Method for determining quality characteristics of ball and rod lattices

Abstract

A method for determining quality characteristics of a rod and ball lattice (400) is provided. The method includes: determining a quality characteristic of each ball (410, 420, 430) in a lattice; determining, for each rod (440, 450), a mass characteristic of a portion comprising an interbody volume between the end balls (410, 420, 430) of the rod (440, 450); generating an initial estimate of the mass characteristics for the lattice (400) based on the mass characteristics of the ball (410, 420, 430) and the portion of the rod (440, 450); and identifying, for each ball (410, 420, 430), an overlap portion (460) terminating between a pair of rods (440, 450) of the ball (410, 420, 430), and estimating a quality characteristic of each identified overlap portion (460); and modifying the initial estimate of the quality characteristic of the lattice (400) based on the estimate of the quality characteristic of the overlapping portion (460).

Description

TECHNICAL FIELD

[0001] The present invention relates to a computer-implemented method for determining quality properties of a lattice in a three-dimensional model. BACKGROUND

[0002] Computer-aided design (CAD) systems are used in many fields of engineering, manufacturing and design to create and manipulate solid modeling representations of objects, for example in additive manufacturing. Additive manufacturing is the process of creating three-dimensional objects using a 3D printer based on a CAD or other digital three-dimensional model. Objects can be scanned as a precursor to creating a CAD model, or can be designed from scratch and stored in an STL (stereolithography file format) or AMF (additive manufacturing file format) file for future printing.

[0003] Lattices are a common type of internal space filler used in CAD systems and additive manufacturing. Lattice structures can be used for heat transfer, filtration and structural components due to their physical and mechanical properties. In B-rep (boundary representation) modeling, a lattice structure can be enclosed by a set of closed, connected faces, where each face is a part of a two-dimensional surface. These faces have boundary edges, which are defined by curves where the individual faces intersect each other.

[0004] Bar and ball lattices are lattices that include a plurality of lattice topologies, where the lattice topologies can be bars or balls. Bars can be cylindrical or conical, while balls can be spherical. Each bar is joined to other bars by balls, thereby forming a lattice structure. The radius of the balls can remain constant throughout the lattice, or can vary throughout the lattice, or both. Similarly, the thickness of the bars can also vary linearly along their length. However, bars and balls can only exist as a whole within the lattice, which means that the lattice cannot contain a part of a ball, and all bars must be terminated by a ball.

[0005] In modeling applications, it is desirable to be able to efficiently determine properties of lattices. Quantities such as surface area, volume, center of mass and inertia, also referred to as quality properties in this document, are particularly important in many practical applications for understanding the physical properties of a modeled object. Control and estimation of the margin of error in the quality property computation is also crucial, as it allows the user to specify the degree of trade-off between computational effort and accuracy, and to quantitatively assess the accuracy of the results. In the context of a complete boundary representation model, the lattice geometry can be contained within certain regions. To compute how the lattice region affects the quality properties of the larger model, it is also necessary to consider how the lattice is trimmed by the boundaries of the region.

[0006] Meshing can be used to compute mass properties of a modeled object. A mesh is a subdivision of a continuous geometric space into discrete geometric and topological units, referred to as facets. With respect to a lattice, mass properties can be determined by extracting a mesh representation of the lattice and then computing mass properties of the mesh.

[0007] Unfortunately, meshing the entire lattice in order to compute its mass properties does not efficiently scale with the number of rods and spheres in the lattice. Furthermore, the large number of interactions of rods and spheres can affect the complexity of the mass property computation. It is therefore desirable to be able to compute mass properties of a lattice in a way that efficiently scales with the number of rods and spheres and that has sufficient accuracy and robustness even as the degree of interaction between lattice elements increases. SUMMARY

[0008] It is the task of the present invention to provide a method for determining mass properties of a lattice in a three-dimensional model.

[0009] The above and other tasks are achieved by the features according to the present invention. Further implementations are evident from the description and the drawings.

