can generate the third SDF and the fourth SDF during multiple passes on the GPU, such that a pass corresponds to each of the first and second bound tubes.

[0036] In another example aspect, the first mesh model can define a first plurality or set of faces including the first face, and the second mesh model can define a second plurality or set of faces including the second face. In such an example, the system can convert the blend surface SDF to the blend surface mesh representative of the bend face, such that the blend face is defined between the first plurality of faces and the second plurality of faces.

[0037] FIG. 11 illustrates an example of a computing environment that can include the simulation system within which embodiments of the present disclosure may be implemented. A computing environment 1400 includes a computer system 1410 that may include a communication mechanism such as a system bus 1421 or other communication mechanism for communicating information within the computer system 1410. The computer system 1410Docket No. 202413055 further includes one or more processors 1420 coupled with the system bus 1421 for processing the information. The computing system described herein may include, or be coupled to, the one or more processors 1420.

[0038] The processors 1420 may include one or more central processing units (CPUs), graphical processing units (GPUs), or any other processor known in the art. More generally, a processor as described herein is a device for executing machine-readable instructions stored on a computer readable medium, for performing tasks and may comprise any one or combination of, hardware and firmware. A processor may also comprise memory storing machine-readable instructions executable for performing tasks. A processor acts upon information by manipulating, analyzing, modifying, converting or transmitting information for use by an executable procedure or an information device, and / or by routing the information to an output device. A processor may use or comprise the capabilities of a computer, controller or microprocessor, for example, and be conditioned using executable instructions to perform special purpose functions not performed by a general purpose computer. A processor may include any type of suitable processing unit including, but not limited to, a central processing unit, a microprocessor, a Reduced Instruction Set Computer (RISC) microprocessor, a Complex Instruction Set Computer (CISC) microprocessor, a microcontroller, an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), a System-on-a-Chip (SoC), a digital signal processor (DSP), and so forth. Further, the processor(s) 1420 may have any suitable micro architecture design that includes any number of constituent components such as, for example, registers, multiplexers, arithmetic logic units, cache controllers for controlling read / write operations to cache memory, branch predictors, or the like. The micro architecture design of the processor may be capable of supporting any of a variety of instruction sets. A processor may be coupled (electrically and / or as comprising executable components) with any other processor enabling interaction and / or communication there-between. A user interface processor or generator is a known element comprising electronic circuitry or software or a combination of both for generating display images or portions thereof. A user interface comprises one or more display images enabling user interaction with a processor or other device.

[0039] The system bus 1421 may include at least one of a system bus, a memory bus, an address bus, or a message bus, and may permit exchange of information (e.g., data (including computer-executable code), signaling, etc.) between various components of the computerDocket No. 202413055 system 1410. The system bus 1421 may include, without limitation, a memory bus or a memory controller, a peripheral bus, an accelerated graphics port, and so forth. The system bus 1421 may be associated with any suitable bus architecture including, without limitation, an Industry Standard Architecture (ISA), a Micro Channel Architecture (MCA), an Enhanced ISA (EISA), a Video Electronics Standards Association (VESA) architecture, an Accelerated Graphics Port (AGP) architecture, a Peripheral Component Interconnects (PCI) architecture, a PCI-Express architecture, a Personal Computer Memory Card International Association (PCMCIA) architecture, a Universal Serial Bus (USB) architecture, and so forth.

[0040] Continuing with reference to FIG. 11, the computer system 1410 may also include a system memory 1430 coupled to the system bus 1421 for storing information and instructions to be executed by processors 1420. The system memory 1430 may include computer readable storage media in the form of volatile and / or nonvolatile memory, such as read only memory (ROM) 1431 and / or random access memory (RAM) 1432. The RAM 1432 may include other dynamic storage device(s) (e.g., dynamic RAM, static RAM, and synchronous DRAM). The ROM 1431 may include other static storage device(s) (e.g., programmable ROM, erasable PROM, and electrically erasable PROM). In addition, the system memory 1430 may be used for storing temporary variables or other intermediate information during the execution of instructions by the processors 1420. A basic input / output system 1433 (BIOS) containing the basic routines that help to transfer information between elements within computer system 1410, such as during start-up, may be stored in the ROM 1431. RAM 1432 may contain data and / or program modules that are immediately accessible to and / or presently being operated on by the processors 1420. System memory 1430 may additionally include, for example, operating system 1434, application programs 1435, and other program modules 1436. Application programs 1435 may also include a user portal for development of the application program, allowing input parameters to be entered and modified as necessary.

