The combination of model conversion and visual CSG modeling

In Step 1, we divided the CAD model into convertible and non-convertible solids. To ensure the usability of the entire model, non-convertible solids should be processed to make these convertible. In practical engineering applications, the usual approach is to return to the CAD system, perform model simplification and repair, output the BRep model, and then perform the BRep-to-CSG conversion. Because of issues such as model repair failure, accuracy loss during STEP file data exchange, and failure of Boolean operations during the conversion process, this process requires repeated execution and is time-consuming. For non-convertible solids, if incremental CSG modeling can be performed directly on the converted CSG model, the workload can be reduced effectively (Fig. 2).

Fig. 2Full-screen View

The combination of model conversion and visual CSG modeling

The J Large-scale Automatic Modeling Tool (JLAMT) [44] is a CSG visualization modeling tool for large-scale scenes. It is implemented using Siemens NX software [45]. Siemens NX is a widely used CAD and CAM platform in the industrial manufacturing and engineering fields, with superior geometric modeling and interaction capabilities. NX provides users with the highly effective secondary development tool, NX Open API. It supports them in developing various geometric modeling functions on the NX platform. JLAMT is a dedicated module for Monte Carlo CSG geometric modeling. It was constructed based on the NX Open API. It enables users to create basic geometry primitives such as boxes, spheres, cylinders, cones, and tori. Based on these geometric primitives, JLAMT supports users in constructing solids with more complex geometries through Boolean operations. Users can specify father–child relationships to achieve nesting between geometric solids and create repetitive structures to achieve rapid modeling of an array model. The created CSG model can be exported as a geometric description markup language (GDML) file for JMCT simulations.

To combine the BRep-to-CSG model conversion capability of the CMGC with the visual CSG modeling capability of the JLAMT, we proposed the following technical approach:

(1) For convertible solids, CMGC first converts these into a GDML file. JLAMT parses the information stored in the GDML file and then, converts it into a complete JLAMT project that includes the modeling history, geometry solids, father–child relationships, repetitive structures, rotation and translation matrices, materials, and names.

(2) For non-convertible solids, CMGC outputs the parameters of the surface and coordinate systems. Based on this information, incremental modeling is performed manually in JLAMT for the imported GDML model. The JLAMT examines or ensures that the incrementally created CSG model does not overlap or encounter naming conflicts with the imported GDML model.

(3) Finally, the JLAMT outputs a complete GDML file corresponding to the original CAD model including convertible and non-convertible geometry solids.

To achieve this technical approach, we developed a GDML reverse conversion functionality in JLAMT. It converts multiple GDML files into JLAMT projects. Both GDML and JLAMT models can be described as geometric solid multibranch trees and multiple Boolean operation binary trees, respectively. Geometric solids are nested within each other to form father–child relationships. Multiple levels of solid nesting form a solid-geometry multibranch tree. Each solid geometry can be composed of basic geometric primitives through multiple Boolean operations to form a binary tree. Figure 3(a) shows the CSG model constructed in JLAMT. Figure 3(b) shows the corresponding geometry of the solid multibranch tree and Boolean operation binary trees.

Fig. 3Full-screen View

(Color online) An example of geometry solid multibranch tree and Boolean operation binary trees

To convert the GDML model into a JLAMT model, two problems should be solved. First, the implicit expressions of the geometry multibranch tree and Boolean operation binary tree in the GDML model should be converted into explicit expressions in the JLAMT model. The GDML organizes data items in the form of key-value pairs. Data items can refer to each other and have a free order. Their tree structure is implicit in the reference relationships between data items. However, the JLAMT model is a CAD model represented by CSG. Its tree structure is its sequential modeling history, which should be expressed explicitly. Second, the relative positions of the geometric solids in the GDML should be converted to the absolute positions in the JLAMT. In the GDML model, for the father–child relationship, the position of the child geometry solid is specified relative to the coordinate system of its father geometry solid. For the Boolean operation, the position of the tool body is given relative to the coordinate system of the target. That is, the position of a node in the geometric solid multibranch tree and Boolean operation binary tree in the GDML model is a relative position based on its father node. However, in the JLAMT, the positions of all nodes are determined based on the absolute coordinate system. Therefore, we implemented the conversion from the GDML model to the JLAMT model using the following method:

(1) Extract the data items in the GDML file using an XML parser. These include five types of key-value data items: geometry solids, father–child relationships, Boolean operations, basic geometry primitives, and materials.