[0010] According to a first aspect, a method for determining mass properties of a lattice comprising a plurality of rods and spheres is proposed. The method comprises: a) determining mass properties of each sphere in the lattice; b) for each rod, determining mass properties of a portion comprising a volume between terminal spheres of the rod; c) generating an initial estimate of mass properties for the lattice based on the mass properties of the plurality of portions of spheres and rods; and e) for each sphere: i) identifying overlapping portions between pairs of rods terminating at the sphere; ii) estimating mass properties of each identified overlapping portion; and g) modifying the initial estimate of mass properties of the lattice based on the estimates of mass properties of the overlapping portions.

[0011] The method according to the first aspect enables efficient computation of mass properties of a lattice of rods and spheres. The method exploits specific properties of certain types of lattice structures to improve the performance and accuracy of the overall mass property computation.

[0012] In a first implementation, the mass properties are surface area, mass, volume, center of mass, or moment of inertia.

[0013] In a second implementation, estimating mass properties of each overlapping portion comprises: representing the mass properties as a surface area integral over a surface of the overlapping portion; subdividing the surface of the overlapping portion into a plurality of sub-regions; evaluating the surface area integral over each sub-region; and estimating the mass properties of the overlapping portion based on the evaluations of the surface area integral over each sub-region.

[0014] In a third implementation, subdividing the surface of the overlapping portion comprises: generating a representation of a surface of each sphere in the overlapping portion as a plurality of facets.

[0015] In a fourth implementation, subdividing the surface of the overlapping portion comprises subdividing the surface of the rod in the overlapping portion into a plurality of parametrized sub-regions.

[0016] In a fifth implementation, the method according to the first aspect comprises weighting the surface integral based on a number of overlapping rods in the sub-region.

[0017] In a sixth implementation, the method according to the first aspect further comprises identifying one or more further overlapping portions of the lattice, estimating a mass property of each further overlapping portion, and modifying the initial estimate of the mass property of the lattice based on the estimates of the mass properties of the further overlapping portions.

[0018] In a seventh implementation, the further overlapping portion comprises: a) a sphere-sphere intersection; b) a rod-sphere intersection, wherein the sphere is not a terminal sphere of the rod; or c) a rod-rod intersection, wherein the first rod is not adjacent to the second rod.

[0019] In an eighth implementation, subdividing the surface of the overlapping portion into a plurality of sub-regions comprises generating a first subdivision of the boundary of the surface extending outside the overlapping portion, and generating a second subdivision of the boundary of the surface contained within the overlapping portion.

[0020] In a ninth implementation, estimating the mass property of the overlapping portion based on the evaluation of the surface integral for each sub-region comprises generating a first value based on the first subdivision of the boundary, the first value comprising an overestimation of the surface integral of the surface of the overlapping portion; generating a second value based on the second subdivision of the boundary, the second value comprising an underestimation of the surface integral of the surface of the overlapping portion; and generating a third value based on the first value and the second value, the third value comprising an estimate of an error in the mass property of the overlapping portion.

[0021] In a second aspect, there is provided a computer program comprising code which, when executed by a data processing system, causes the data processing system to perform the steps of any of the above methods.

[0022] These and other aspects of the application will be apparent from the (one or more) embodiments described below. BRIEF DESCRIPTION OF DRAWINGS

[0023] For a fuller understanding of the present disclosure and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings, in which:

[0024] Figure 1 is a schematic perspective view of a lattice;

[0025] Figure 2 is a cross-sectional view of a lattice;

[0026] Figure 3a is a cross-sectional view of a truncated cone;

[0027] Figure 3b is a cross-sectional view of a spherical half-lens.

