Level-set-based interactive topology optimization method for three-dimensional structure

Abstract

The present invention relates to the technical fields of computer-aided design, topology optimization, and interactive design. Disclosed is a level-set-based interactive topology optimization method for a three-dimensional structure. The method comprises: establishing a topology optimization design domain for a three-dimensional structure; importing a level set field or a three-dimensional model file of an initial structure, and generating an initial level set field; using a Marching Cubes method to extract a geometric structure from the level set field, and rendering and displaying an initial model; performing level set topology optimization on the structure, and updating, and rendering and displaying the structural morphology in real time; and during the optimization, pausing a process at any time for interactive modification, using a forced or non-forced intervention mode to perform structural addition / removal or morphology fine modification by means of interactive spheres, and updating the level set field in real time to continue the optimization. Thus, by means of the method, topology optimization of a complex initial model is efficiently implemented, and the structural morphology is dynamically adjusted, thereby effectively reducing cumbersome post-processing steps required by traditional methods, and improving the efficiency, accuracy, and flexibility of structural design.

Description

An Interactive Topology Optimization Method for 3D Structures Based on Level Sets Technical Field

[0001] This invention relates to the fields of computer-aided design, topology optimization, and interactive design, and in particular to an interactive topology optimization method for three-dimensional structures based on level sets. Background Technology

[0002] Topology optimization is a technique that improves structural performance by iteratively evolving the material distribution within a given design space. This method not only satisfies or enhances mechanical properties but also significantly reduces material usage, thus finding widespread application in aerospace, mechanical engineering, biomedicine, and civil engineering. However, the topological configurations generated by existing technologies often exhibit highly irregular geometric shapes, making it difficult to directly meet the technological constraints of engineering manufacturing on structural geometric characteristics. They typically only serve as conceptual design schemes and require complex post-processing for engineering transformation.

[0003] Currently, some feasible methods have been proposed to address the aforementioned issues. For example, the paper "Interactive 3D structural design in virtual reality using preference-based topology optimization" proposes a topology optimization method based on subjective preferences. This method introduces the designer's subjective preferences into the traditional bidirectional evolutionary structural optimization (BESO) approach, allowing the designer to more intuitively control the structural optimization results. Furthermore, "An interactive playground for real-time immersed topology optimization" proposes an immersive topology optimization method combining augmented reality (AR) technology. This method allows users to define, manipulate, and solve topology optimization problems in real time within an AR environment, providing a more intuitive interactive mode.

[0004] However, the aforementioned methods still have several core problems that urgently need to be addressed. First, both methods require the initial shape design of the structure to be completed before optimization begins. Once the optimization process starts, the optimization path tends to be fixed, making it difficult to dynamically adjust the structural shape or optimization direction during the optimization process. Further adjustments or refinements to the optimized structure typically require cumbersome and complex post-processing steps, reducing the interactivity and efficiency of the optimization methods. Second, current methods lack the ability to import external model files. When topology optimization of complex initial models is required, users must manually complete the modeling operation within the software. This process is not only cumbersome and time-consuming but also significantly reduces user convenience and design efficiency. Third, the aforementioned methods all use a density-based implicit representation to model and optimize the structure. This representation is difficult to clearly and accurately describe the boundary contours of complex structures, often requiring additional filtering or post-processing steps to generate an optimized structure with clear boundaries, further increasing the complexity of the process. Summary of the Invention

[0005] The purpose of this invention is to provide an interactive topology optimization method for three-dimensional structures based on level sets, which can efficiently optimize the topology of complex initial models, dynamically adjust the structural morphology, and improve the efficiency, accuracy and flexibility of structural design.

[0006] To achieve the above objectives, this invention provides a three-dimensional interactive topology optimization method based on level sets, comprising the following steps:

[0007] S1. Set the number of nodes in the XYZ directions, establish a three-dimensional structural topology optimization design region, define boundary conditions and configuration parameters. The boundary conditions are structural loads and constraints, the configuration parameters are iterative parameters in the topology optimization process, and the nodes are grid points in the design region.