[0041] The operating system 1434 may be loaded into the memory 1430 and may provide an interface between other application software executing on the computer system 1410 and hardware resources of the computer system 1410. More specifically, the operating system 1434 may include a set of computer-executable instructions for managing hardware resources of the computer system 1410 and for providing common services to other application programs (e.g., managing memory allocation among various application programs). In certain example embodiments, the operating system 1434 may control execution of one or more of the programDocket No. 202413055 modules depicted as being stored in the data storage 1440. The operating system 1434 may include any operating system now known or which may be developed in the future including, but not limited to, any server operating system, any mainframe operating system, or any other proprietary or non-proprietary operating system.

[0042] The computer system 1410 may also include a disk / media controller 1443 coupled to the system bus 1421 to control one or more storage devices for storing information and instructions, such as a magnetic hard disk 1441 and / or a removable media drive 1442 (e.g., floppy disk drive, compact disc drive, tape drive, flash drive, and / or solid state drive). Storage devices 1440 may be added to the computer system 1410 using an appropriate device interface (e.g., a small computer system interface (SCSI), integrated device electronics (IDE), Universal Serial Bus (USB), or FireWire). Storage devices 1441, 1442 may be external to the computer system 1410.

[0043] The computer system 1410 may also include a field device interface 1465 coupled to the system bus 1421 to control a field device 1466, such as a device used in a production line. The computer system 1410 may include a user input interface or GUI 1461, which may comprise one or more input devices, such as a keyboard, touchscreen, tablet and / or a pointing device, for interacting with a computer user and providing information to the processors 1420.

[0044] The computer system 1410 may perform a portion or all of the processing steps of embodiments of the invention in response to the processors 1420 executing one or more sequences of one or more instructions contained in a memory, such as the system memory 1430. Such instructions may be read into the system memory 1430 from another computer readable medium of storage 1440, such as the magnetic hard disk 1441 or the removable media drive 1442. The magnetic hard disk 1441 (or solid state drive) and / or removable media drive 1442 may contain one or more data stores and data files used by embodiments of the present disclosure. The data store 1440 may include, but are not limited to, databases (e.g., relational, object-oriented, etc.), file systems, flat files, distributed data stores in which data is stored on more than one node of a computer network, peer-to-peer network data stores, or the like. The data stores may store various types of data such as, for example, skill data, sensor data, or any other data generated in accordance with the embodiments of the disclosure. Data store contents and data files may be encrypted to improve security. The processors 1420 may also be employed in a multi-processing arrangement to execute the one or more sequences of instructions contained in system memory 1430. In alternative embodiments, hard-wiredDocket No. 202413055 circuitry may be used in place of or in combination with software instructions. Thus, embodiments are not limited to any specific combination of hardware circuitry and software.

[0045] As stated above, the computer system 1410 may include at least one computer readable medium or memory for holding instructions programmed according to embodiments of the invention and for containing data structures, tables, records, or other data described herein. The term “computer readable medium” as used herein refers to any medium that participates in providing instructions to the processors 1420 for execution. A computer readable medium may take many forms including, but not limited to, non-transitory, nonvolatile media, volatile media, and transmission media. Non-limiting examples of non-volatile media include optical disks, solid state drives, magnetic disks, and magneto-optical disks, such as magnetic hard disk 1441 or removable media drive 1442. Non-limiting examples of volatile media include dynamic memory, such as system memory 1430. Non-limiting examples of transmission media include coaxial cables, copper wire, and fiber optics, including the wires that make up the system bus 1421. Transmission media may also take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications.

[0046] Computer readable medium instructions for carrying out operations of the present disclosure may be assembler instructions, instruction- set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, statesetting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable programDocket No. 202413055 instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0047] Aspects of the present disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, may be implemented by computer readable medium instructions.

[0048] The computing environment 1400 may further include the computer system 1410 operating in a networked environment using logical connections to one or more remote computers, such as remote computing device 1480. The network interface 1470 may enable communication, for example, with other remote devices 1480 or systems and / or the storage devices 1441, 1442 via the network 1471. Remote computing device 1480 may be a personal computer (laptop or desktop), a mobile device, a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to computer system 1410. When used in a networking environment, computer system 1410 may include modem 1472 for establishing communications over a network 1471, such as the Internet. Modem 1472 may be connected to system bus 1421 via user network interface 1470, or via another appropriate mechanism.