[0028] Figure 4a is a schematic perspective view of a lattice;

[0029] Figure 4b is a diagram showing overlapping regions of rods on spheres in a lattice;

[0030] Figure 5a is a schematic perspective view of a parametrized surface;

[0031] Figure 5b is a schematic perspective view of a surface;

[0032] Figures 6a and 6b show schematic perspective views of a lattice;

[0033] Figures 7a to 7c show schematic perspective views of a lattice;

[0034] Figures 8a to 8c show cubic lattices;

[0035] Figure 9 is a block diagram of a method for determining quality characteristics of a lattice;

[0036] Figure 10 is a simplified schematic diagram of a computing system according to an example. DETAILED DESCRIPTION

[0037] Example embodiments are subsequently described in sufficient detail to enable those skilled in the art to make and use it, and it is not the intention to limit the system and process described herein to only those example embodiments. It is to be understood that the example embodiments can be provided in many alternate forms and that they should not be construed as limited to only those set forth herein.

[0038] Accordingly, while the example embodiments can be modified in various ways and take on various alternative forms, specific embodiments thereof have been shown by way of example in the drawings and will subsequently be described in detail in this disclosure. This is not intended to limit the application to the particular forms disclosed. On the contrary, it is intended to cover all modifications, equivalents, and alternatives falling within the scope of the appended claims. Elements of the example embodiments are consistently denoted throughout the drawings and written description with the same reference numerals (where appropriate).

[0039] The terminology used in the description herein is not intended to be limiting in scope. The articles "a", "the", and "the" are singular in that they have a single referent, but the document can use the singular when referring to one or more of the referents. In other words, the elements referred to in the singular can be one or more unless the context clearly dictates otherwise. It will be further understood that the terms "comprises" and / or "comprising", when used in this document, specify the presence of stated features, items, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, items, steps, operations, elements, components, and / or groups thereof.

[0040] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0041] Figure 1 is a schematic perspective view of a volume lattice 100 according to an example. Lattice 100 is an example of a simple "dumbbell" shaped rod and ball lattice, comprising cylindrical rods 110 and terminal balls 120, 130. In general, the rods and balls forming a lattice can be referred to as a lattice body or lattice topology. For a given ball, the rods meeting at the ball are referred to as being adjacent to each other and to the ball. Other rods and balls in the lattice are referred to as being non-adjacent to each other. A self-intersection of a lattice refers to the intersection of a rod or ball with a non-adjacent rod or ball.

[0042] Figure 2 is shown. Lattice 200 comprises tapered rods 210 and terminal balls 220, 230 of radii Figure 1 and and respectively. The volume located between balls 220, 230 comprises the portion of rods 210 that is not located inside either of balls 220, 230, referred to herein as concave rods 240. Geometrically, concave rods 240 comprise truncated cones of radii and respectively, length h, with a spherical half-lens removed at each end.

[0043] The mass properties of simple lattices such as lattice 100 and lattice 200, which have no body-body intersections other than the intersection of a rod with its corresponding terminal ball, can be determined using classical geometry. In particular, the mass properties can be determined analytically from classical equations for the mass properties of truncated cones and balls (after removing the half-lenses). Starting with the ball, of radius Rand a sphere of center b (assuming constant density p = 1) has the following mass properties: Area Volume Center of mass Moment of inertia

[0044] Figure 3a is a cross-sectional view of a truncated cone 300 similar to the truncated cone of volume 240. The truncated cone 300 is a conical solid 305 of length h with planar caps 310, 315 of radii and respectively, perpendicular to the cone axis 320. The base point b of the cone 300 lies within the cap of radius The frame of the body is chosen such that points from b along the axis 320 of the cone to the cap 315 of radius The area and volume of the truncated cone 300 are:

[0045] Similarly, the formulas for the center of mass and moment of inertia about the principal axes can be determined as functions of , and

[0046] Figure 3b shows a cross-sectional view of a spherical hemilens 350. This is the solid region 355 bounded by a spherical cap 360 of radius of curvature R and a plane 365 that cuts the sphere such that the height of the cap 360 is h The base point b lies at the center of the disc 370, where the third element of the frame points along the axis of symmetry 375 to the cap 360. The area of the hemilens spherical cap 360 and the volume of the solid region 355 are:

[0047] Similarly, the formulas for the center of mass and moment of inertia about the principal axes can be determined as functions of , and R

[0048] Figure 2 The recessed bars in the lattice 200 shown can be characterized by the following numerical quantities: ​​h - the length of the truncated cone 240; - the radius of intersection between the truncated cone 240 and each of its balls 220, 230; b - the center of intersection of the truncated cone 240 with the ball 220; - the body frame, where points along the axis towards the ball 230; - the radius of the balls 220, 230.

[0049] the height of the half-lens at the balls 220, 230 is provided by = The volume of the individualized assembly cone and half-lens is: = )

[0050] Combining all equations, the volume and area of the concave rod 240 in Figure 2 are:

[0051] In these equations, the cap area of the half-lens gives a negative contribution, as the total area of the corresponding ball is computed, and the cap term of the half-lens can correct the area of the rod-ball intersection. Based on the previously computed volumes, centers of mass, and moments of inertia for the half-lens and the truncated cone, similar formulas can be determined for the center of mass and the moment of inertia of the concave rod.

[0052] In some cases, the rod can be completely absorbed within its terminal ball. This can be considered as a concave rod with a truncated cone of zero length, i.e. the contribution of two subtracted half-lenses at the ball intersection is completely negative.

[0053] In a simple lattice, with no intersection of the rods with their terminal balls, the mass properties of the lattice can be determined exactly using the above equations. For example, for the area and volume, the areas and volumes of the corresponding rods and balls can be summed:

[0054] In any lattice, these equations can be used in a first stage to provide a leading order calculation of the mass properties of the lattice, which does not take into account the overlapping regions between the rods and the balls, except for the overlap between the rods and their corresponding terminal balls.

[0055] Figure 4a is a schematic perspective view of a rod and ball lattice 400, according to an example. Lattice 400 includes balls 410, 420, 430 and interconnected rods 440, 450. Rod 440 connects balls 410 and 420, while rod 450 connects balls 410 and 430. In other words, ball 410 is a common terminal ball for rods 440 and 450, and rods 440 and 450 are adjacent to each other. Similarly, ball 410 is adjacent to rods 440 and 450. Furthermore, the rods overlap in a region 460. Due to the shape of the overlap between rods 440 and 450, region 460 is referred to herein as a duckbill region. Ball 410 and the adjacent rods 440, 450 are collectively referred to herein as a hub. In general, the overlap between rods at a given hub can be characterized by the intersecting circles on the surface of the hub's ball.

[0056] Figure 4b is a diagram showing the intersecting circles of three adjacent overlapping rods 470, 480, 490 on the surface of a ball. The numbers indicate the degree of correction to the leader order mass property calculation. For example, the regions labeled 1 correspond to double overlaps, and the volume of these regions should be subtracted once from the total volume calculation. Similarly, for the regions labeled 2 (where there is a triple overlap), the volume of this region should be subtracted twice from the total volume calculation.

[0057] Using the divergence theorem, the volume of an overlap region, such as region 460 in Figure 4a, can be determined by where the first integral is over the surface of the rods in the overlap region, and the second integral is over the surface of the footprint of the rods in the overlap region on the ball, similar to the regions shown in Figure 4b: (1)

[0058] In this formula, is a function that takes a point in three-dimensional space and returns the number of rods (including rod boundaries) that the point lies on.

[0059] The integrals in equation (1) can be evaluated on a per-hub basis. At a given hub, an adjacency matrix can be generated that records pairwise collisions between the rods in the hub. As previously mentioned, the simplest pairwise overlap case is the duckbill region 460 shown in Figure 4a.