[0008] S2. Import the initial model's horizontal set field φ(X) into the design area, or import and display the model file and calculate the model's SDF symbolic distance function, then use the horizontal set generation formula based on the SDF symbolic distance function to calculate the horizontal set field φ(X).

[0009] S3. Using the horizontal field φ(X), the initial structure display model is generated by rendering in the design area using the Marching Cubes method;

[0010] S4. According to the configuration parameters, use level set topology optimization to solve for the design variables, which include mathematical variables describing the structural shape and topology in the level set topology optimization method;

[0011] S5. Observe the optimization status of the display model. When the optimization does not meet the design requirements, pause the optimization process. The design requirements include aesthetic design, global optimal design, and avoidance of stress concentration.

[0012] S6. Select mandatory intervention or non-mandatory intervention. Mandatory intervention means that the modification of the structure will not change as optimization continues, while non-mandatory intervention means that the modification of the structure will change as optimization continues.

[0013] S7. Generate an interactive sphere, set the radius R of the interactive sphere to control the interaction precision, move the interactive sphere through the interactive device, and perform operations to delete or add structures to the display model in the movement trajectory of the interactive sphere, display the modified content in real time, and record the node positions Xc passed by the movement trajectory.

[0014] S8. Change the size of the interactive sphere to determine the operation range, pick the structural surface of the model displayed within the operation range of the interactive sphere, generate surface control points on the structural surface, select and drag the control points through the interactive device to finely modify the surface shape, and record the modified surface control point position Xd.

[0015] S9. Calculate the SDF symbolic distance function of the modified display model, and use the SDF-based level set generation formula to calculate the updated level set field Φnew(X);

[0016] S10. Continue to optimize the process, adopt the horizontal cube interactive iterative optimization algorithm, iteratively update the adjusted horizontal cube Φnew(X), and use the Marching Cubes method to render and display the model in real time.

[0017] S11. Repeat steps S5 to S10 until the iteration converges. Optimize to obtain a horizontal set field that meets the design requirements. Then import the horizontal set field into software that supports implicit modeling, export the optimized structure, and complete the interactive structural design.

[0018] The preferred mathematical model for level sets is as follows:

[0019] Preferably, in step S2, the displayed model file is a three-dimensional geometric structure file, including OBJ, STL, and PLY formats.

[0020] Preferably, the SDF symbolic distance function represents the shortest distance from any point in three-dimensional space to the surface of an object, and the level set generation formula φ(X) based on the SDF symbolic distance function is: d max =max(|SDF min |,|SDF max |);

[0021] In the formula, SDF min SDF max This represents the minimum and maximum values ​​of the SDF symbolic distance function for all nodes in the design region. Let represent the gradient magnitude of the SDF field, β represent the smoothing coefficient, and (x,y,z) represent the three-dimensional spatial coordinates.

[0022] Preferably, in step S5, the optimization of the model is observed using a head-mounted display or a 3D display, and the observation angle and position of the structure are controlled by an interactive device to observe the changes of the structure from multiple perspectives, both inside and outside the structure.

[0023] Preferably, in step S5, the surface control points are generated using a method based on Bézier surfaces.

[0024] Preferably, in step S10, the horizontal set-field interactive iterative optimization algorithm is as follows: Φ n (X)=Φ new (X)

[0025] When choosing mandatory intervention:

[0026] When choosing non-mandatory intervention:

[0027] In the formula, X c X represents the node positions traversed by the trajectory of the interactive sphere. d denoted as the position of the surface control points after model modification; B is the evolution velocity field of the level set function; dt is the iteration time step; α∈[0,1] is the non-forced intervention weight coefficient, which is adjusted in real time by the slider; n is the number of iteration steps when modifying the model.

[0028] Preferably, in steps S7 and S8, the interactive operations of the interactive sphere are recorded to form a design history tree, which supports backtracking or redoing any step of the modification operation by sliding the timeline.

[0029] Preferably, in steps S5 to S11, with the help of multi-person real-time collaboration technology, the 3D model can be observed in the same environment and the structure can be modified in real time.