(2) Reconstruct the geometry of the solid multibranch tree. Starting from the geometric solid data item of the world that envelops the entire particle transportation space, construct the geometry solid multibranch tree of JLAMT based on depth-first traversal using father–child relationships as the upper-lower relationships of the tree. Convert the material information simultaneously.

(3) Reconstruct all the Boolean operation binary trees. Starting from each leaf node of the geometric solid multibranch tree, construct the corresponding Boolean operation binary tree of JLAMT based on depth-first traversal using Boolean operations as the upper-lower relationships of the tree.

(4) During the reconstruction process of the geometric solid multibranch tree and Boolean operation binary trees, record the rotation and translation matrices between the upper and lower nodes, and perform matrix multiplication sequentially to obtain the rotation and translation matrix of each basic geometry primitive relative to the geometric solid of the world.

(5) Reconstruct all the basic geometry primitives in the JLAMT. That is, recover the parametric modeling process of the primitives in JLAMT based on the parameter information of the geometric primitives in GDML. For example, for a generalized cylinder defined by the inner radius, outer radius, height, and azimuth range, two arcs determined based on the inner and outer radii, and two line segments determined based on the azimuth range can be connected end-to-end to form a sector. Using this sector as the contour line, stretch it in the direction perpendicular to the plane where the contour line is located, with a stretch distance equal to the height of the cylinder.

Optimization of splitting surface assessment method

In Steps 3 and 4, the splitting surfaces need to be assessed. The CMGC categorizes splitting surfaces into direct, indirect, and auxiliary splitting surfaces [15]. This is illustrated in Fig. 4.

Fig. 4Full-screen View

Different types of splitting surfaces

A direct splitting surface is a natural surface of solid geometry that contains at least one splitting edge. In an infinitesimal neighborhood of any point on the splitting edge, the solid geometry is located on both sides of the direct splitting surface. Direct splitting surfaces and splitting edges can be determined based on the curvatures and normals of the surfaces [15]. An indirect splitting surface is also a natural surface. However, it does not contain splitting edges. An auxiliary splitting surface is not a natural surface (the reason for supplementing auxiliary surfaces is introduced in Sect. 2.3). When assessing indirect and auxiliary splitting surfaces, intersection Boolean operations are required to test whether the geometric solid is located on both sides of the surface. Boolean operations of geometry entities involve complex computational geometry algorithms such as curves and surface intersections. Moreover, their stabilities and accuracies depend on the geometry modeler. However, the Boolean operations of the Open Cascade occasionally cause conversion failures or program crashes.

To address this issue, we improved the method, as shown in Fig. 5. We adopted a method of faceting the boundaries of solids to determine the indirect and auxiliary splitting surfaces. First, the surfaces of the geometric solids were discretized into triangular facets. Then, the vertices of all the triangular facets were obtained. Simultaneously, the implicit equation F(x, y, z) = 0 for the surface to be assessed was calculated. The positions of these vertices relative to the surface were then determined by substituting the coordinates into the implicit equation of the surface and evaluating the sign of the computed results. If vertices are located in the positive half-space of the surface (the half-space pointing toward the exterior of the solid), the surface is a splitting surface. Moreover, the larger the number of vertices located in the positive half-space of the surface, the higher is the priority of the splitting surface. As shown in Fig. 5, splitting surface 1 has a higher priority than splitting surface 2. After decomposition by splitting surface 1, the solid no longer contains splitting surfaces. However, if splitting surface 2 is used first, splitting surface 1 remains unaltered. Because the splitting surface assessment method does not require a high discrete accuracy, it is faster than methods based on Boolean operations. The speed difference depends on the complexity of the model.