[0060] Figure 5a shows a schematic perspective view of a parameterized surface 500, according to an example. Surface 500 includes subdividing the intersection surface of rods 440 and 450 in duckbill region 460 into a plurality of parametric patches 510. In the example shown in Figure 5a, parametric patches 510 are four-sided facets, referred to herein as quadrilaterals. These quadrilaterals are aligned with the principal curvature parameters of their parameterized surface. The first integral in equation (1) can be determined in each quadrilateral in the overlap region. Since the quadrilaterals are parameter rectangles on a cone, the surface integral can be computed exactly.

[0061] The contribution from the parametric patches at boundary 520 of the overlap region can be approximated by estimating the fraction of each patch inside the boundary region. The error that arises in this approximation can also be modeled by tracking the quality characteristic contributions from overestimating and underestimating this fraction. The parametric patches can be recursively subdivided near the boundary. This enables the approximation to closely capture the true geometry of the overlapping surface.

[0062] Figure 5b shows a schematic perspective view of a surface 550, according to an example. Surface 550 includes a faceted representation of the surface imprinted by rods 440, 450 on sphere 410. Determining the contribution from the local quality characteristic of the imprinted surface on sphere 410 is similar to the method used for surface 500, except that surface 550 is faceted into a plurality of flat triangular mesh elements. This is efficient, and the additional approximation that arises using a faceted representation does not significantly increase the overall error. Once the contributions from the facets are determined, equation (1) can be used to determine the quality characteristic contribution of the entire overlapping volume 460.

[0063] Figures 6a and 6b show schematic perspective views of a volume rod and sphere lattice 600, according to an example. Lattice 600 includes spheres 610, 620, 630 and interconnecting rods 640, 650. Rod 640 connects spheres 610 and 620, while rod 650 connects spheres 620 and 630. Sphere 620 is a common terminal sphere for rods 640 and 650. In addition, sphere 610, which is a non-terminal sphere for rod 650, intersects rod 650 in overlap region 660.

[0064] The quality characteristic calculation must account for the overlap of sphere 610 with rod 650 in region 660. In this case, the previously described method can still be used to determine the quality characteristic of lattice 600, even though there is an intersection between non-adjacent bodies in the lattice. In Figure 6b, the surface 670 of spheres 610, 620 in the overlap region is faceted, while the surface 680 of rods 640, 650 is parameterized using quadrilaterals, as previously described. Surface integrals can be evaluated on these sub-regions to determine the quality characteristic contribution of overlap region 660.

[0065] Figure 7a shows a schematic perspective view of a volume bar and a sphere lattice 700, according to an example. The lattice 700 comprises a region 710 with multiple intersecting bars. The region 710 is too complex to be efficiently processed using the previously described method. Instead of attempting to determine the mass properties by evaluating the surface integral in the surface sub-regions of the overlapping bars, it is more efficient to divide the lattice into multiple sub-lattices.

[0066] Figures 7b and 7c show schematic perspective views of the lattice 700, with new spheres inserted to split the lattice 700 into a set of sub-lattices. A first set of sub-lattices 720 is shown in Figure 7b. The mass properties of the sub-lattices 720 can be determined using the previously described method. These sub-lattices are simple lattices that do not include any self-intersecting parts between non-adjacent lattice bodies.

[0067] In Figure 7c, additional spheres are added to the remaining part of the lattice 700 to form sub-lattices 730. The sub-lattices 730 include the non-trivial intersecting region 710. Instead of attempting to use the previously described method for the sub-lattices 730, the mass properties of the sub-lattices 730 can be determined by tessellating the sub-lattices into meshes and determining the mass properties of the meshes. Tessellation of self-intersecting lattices can be efficiently performed using the techniques described in US Patent Application US 17 / 388,771. This approach is more efficient than tessellating the entire lattice 700 into meshes.

[0068] In the context of a complete three-dimensional boundary representation model, a lattice geometry is typically contained within a specific region of the model. To compute how the lattice region contributes to the mass properties of the larger model, it is also necessary to consider how the lattice is trimmed by the boundaries of the region.