[0030] Therefore, the present invention employs the above-mentioned interactive topology optimization method for three-dimensional structures based on level sets, which has the following technical effects:

[0031] (1) This invention employs the level set method to accurately express structural boundaries using implicit functions, enabling precise description and flexible adjustment of structural boundaries. Furthermore, during the optimization process, it features interactive pause and intervention functions, allowing designers to adjust the overall structure's shape using interactive spheres and optimize local details using surface control points. It also supports both forced and non-forced intervention modes, allowing designers to freely adjust the structure's design. In addition, since no additional filtering operations are required, this invention effectively ensures the consistency between the implicit expression model (defined by the level set function) and the final displayed model (the structural geometry of the optimized result), ensuring the accuracy and reliability of structural optimization.

[0032] (2) This invention supports importing 3D geometric files such as OBJ, STL, and PLY into the design domain and efficiently constructing horizontal ensemble fields through rapid calculation of the symbolic distance function (SDF), thereby enabling direct processing of complex initial structural models. Unlike traditional topology optimization methods that are only applicable to regular or simplified models, the technical solution of this invention is compatible with the topology optimization needs of complex shapes, heterogeneous structures, or porous structures, greatly expanding the application scope of this method in industrial and scientific research fields.

[0033] (3) This invention achieves real-time visualization of the entire interactive operation process and provides support for operation record backtracking and collaborative design. Based on the Marching Cubes method, this invention can render the structural morphology update in real time during the optimization iteration process, and with the help of interactive devices and multi-view displays, designers can instantly observe structural changes in VR / AR / XR or 3D display environments. At the same time, the interactive operation process automatically generates a modification history, supporting backtracking and redoing by sliding the timeline. In addition, this invention also has a multi-person real-time collaboration function, which significantly improves the efficiency of team collaboration in complex projects and the traceability of the design process.

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0035] Figure 1 is a flowchart of a three-dimensional interactive topology optimization method based on level sets;

[0036] Figure 2 is a schematic diagram of the design region and boundary conditions in an embodiment of a three-dimensional interactive topology optimization method based on level sets;

[0037] Figure 3 shows the initial optimization model of the structure drawn in Rhino modeling software in an embodiment of a three-dimensional interactive topology optimization method based on level sets.

[0038] Figure 4 shows the initial optimization model of the structure rendered in UE4.27 in an embodiment of a three-dimensional interactive topology optimization method based on level sets.

[0039] Figure 5 is a schematic diagram of the optimized structure of two adjacent iteration steps rendered in Ue4.27 in an embodiment of a three-dimensional interactive topology optimization method based on level sets. (a) is the external view of the structure of the nth iteration step, (b) is the internal view of the structure of the nth iteration step, (c) is the external view of the structure of the (n+1)th iteration step, and (d) is the internal view of the structure of the (n+1)th iteration step.

[0040] Figure 6 is a schematic diagram of the structural model rendered in UE4.27 when the iterative optimization is paused in an embodiment of a three-dimensional interactive topology optimization method based on level sets, where (a) is the first view and (b) is the second view.

[0041] Figure 7 is a schematic diagram of the control points of the Bézier surface in Ue4.27 in an embodiment of an interactive topology optimization method for three-dimensional structures based on level sets;

[0042] Figure 8 is a schematic diagram of the result of rendering the structure optimized by interactive spheres in UE4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on level set. (a) is the optimized structure in step S7, and (b) is the optimized structure in step S8.

[0043] Figure 9 is a schematic diagram of the optimized structure rendered in UE4.27 in an embodiment of an interactive topology optimization method for three-dimensional structures based on level sets.

[0044] Figure 10 is a schematic diagram of the rendering result of the structure designed by the existing method in UE4.27 in an embodiment of an interactive topology optimization method for three-dimensional structures based on level sets. Detailed Implementation

[0045] The present invention will be explained in more detail through the following embodiments. The purpose of disclosing the present invention is to protect all changes and modifications within the scope of the present invention. The present invention is not limited to the following embodiments.