Fig. 5Full-screen View

(Color online) Facet the surfaces of geometry solid to assess splitting surfaces

Furthermore, it can be demonstrated that when the boundaries of a geometric solid consist only of planes, there are no indirect splitting surfaces. However, because of modeling errors and precision loss from data exchanges between different CAD systems, situations in which the two planes are offset marginally are common in large-scale urban scene models. As shown in Fig. 6, the adjacent red and green planes are offset by 1×10^–5 cm. The CMGC cannot assess these as direct splitting surfaces. Rather, it classifies these as indirect splitting surfaces. Further decomposition of solids through Boolean operations is vulnerable to failure. Therefore, if a solid consists only of planes, CMGC does not attempt to determine the indirect splitting surfaces.

Fig. 6Full-screen View

(Color online) Three examples where two planes are offset marginally

Optimization of auxiliary surface generation algorithm

When a geometric solid contains concave surfaces, it may be necessary to supplement the auxiliary surfaces to ensure that the solid can be represented by the CSG. As shown in Fig. 7(a), the natural surfaces of solid S contain a concave surface F₁ and five planes (denoted as F₂-F₆). Assuming that the normals of all the surfaces point toward the exterior of the solid, the result of the CSG expression $\overline{{\text{F}}_1}\cap \overline{{\text{F}}_2}\cap \overline{{\text{F}}_3}\cap \overline{{\text{F}}_4}\cap \overline{{\text{F}}_5}\cap \overline{{\text{F}}_6}$ is $\text{S}\cup \text{S"}$ rather than the solid S. Therefore, it is necessary to supplement the auxiliary surface AF₁ to ensure that solid S can be represented by the CSG, as shown in Fig. 7(b).

Fig. 7Full-screen View

(Color online) An example of an auxiliary surface to be supplemented

Typically, an auxiliary surface is constructed based on the boundary of the corresponding naturally concave surface. As shown in Fig. 8(a), auxiliary surface ${\text{AF}}_1$ can be constructed using vertices ${\text{V}}_1$, ${\text{V}}_2$, ${\text{V}}_3$, and ${\text{V}}_4$. However, in the STEP files exported from a CAD system, the surface of a solid may be composed of multiple parts. As shown in Figure 8(b), the concave cylindrical surface is divided into two parts by edges $\overrightarrow{{\text{V}}_5{\text{V}}_6}$, and the previous auxiliary surface generation algorithm generates two auxiliary surfaces according to ${\text{V}}_1$, ${\text{V}}_2$, ${\text{V}}_5$, ${\text{V}}_6$ and ${\text{V}}_3$, ${\text{V}}_4$, ${\text{V}}_5$, ${\text{V}}_6$. This causes an excessive decomposition of the solid. An excessive decomposition increases the probability of Boolean operation failures. An excessive decomposition during transportation calculations increases the number of geometric boundaries. This, in turn, results in redundant particle tracking calculations, thereby reducing the transportation efficiency. To prevent this, a surface-merging process was added to the auxiliary surface generation algorithm. Before generating auxiliary surfaces, CMGC analyzes the topological adjacency of concave surfaces using the same surface equation and combines adjacent surfaces topologically.

Fig. 8Full-screen View

(Color online) An example wherein a surface is composed of two parts

The method of topological combination of concave surfaces is as follows.

(1) Traverse all the concave surfaces of a solid geometry, and divide geometrically identical concave surfaces into the same set of concave surfaces. Determine the geometrically identical concave surfaces by sequentially comparing the surface types and parameters of the surface equations.