[0069] The interaction of the lattice with its containing region is explained in a similar manner to the lattice 700. The lattice elements that interact with the region boundaries are identified, and new spheres are inserted to split the lattice into boundary sub-lattices (some of whose components intersect the boundary) and interior sub-lattices (which do not join with the region boundaries). The inserted spheres must not interact with the boundary, as they must be valid members of both the boundary sub-lattices and the interior sub-lattices.

[0070] The mass properties of the interior sub-lattices can be computed using the previously described method, while the mass properties of the boundary sub-lattices can be computed using mesh tessellation techniques. The results of all the sub-lattices are then appropriately accumulated, as in the final stage of the previously described method, adjusting the overlaps at the inserted spheres to derive the total mass properties result for the entire lattice region.

[0071] Figure 8a shows a cubic stick and ball lattice 800, according to an example. The lattice 800 is embedded in a region with a cylindrical boundary 810. Figure 8b shows the same lattice 800 and boundary 810. Applying the described method, lattice elements 820 that interact with the boundary 810 can be identified. Additional balls 830, 840 are inserted to partition the lattice 800 so that the cells 820, 830 and 840 form a boundary sub-lattice. The cells 850 and balls 830 form an interior sub-lattice. Figure 8c shows a grid representation 860 of the boundary sub-lattice trimmed to the boundary 810. The quality properties of the interior sub-lattice can be determined using the previously described methods. The quality properties of the grid can be determined and combined with the quality properties of the interior sub-lattice, and adjusted for the overlapping balls 830.

[0072] Figure 9 A block diagram of a computer-implemented method 900 for determining a quality property of a lattice comprising a plurality of sticks and balls in a three-dimensional model is shown. The method 900 can be used in conjunction with the other methods described herein. The quality property can be a surface area, a mass, a volume, a center of mass, or a moment of inertia of the lattice.

[0073] At block 910, the method includes determining a quality property of each ball in the lattice. According to an example, the quality property of each ball can be determined using the classical formula described earlier.

[0074] At block 920, the method 900 includes determining, for each stick, a quality property of a portion of the lattice comprising an interstitial volume between the terminal balls of the stick. According to an example, the interstitial volume comprises a volume similar to Figure 2 A concave stick shown in Figure 2.

[0075] At block 930, the method 900 includes generating an initial estimate of the quality property for the lattice based on the quality properties of the balls and the portions of the sticks.

[0076] At block 940, the method 900 includes, for each ball, identifying overlapping portions between pairs of sticks that terminate at the ball, and estimating a quality property of each identified overlapping portion. According to an example, estimating the quality property of each overlapping portion can include representing the quality property as a surface area integral over a surface of the overlapping portion, subdividing the surface of the overlapping portion into a plurality of sub-regions, evaluating the surface area integral over each sub-region, and estimating the quality property of the overlapping portion based on the evaluations of the surface area integral over each sub-region.

[0077] At block 950, the method 900 includes modifying the initial estimate of the quality property of the lattice based on the estimates of the quality properties of the overlapping portions.

[0078] The staged approach to mass property computation described herein leverages specific properties of certain types of lattices to improve the performance and accuracy of the computation. Approximations are used only when necessary. This reduces error compared to other approaches while maintaining efficiency. For example, the analytic approach in the first stage of the computation is very fast, and for certain sub-classes of lattices, this is sufficient to compute all mass properties accurately.

[0079] Similarly, for more general non-self-intersecting lattices, the second stage based on surface integral computation can be used to refine the initial estimate from the first stage computation to approximate the lattice in a way sufficient to achieve a user-specified accuracy. This can also be used to provide meaningful error estimates for each type of mass property. In both the first and second stages, the lattice data structure can be traversed in parallel computing threads to speed up the overall computation.