[0046] Please refer to Figure 1. This invention provides an interactive topology optimization method for three-dimensional structures based on level sets. It aims to avoid the drawbacks of traditional methods that require extensive post-processing after optimization, allowing designers to dynamically adjust the structure in real time during the optimization process. This effectively avoids tedious subsequent manual modifications and repetitive calculations. Furthermore, it allows designers to easily add constraints based on actual engineering manufacturing constraints, greatly improving the efficiency of structural optimization and design modification, and meeting the needs of engineering practice. Specifically, it includes the following steps:

[0047] S1. Based on the design space required by actual needs, set the number of nodes in the X, Y, and Z directions to establish a three-dimensional structural topology optimization design region; simultaneously, define boundary conditions and configuration parameters according to the optimization model and optimization objectives required by actual needs. The boundary conditions include structural loads and constraints, the configuration parameters include iterative parameters in the topology optimization process, and the nodes are the grid points of the design region.

[0048] In one embodiment, the design space is a cuboid; in other embodiments, it can be designed with different shapes. This embodiment uses a cuboid with 31 nodes in the three directions (X, Y, and Z) as the design space; the number of nodes can be adjusted according to actual needs. The configuration parameters are set as follows: iteration count nloop = 500, target volume fraction volfrac = 0.3, elastic modulus E0 = 1, Poisson's ratio nu = 0.3, and iteration time step dt = 0.5. In other embodiments, the configuration parameters can be adjusted according to the optimization objective. The boundary conditions in this embodiment are a cantilever beam with a fixed constraint at the left end and a unit force applied vertically downwards at the center node at the right end, as shown in the red portion of Figure 2.

[0049] S2. Import the horizontal set field φ(X) of the initial model within the design domain; or import the display model file, calculate the SDF symbolic distance function of the display model, and then use the horizontal set generation formula based on the SDF symbolic distance function to calculate the horizontal set field φ(X). Here, the horizontal set field φ(X) refers to the implicit definition of the material distribution and topology within the design domain through a continuous scalar function, where X is the spatial coordinate. The horizontal set generation formula based on the SDF symbolic distance function is: d max =max(|SDF min |,|SDF max |);

[0050] In the formula, the SDF symbolic distance function is a mathematical tool widely used in geometric processing and 3D modeling. It represents the shortest distance from any point in three-dimensional space to the surface of an object, and distinguishes whether the point is outside the object (positive value) or inside the object (negative value) by the sign; SDFmin represents the minimum value of the SDF symbolic distance function for all nodes in the design area; SDFmax represents the maximum value of the SDF symbolic distance function for all nodes in the design area; dmax is the global maximum absolute value of SDF. β is the gradient magnitude (intensity of local variation) of the SDF field; β is the smoothing coefficient, which controls the effect of the gradient on normalization. In this embodiment, the value is 0.1dmax, which can be adjusted according to the requirements of the model smoothness during the design.

[0051] In one embodiment of the present invention, an initial optimized structural model is drawn in Rhino modeling software (see Figure 3), and its OBJ file is exported. The SDF symbolic distance function of the model is then calculated using the ray tracing method. In other embodiments, the SDF symbolic distance function can also be obtained using other calculation methods commonly found in computer graphics, such as the fast tracing method and octree search.

[0052] S3. Using the horizontal field φ(X), the Marching Cubes method is used to render and generate a display model of the initial structure in the design area. The Marching Cubes method is a common surface reconstruction method that extracts explicit geometric boundaries from the horizontal field φ(X).

[0053] In one embodiment of the present invention, the Ue4.27 game engine is used to render the display model of the optimized structure, as shown in Figure 4.

[0054] S4. According to the configuration parameters, perform level set topology optimization on the design variables, update the level set field φ(X), and then use the Marching Cubes method to render and display the model in real time. The design variables include the mathematical variables describing the structural shape and topology in the level set topology optimization method.

[0055] In one embodiment of the present invention, the Ue4.27 game engine is used to display the rendering structure and the interactive modification structure. Please refer to Figure 5, (a) and (b) are the optimization models for the nth iteration step, (a) is the external view of the structure, and (b) is the internal view of the structure; (c) and (d) are the optimization models for the (n+1)th iteration step, (c) is the external view of the structure, and (d) is the internal view of the structure.