(2) Traverse all the surfaces into a set of concave surfaces, and divide the topologically adjacent surfaces into the same set of adjacent concave surfaces. The geometric solids converted by CMGC are manifolds. An undirected edge can be shared by only two surfaces. The topological adjacency of the surfaces can be determined using edges. An edge has its direction in BRep, which is determined by the order of its two vertices. If the geometries of the two edges are identical and the directions are opposite, such as $\overrightarrow{{\text{V}}_5{\text{V}}_6}$ and $\overrightarrow{{\text{V}}_6{\text{V}}_5}$, these are called adjacent edge pairs. The two surfaces to which an adjacent edge pair belongs are topologically adjacent

(3) Topologically combine surfaces belonging to the same set of adjacent concave surfaces. The combination method eliminates all adjacent edge pairs and reconstructs the loops of the surface according to the edge–vertex topological relationship. Delete vertices that are no longer used by the remaining edges, such as vertices ${\text{V}}_5$ and ${\text{V}}_6$.

Applications in the conceptual designs of CFETR blankets

The design of the CFETR requires detailed geometric modeling and numerical simulations, including Monte Carlo transportation [46-48]. In the preliminary design of the CFETR, three fusion blanket concepts were developed: the water-cooled ceramic blanket concept of the Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP); helium-cooled ceramic blanket concept of the Southwestern Institute of Physics (SWIP), China National Nuclear Corporation; and dual-cooled blanket concept of lithium-lead of the Institute of Nuclear Energy Safety Technology (INEST), Chinese Academy of Sciences. In addition, the Beijing Institute of Applied Physics and Computational Mathematics (IAPCM) and Institute of Nuclear Physics and Chemistry (INPC) developed two water-cooled natural uranium blanket concepts. In the CFETR model, multiple geometric solids including diverters contain spline surfaces. Six months were required to manually create a CFETR baseline model using JLAMT before we developed the combined capabilities of the CMGC model conversion and JLAMT visual modeling. Before the Monte Carlo simulations, it was necessary to remove the blanket from the CFETR baseline model and establish new blanket models based on the designs of different research institutes. Without the combined capabilities of the CMGC model conversion and JLAMT visual modeling, we need to manually combine the blanket part and baseline model for the five conceptual designs. Each blanket concept contains hundreds to thousands of geometric solids, and the workload for manually constructing these models is substantial.

In this study, utilizing combination capabilities, we achieved automatic replacement of different blanket conceptual designs. First, we deleted the original blanket from the baseline model in the JLAMT. Second, we used CMGC to automatically convert the CAD model of the blanket conceptual design into a GDML file. Third, the obtained GDML file was imported into JLAMT and automatically combined with the remaining parts of the baseline model. Finally, JLAMT outputted the newly completed CFETR model in the GDML format.

Figure 9 shows the CFETR model visualized in JLAMT using the blanket concept designed by the IAPCM. The complete CFETR model is illustrated in Fig. 9(a). The blanket parts are indicated in red. The detailed structure of the blanket is shown in Fig. 9(b). The green pipeline in Fig. 9(b) represents the fuel zone, and the red pipeline represents the tritium breeding zone. The thicknesses of the fuel and tritium breeding zones are identical. The conversion from the CAD model to the GDML file for the blanket parts required 1483 s using OpenMP parallel conversion on eight cores. The relative volume error was less than 0.0001% before and after conversion.

Fig. 9Full-screen View

(Color online) The conceptual designs of CFETR blankets of IAPCM

After constructing the CSG models, transportation calculations were performed using JMCT to determine the tritium breeding ratio (TBR). The calculation results were compared with those obtained using MCNP. Table 1 lists the comparison results for the IAPCM, including the number of geometric solids in the blankets and tritium breeding zone, TBR values, and relative deviation [49]. The calculation results of the other four conceptual designs were also in good agreement with those of MCNP. The application effects validated the correctness of the CMGC model conversion and the combined capability of the CMGC and JLAMT. It should be noted that a CAD geometry solid can be represented by different CSG expressions. The CSG expressions of the IAPCM model converted by CMGC were inconsistent with those established manually for MCNP. Therefore, the number of geometric solids of the blanket for JMCT and MCNP were inconsistent, whereas those of the tritium breeding zone were identical.