[0049] Network 1471 may be any network or system generally known in the art, including the Internet, an intranet, a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a direct connection or series of connections, a cellular telephone network, or any other network or medium capable of facilitating communication between computer system 1410 and other computers (e.g., remote computing device1480). The network 1471 may be wired, wireless or a combination thereof. Wired connections may be implemented using Ethernet, Universal Serial Bus (USB), RJ-6, or any other wired connection generally known in the art. Wireless connections may be implemented using Wi-Fi, WiMAX, and Bluetooth, infrared, cellular networks, satellite or any other wireless connection methodology generally known in the art. Additionally, several networks may work alone or in communication with each other to facilitate communication in the network 1471.

[0050] It should be appreciated that the program modules, applications, computer-executable instructions, code, or the like depicted in FIG. 11 as being stored in the system memory 1430Docket No. 202413055 are merely illustrative and not exhaustive and that processing described as being supported by any particular module may alternatively be distributed across multiple modules or performed by a different module. In addition, various program module(s), script(s), plug-in(s), Application Programming Interface(s) (API(s)), or any other suitable computer-executable code hosted locally on the computer system 1410, the remote device 1480, and / or hosted on other computing device(s) accessible via one or more of the network(s) 1471, may be provided to support functionality provided by the program modules, applications, or computer-executable code depicted in FIG. 11 and / or additional or alternate functionality. Further, functionality may be modularized differently such that processing described as being supported collectively by the collection of program modules depicted in FIG. 11 may be performed by a fewer or greater number of modules, or functionality described as being supported by any particular module may be supported, at least in part, by another module. In addition, program modules that support the functionality described herein may form part of one or more applications executable across any number of systems or devices in accordance with any suitable computing model such as, for example, a client-server model, a peer-to-peer model, and so forth. In addition, any of the functionality described as being supported by any of the program modules depicted in FIG. 11 may be implemented, at least partially, in hardware and / or firmware across any number of devices.

[0051] It should further be appreciated that the computer system 1410 may include alternate and / or additional hardware, software, or firmware components beyond those described or depicted without departing from the scope of the disclosure. More particularly, it should be appreciated that software, firmware, or hardware components depicted as forming part of the computer system 1410 are merely illustrative and that some components may not be present or additional components may be provided in various embodiments. While various illustrative program modules have been depicted and described as software modules stored in system memory 1430, it should be appreciated that functionality described as being supported by the program modules may be enabled by any combination of hardware, software, and / or firmware. It should further be appreciated that each of the above-mentioned modules may, in various embodiments, represent a logical partitioning of supported functionality. This logical partitioning is depicted for ease of explanation of the functionality and may not be representative of the structure of software, hardware, and / or firmware for implementing the functionality. Accordingly, it should be appreciated that functionality described as being provided by a particular module may, in various embodiments, be provided at least in part byDocket No. 202413055 one or more other modules. Further, one or more depicted modules may not be present in certain embodiments, while in other embodiments, additional modules not depicted may be present and may support at least a portion of the described functionality and / or additional functionality. Moreover, while certain modules may be depicted and described as sub-modules of another module, in certain embodiments, such modules may be provided as independent modules or as sub-modules of other modules.

[0052] Although specific embodiments of the disclosure have been described, one of ordinary skill in the art will recognize that numerous other modifications and alternative embodiments are within the scope of the disclosure. For example, any of the functionality and / or processing capabilities described with respect to a particular device or component may be performed by any other device or component. Further, while various illustrative implementations and architectures have been described in accordance with embodiments of the disclosure, one of ordinary skill in the art will appreciate that numerous other modifications to the illustrative implementations and architectures described herein are also within the scope of this disclosure. In addition, it should be appreciated that any operation, element, component, data, or the like described herein as being based on another operation, element, component, data, or the like can be additionally based on one or more other operations, elements, components, data, or the like. Accordingly, the phrase “based on,” or variants thereof, should be interpreted as “based at least in part on.”