[0056] S5. Please refer to Figure 6 to observe the optimization status of the displayed model. When the optimization does not meet the design requirements, pause the optimization process and execute step S6. The design requirements include aesthetic design, globally optimal design, and avoidance of stress concentration.

[0057] In one embodiment of the invention, the designer needs to consider drawing the letter "A" at the center of the cantilever beam for aesthetic design and make detailed adjustments to the structure. In other embodiments, the designer can also consider design issues such as global optimization and avoiding stress concentration based on their experience.

[0058] S6. Choose between mandatory intervention or non-mandatory intervention: Mandatory intervention means that the modifications to the structure will not change as optimization continues, while non-mandatory intervention means that the modifications to the structure will change as optimization continues.

[0059] When choosing mandatory intervention:

[0060] When choosing non-mandatory intervention:

[0061] In the formula, X c X represents the node positions traversed by the trajectory of the interactive sphere. d denoted as B, representing the position of the control points on the surface after model modification; B represents the evolution velocity field of the level set function; dt represents the iteration step size; α∈[0,1] represents the non-forced intervention weight coefficient, which is adjusted in real time by the slider, and is set to 0.3 in this embodiment; n represents the number of iteration steps when modifying the model.

[0062] In one embodiment of the present invention, the drawing of the letter "A" was subject to mandatory intervention, while the adjustment of other areas of the model was subject to non-mandatory intervention.

[0063] S7. Generate an interactive sphere and set its radius R to control the interaction precision; using the interactive device, move the interactive sphere and perform operations such as deleting and adding structures to the displayed model along its motion trajectory, displaying the modified content in real time, and recording the node positions X along the motion trajectory. c .

[0064] In one embodiment of the invention, the designer used an interactive sphere to draw the letter "A" at the center of the cantilever beam by deleting and adding structures, and made aesthetic design adjustments to other areas of the model.

[0065] S8. Change the size of the interactive sphere to determine the operating range, pick the structural surface of the displayed model within the operating range of the interactive sphere, and generate surface control points on the structural surface; select and drag the control points through the interactive device to finely modify the surface shape, and record the modified surface control point position X. d Please refer to Figure 7. The surface control points are generated using a method based on Bézier surfaces. The green spheres in the figure are interactive spheres.

[0066] In one embodiment of the present invention, the designer made fine adjustments to the shape of the letter "A" by adjusting the position of the surface control points, and made aesthetic design adjustments to other areas of the model, as shown in Figure 8.

[0067] S9. Calculate the SDF symbolic distance function of the modified model, and then use the SDF-based level set generation formula to calculate the updated level set field Φnew(X).

[0068] S10. Continue optimizing the process by employing a horizontal cube interactive iterative optimization algorithm to iteratively update the adjusted horizontal cube Φnew(X), and then use the Marching Cubes method to render and display the model in real time. The horizontal cube interactive iterative optimization algorithm is as follows: Φ n (X)=Φ new(X).

[0069] S11. Repeat steps S5 to S10 until the design requirements are met and the iteration converges to obtain the horizontal field Φ(X) that meets the design requirements. Then, import the horizontal field Φ(X) into software that supports implicit modeling to export the optimized structure and complete the interactive design of the structure.

[0070] During the iteration process, the result of rendering the display model of the optimized structure in UE4.27 is shown in Figure 9. The rendering and display of the design structure without the method of this invention in UE4.27 is shown in Figure 10.

[0071] The interactive topology optimization method for three-dimensional structures based on level sets described in this invention has been developed and used in mainstream game engines such as Unreal Eigen and Unity 3D, and has been applied in scenarios such as VR, AR, XR and 3D displays.