Model conversion for urban and ship scenes

Radiation transportation scenes such as those at the city and ship levels are highly complex and contain a large number of geometric solids. The workload of manual modeling is significant. This necessitates the use of a Monte Carlo modeling method for automatic model conversion. The CMGC has achieved fully automatic conversion from CAD BRep models to JMCT CSG models for many large-scale radiation transportation scenarios. The following are two examples of urban and shipping scenarios.

3.2.1

Urban building cluster scene

Figure 10 shows the converted GDML model for a typical urban building cluster. The left side of the figure shows a near-Earth panoramic view of the building cluster. The building cluster including the foundation has a total length of 9585 m in the X-direction and 12797 m in the Y-direction. It comprises 3381 geometric solids including buildings of varying heights, hills, and rivers. Building clusters include both simplified and detailed buildings. The red pentagram represents a detailed building [15] within a scene. As shown on the right side of Fig. 10, it consists of five floors, primarily made of concrete. It includes detailed window frames and glass. Owing to the optimization of the splitting surface assessment method, the conversion speed increased by 1.4 times. The number of solids that failed to convert decreased from hundreds to zero.

Fig. 10Full-screen View

A typical urban building cluster scene

An isotropic point source of photons was located 1000 m above the ground with the ground projection position at (0 m, 0 m). A blackbody spectrum was used as the source [50]. The blue dots represent the ground projection of the particle source in the air. The distribution of the radiation dose near the ground was tallied and analyzed, as shown in Fig. 11.

Fig. 11Full-screen View

(Color online) The distribution of radiation dose in the urban building cluster scene

Figure 11(a) shows that the radiation dose near the ground decreases with an increase in the distance from the ground projection of the source. Influenced by the proximate urban building clusters, the distribution of the radiation dose is non-uniform near the ground. However, it is consistent with the scene near the ground. The surfaces of the buildings facing the source exhibit higher radiation doses. Meanwhile, those facing away from the source receive less radiation owing to the obstruction by the buildings. This results in shadows (white regions) shaped similar to buildings. The radiation dose within the building is shown in Fig. 11(b). Owing to the influence of concrete, the radiation dose inside the building decreases significantly. However, because glass can transmit visible light, a small amount of energy is deposited within the building.

3.2.2

Ship scene

Figure 12(a) depicts a typical CAD model of the ship used for the transportation simulation. The model comprises 9363 components, with a total length of 368.5 m, deck width of 78.5 m, and total height from the bottom plate to the mast of 71.2 m. To obtain the radiation doses in the various compartments within the ship, the model includes detailed internal compartment structures, as shown in Fig. 12(b). The locations of the flight deck, hangar, and cabin are shown in Fig. 12(b). Owing to the optimization of the splitting surface assessment method and auxiliary surface generation algorithm, the conversion speed increased by 95%. The number of solids that failed to convert decreased from seven to two. The two failed solids can be manually added using JLAMT based on the combined capabilities of CMGC model conversion and JLAMT visual modeling.

Fig. 12Full-screen View

(Color online) A CAD model of a ship for transportation simulation

An isotropic point source of neutrons was located 185 m above the center of the deck. A fission spectrum [50] was used as the source. The blue dots represent the deck projection of the particle source in the air. The distribution of the absorbed dose throughout the ship was also calculated. Figure 13(a) shows the absorbed dose in the flight deck area with a minimum value of approximately 200 Gy. Figure 13(b) shows the absorbed dose in the hangar, with a minimum value of approximately 50 Gy. Meanwhile, Fig. 13(c) shows the absorbed dose in the cabin with a minimum value of approximately 10 Gy. The steel structures of the internal compartments within the ship function as shields against neutrons, reducing personnel absorbed dose. Therefore, precise computational models that include detailed geometric structures should be established for accurate calculations. The model conversion capability of the CMGC can reduce the modeling complexity of Monte Carlo CSG geometry and ensure simulation accuracy.

Fig. 13Full-screen View

(Color online) Distributions of absorbed dose on different horizontal planes of the ship