[0080] By using more traditional mass property methods for complex sub-lattices and boundary sub-lattices, the approach described herein ensures robust behavior on complex lattice regions while still benefiting from the speed and accuracy-driven estimates of the first and second stages.

[0081] The present disclosure will be described with reference to flow charts and / or block diagrams that illustrate the methods, apparatus, and systems according to examples of the present disclosure. Although the flow diagrams illustrate a particular order of execution, the order of execution can differ from that which is depicted. Blocks described in connection with one flow diagram can be combined with blocks described in connection with another flow diagram. In some examples, some blocks of a flow diagram can not be necessary, and / or additional blocks can be added. It will be understood that each block of the flow diagrams and / or combinations of blocks in the flow diagrams can be implemented by machine readable instructions.

[0082] The machine readable instructions may, for example, be executed by a general purpose computer, a special purpose computer, an embedded processor, or a processor of other programmable data processing equipment to implement the functions described in the specification and diagrams. In particular, a processor or processing means can execute machine readable instructions. Thus, the various modules of the apparatus can be implemented by a processor executing machine readable instructions stored in a memory, or can be implemented by a processor operating in accordance with instructions embedded in logic circuitry. The term “processor” should be interpreted broadly to encompass a CPU, processing unit, ASIC, logic unit, or programmable gate set, etc. The methods and modules can all be executed by a single processor, or can be dispersed among multiple processors.

[0083] Such machine readable instructions can also be stored in a computer readable storage device which can direct a computer or other programmable data processing equipment to function in a particular manner.

[0084] Figure 10An example 1000 of a processor 1010 associated with a memory 1020 is shown. The memory 1020 includes computer-readable instructions 1030 executable by the processor 1010.

[0085] The instructions 1030 cause the processor to determine a mass property of a lattice in a three-dimensional model. Specifically, the instructions cause the processor to determine a mass property of each sphere in the lattice; determine, for each rod, a mass property of a portion of the lattice that includes a volume between terminal spheres of the rod; and generate an initial estimate of the mass property of the lattice based on the mass properties of the spheres and the portions of the rods. The instructions also cause the processor to identify, for each sphere, overlapping portions between pairs of rods that terminate at the sphere and estimate a mass property of each identified overlapping portion; and modify the initial estimate of the mass property of the lattice based on the estimates of the mass properties of the overlapping portions.

[0086] The application can be embodied in other specific apparatus and / or methods. The described embodiments are to be considered in all respects only as illustrative and not restrictive. Specifically, the scope of the application is to be determined by the appended claims rather than the specification and drawings. All changes that come within the meaning of equivalency of the claims are to be embraced within the scope of the claims. Docket Number: 1001.0001WO1

[0087] It will be understood that the elements and features of the attached claims can be combined in a variety of ways to produce new claims that are also within the scope of the application. Thus, although the dependent claims following the independent claims can refer to the independent claims as a single potential combination, it is also possible that more than one independent claim can act as a precursor to the dependent claims. Consequently, the dependent claims refer to each independent claim as an antecedent, regardless of whether the individual dependent claims refer to the independent claim in a particular combination. In general, the application is intended to cover any combination of one or more of the elements or features of the various embodiments.

Claims

1. A computer-implemented method for determining the mass properties of a lattice in a three-dimensional model, the lattice comprising a plurality of bars and a plurality of spheres, the method comprising: Determine the mass characteristics of each of the plurality of spheres in the lattice; For each of the plurality of rods, determine the mass characteristics of a portion of the interbody volume between the terminal spheres of the respective rod; An initial estimate of the mass characteristics of the lattice is generated based on the mass characteristics of the plurality of spheres and the mass characteristics of the portions of the plurality of rods; For each of the plurality of balls, identify the overlapping portion between the stick pairs that terminate at the corresponding ball; For each of the plurality of balls, estimate the mass characteristics of each identified overlapping portion; as well as The initial estimate of the quality characteristics of the lattice is modified based on the estimate of the quality characteristics of the overlapping portion.