[0072] Therefore, the present invention adopts the above-mentioned interactive topology optimization method for three-dimensional structures based on level sets. Designers do not need to directly modify complex mathematical formulas, but can effectively introduce subjective design intentions into the algorithm model, and can adjust structural parameters in real time during the optimization calculation process, so that the structural performance can better meet the specific needs of actual engineering applications.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A three-dimensional interactive topology optimization method based on level sets, characterized in that, Includes the following steps: S1. Set the number of nodes in the XYZ directions, establish a three-dimensional structural topology optimization design region, define boundary conditions and configuration parameters. The boundary conditions are structural loads and constraints, the configuration parameters are iterative parameters in the topology optimization process, and the nodes are grid points in the design region. S2. Import the initial model's horizontal set field φ(X) into the design area, or import and display the model file and calculate the model's SDF symbolic distance function, then use the horizontal set generation formula based on the SDF symbolic distance function to calculate the horizontal set field φ(X). S3. Using the horizontal field φ(X) from step S2, render the initial structure display model in the design area using the Marching Cubes method; S4. According to the configuration parameters, use level set topology optimization to solve for the design variables, which include mathematical variables describing the structural shape and topology in the level set topology optimization method; S5. Observe the optimization status of the display model. When the optimization does not meet the design requirements, pause the optimization process. The design requirements include aesthetic design, global optimal design, and avoidance of stress concentration. S6. Select mandatory intervention or non-mandatory intervention. Mandatory intervention means that the modification of the structure will not change as optimization continues, while non-mandatory intervention means that the modification of the structure will change as optimization continues. S7. Generate an interactive sphere, set the radius R of the interactive sphere to control the interaction precision, move the interactive sphere through the interactive device, and perform operations such as deleting or adding structures to the displayed model along the movement trajectory of the interactive sphere. Display the modified content in real time and record the node positions X passed by the movement trajectory. c ; S8. Change the size of the interactive sphere to determine the operating range, pick the structural surface of the displayed model within the operating range of the interactive sphere, generate surface control points on this structural surface, select and drag the control points using the interactive device to fine-tune the surface shape, and record the modified surface control point positions X. d ; S9. Calculate the SDF symbolic distance function of the modified display model, and use the SDF-based level set generation formula to calculate the updated level set field Φnew(X); S10. Continue to optimize the process, adopt the horizontal cube interactive iterative optimization algorithm, iteratively update the adjusted horizontal cube Φnew(X), and use the Marching Cubes method to render and display the model in real time. S11. Repeat steps S5 to S10 until the iteration converges. Optimize to obtain a horizontal set field that meets the design requirements. Then import the horizontal set field into software that supports implicit modeling, export the optimized structure, and complete the interactive structural design.

2. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, The mathematical model for level sets is as follows:

3. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, In step S2, the model file is displayed as a three-dimensional geometric structure file, including OBJ, STL, and PLY formats.

4. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, The SDF symbolic distance function represents the shortest distance from any point in 3D space to the surface of an object. The formula for generating the level set φ(X) based on the SDF symbolic distance function is: d max =max(|SDF min |,|SDF max |); In the formula, SDF min SDF max This represents the minimum and maximum values ​​of the SDF symbolic distance function for all nodes in the design region. Let represent the gradient magnitude of the SDF field, β represent the smoothing coefficient, and (x,y,z) represent the three-dimensional spatial coordinates.

5. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, In step S5, the optimization of the model is observed using a head-mounted display or a 3D display. The observation angle and position of the structure are controlled through interactive devices, and the changes in the structure are observed from multiple perspectives, both inside and outside the structure.

6. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, In step S5, the surface control points are generated using a method based on Bézier surfaces.

7. In the interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, step S10, the interactive iterative optimization algorithm for the level set field, is as follows: Φ n (X)=Φ new (X); When choosing mandatory intervention: When choosing non-mandatory intervention: In the formula, X c X represents the node positions traversed by the trajectory of the interactive sphere. d denoted as the position of the surface control points after model modification; B is the evolution velocity field of the level set function; dt is the iteration time step; α∈[0,1] is the non-forced intervention weight coefficient, which is adjusted in real time by the slider; n is the number of iteration steps when modifying the model.

8. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, In steps S7 and S8, the interactive operations of the interactive sphere are recorded to form a design history tree, which supports backtracking or redoing any step of the modification operation by sliding the timeline.

9. The interactive topology optimization method for three-dimensional structures based on level sets according to claim 1, characterized in that, In steps S5 to S11, the 3D model is observed and its structure is modified in real time in the same environment using multi-person real-time collaboration technology.

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