[0053] Although embodiments have been described in language specific to structural features and / or methodological acts, it is to be understood that the disclosure is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as illustrative forms of implementing the embodiments. Conditional language, such as, among others, “can,” “could,” “might,” or “may,” unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments could include, while other embodiments do not include, certain features, elements, and / or steps. Thus, such conditional language is not generally intended to imply that features, elements, and / or steps are in any way required for one or more embodiments or that one or more embodiments necessarily include logic for deciding, with or without user input or prompting, whether these features, elements, and / or steps are included or are to be performed in any particular embodiment.Docket No. 202413055

[0054] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

Claims

Docket No. 202413055CLAIMSWhat is claimed is:

1. A computer-implemented method for generating a model representative of a part capable of being manufactured, the method comprising: obtaining a first mesh model and a second mesh model, the first mesh model including a first body that defines a first face, the second mesh model including a second body that defines a second face; transferring the first and second mesh models to a graphics processing unit (GPU); generating a first signed distance field (SDF) representation on the GPU, from the first mesh model; generating a second SDF representation on the GPU, from the second mesh model; based on the first SDF representation and the second SDF representation, performing first rolling-ball blend operations so as to generate a blend surface SDF, the first rolling-ball blend operations defining a constant radius blend; and converting the blend surface SDF to a blend surface mesh, the blend surface mesh representative of a blend face between the first face and the second face, the blend face defining the constant radius blend, wherein the model representative of the part capable of being manufactured includes the first face, the second face, and the blend face.

2. The method as recited in claim 1, the method further comprising: on the GPU, determining third and fourth SDF representations of first and second bound tubes, respectively, wherein the first bound tube defines a first boundary along the first face, and the second bound tube defines a second boundary along the second face.

3. The method as recited in claim 2, the method further comprising performing second rolling-ball blend operations based the third SDF representation and the fourth SDF representation, as to generate a first bound curve and a second bound curve, the first bound curve defining a first edge of the blend face along the first face, and the second bound curve defining a second edge of the blend face along the second face.

4. The method as recited in claim 1, the method further comprising:Docket No. 202413055 before converting the blend surface SDF to the blend surface mesh, transferring the blend surface mesh from the GPU to a central processing unit (CPU).

5. The method as recited in claim 1, the method further comprises: generating the first SDF representation and the second SDF representation during multiple passes on the GPU, such that a pass corresponds to each of the first and second mesh models.

6. The method as recited in claim 2, the method further comprising: generating the third SDF representation and the fourth SDF representation during multiple passes on the GPU, such that a pass corresponds to each of the first and second bound tubes.

7. The method as recited in claim 1, wherein the first mesh model defines a first plurality of faces including the first face, and the second mesh model defines a second plurality of faces including the second face, the method further comprising: converting the blend surface SDF to the blend surface mesh representative of the bend face, such that the blend face is defined between the first plurality of faces and the second plurality of faces.

8. A computing system configured to generate a model representative of a part capable of being manufacture, the computing system comprising: a graphics processing unit (GPU); a central processor; and a memory storing instructions that, when executed by the central processor, cause the computing system to: obtain a first mesh model and a second mesh model, the first mesh model including a first body that defines a first face, the second mesh model including a second body that defines a second face; transferring the first and second mesh models to the GPU; generate a first signed distance field (SDF) representation on the GPU, from the first mesh model; generate a second SDF representation on the GPU, from the second mesh model;Docket No. 202413055 based on the first SDF representation and the second SDF representation, perform first rolling-ball blend operations so as to generate a blend surface SDF, the first rollingball blend operations defining a constant radius blend; and convert the blend surface SDF to a blend surface mesh, the blend surface mesh representative of a blend face between the first face and the second face, the blend face defining the constant radius blend, wherein the model representative of the part capable of being manufactured includes the first face, the second face, and the blend face.

9. The computing system as recited in claim 8, the memory further storing instructions that, when executed by the central processor, further cause the computing system to: on the GPU, determine third and fourth SDF representations of first and second bound tubes, respectively, wherein the first bound tube defines a first boundary along the first face, and the second bound tube defines a second boundary along the second face.

10. The computing system as recited in claim 9, the memory further storing instructions that, when executed by the central processor, further cause the computing system to: perform second rolling-ball blend operations based using the third SDF representation and the fourth SDF representation, as to generate a first bound curve and a second bound curve, the first bound curve defining a first edge of the blend face along the first face, and the second bound curve defining a second edge of the blend face along the second face.

11. The computing system as recited in claim 8, the memory further storing instructions that, when executed by the central processor, further cause the computing system to: before converting the blend surface SDF to the blend surface mesh, transfer the blend surface SDF from the GPU to the central processor.

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