2. The method according to claim 1, wherein the mass characteristic is surface area, mass, volume, center of gravity, or moment of inertia.

3. The method of claim 1, wherein estimating the quality characteristic of each overlapping portion comprises: The quality characteristic is expressed as a surface integral on the surface of the overlapping portion; The surface of the overlapping portion is subdivided into multiple sub-regions; Evaluate the surface integral over each of the plurality of sub-regions, and The quality characteristics of the corresponding overlapping portions are estimated based on the evaluation of the surface integral over each of the plurality of sub-regions.

4. The method of claim 3, wherein the surface subdividing the overlapping portion comprises: The surface representation of each sphere in the overlapping portion is generated as multiple facets.

5. The method of claim 3, wherein the surface subdividing the overlapping portion comprises: The surface of the rod in the overlapping portion is subdivided into multiple parameterized sub-regions.

6. The method according to claim 3, further comprising: The surface integral is weighted based on the number of overlapping rods in the plurality of sub-regions.

7. The method according to claim 1, further comprising: Identify one or more additional overlapping portions of the lattice; Estimate the quality characteristics of each of the one or more additional overlapping portions of the lattice; The initial estimate of the quality properties of the lattice is modified based on the estimate of the quality properties of the one or more additional overlapping portions of the lattice.

8. The method of claim 7, wherein one of the additional overlapping portions comprises: Spheres intersect; A stick and a ball intersect, wherein the ball is not the terminal ball of the stick; or The first and second poles intersect in a pole-to-pole configuration, wherein the first and second poles are not adjacent.

9. The method of claim 3, wherein subdividing the surface of the overlapping portion into a plurality of sub-regions comprises: A first subdivision is generated to form the boundary of the surface extending beyond the overlapping portion; as well as A second subdivision is generated to form the boundary of the surface contained within the overlapping portion.

10. The method of claim 9, wherein estimating the quality characteristics of the overlapping portion based on an evaluation of the surface integral for each sub-region comprises: The first subdivision based on the boundary generates a first value, wherein the first value includes an overestimation of the surface integral on the surface of the overlapping portion. A second value is generated based on the second subdivision of the boundary, wherein the second value includes an underestimation of the surface integral of the surface of the overlapping portion; as well as A third value is generated based on the first and second values, wherein the third value includes an estimate of the error in the quality characteristics of the overlapping portion.

11. A computer-implemented method for determining the mass properties of a lattice in a three-dimensional model, the lattice comprising a plurality of bars and a plurality of spheres, the method comprising: Evaluate the intersections between the plurality of rods and the plurality of balls; Based on the assessment, the crystal lattice is subdivided into multiple sub-lattices; Determine the mass characteristics of each of the plurality of spheres in at least one of the plurality of sublattices; For each of the plurality of rods, determine the mass characteristics of a portion of the interbody volume between the terminal spheres of the respective rod; An initial estimate of the mass characteristics of the corresponding sublattice is generated based on the mass characteristics of the plurality of spheres and the mass characteristics of the portions of the plurality of rods; For each of the plurality of balls, identify the overlapping portion between the stick pairs that terminate at the corresponding ball; For each of the plurality of balls, estimate the mass characteristics of each identified overlapping portion; as well as The initial estimate of the quality characteristics of the corresponding sublattice is modified based on the estimate of the quality characteristics of the overlapping portion.

12. The method of claim 11, wherein subdividing the lattice comprises: Identify at least two self-intersections between a first lattice and at least two other lattices, wherein the at least two other lattices are not adjacent to the first lattice; as well as A sublattice is generated, the sublattice comprising at least the first lattice body and a lattice body adjacent to the first lattice body.

13. The method of claim 12, comprising: The sublattice is transformed into a grid; as well as Determine the quality characteristics of the mesh.

14. A computer program comprising code, which, when executed by a data processing system, causes the data processing system to perform the steps of the method according to any one of claims 1 to 13.

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