Method for representing dental objects using binary space partitioning, method for representing objects using binary space partitioning, and computer-readable recording medium having recorded thereon program for executing same on computer

Abstract

A method for representing dental objects using binary space partitioning comprises the steps of: generating internal trees that partition a space including dental objects represented by polygon meshes; and generating leaf trees that represent shapes of the dental objects in spaces generated on the basis of the internal trees. Each of the internal trees and the leaf trees includes internal nodes and leaf nodes.

Description

A method for representing a dental object using binary space division, a method for representing an object using binary space division, and a computer-readable recording medium having recorded thereon a program for executing the method on a computer

[0001] The present invention relates to a method for representing a dental object using binary space partitioning, a method for representing an object using binary space partitioning, and a computer-readable recording medium having recorded thereon a program for executing the same on a computer, and more particularly, to a method for representing a dental object using binary space partitioning that parallelizes operations, a method for representing an object using binary space partitioning, and a computer-readable recording medium having recorded thereon a program for executing the same on a computer.

[0002] In the field of computer graphics, quickly and accurately drawing space can be important. This space can be represented by binary space partitioning. Binary space partitioning is a method of recursively dividing Euclidean space into hyperplanes. For example, if the Euclidean space is two-dimensional, it can be partitioned into two-dimensional straight lines. For example, if the Euclidean space is three-dimensional, it can be partitioned into three-dimensional planes.

[0003] However, the above binary space partitioning may take a very long time to calculate for input data with a complex shape or a large number of geometric elements, and may require a lot of memory space.

[0004] An object of the present invention is to provide a method for representing a dental object using binary space partitioning that improves computational speed, requires less memory space, and effectively parallelizes computations by adaptively and in parallel performing binary space partitioning.

[0005] Another object of the present invention is to provide a method for representing an object using binary space partitioning that performs binary space partitioning adaptively and in parallel to parallelize operations.

[0006] Another object of the present invention is to provide a method for representing a dental object using the binary space division and a computer-readable recording medium having recorded thereon a program for executing the method for representing the object using the binary space division on a computer.

[0007] According to one embodiment of the present invention, a method for representing a dental object using binary space partitioning for realizing the above-described object object includes the steps of generating internal trees for dividing a space including a dental object represented by a polygon mesh, and the steps of generating leaf trees for representing the shape of the dental object in spaces generated based on the internal trees. Each of the internal trees and the leaf trees includes internal nodes and leaf nodes.

[0008] In one embodiment of the present invention, when the space is divided, a median division technique may be performed so that the number of faces of the polygon mesh is halved.

[0009] In one embodiment of the present invention, the internal trees form first to Nth (where N is a natural number greater than or equal to 1) internal tree hierarchies, and internal trees included in the second internal tree hierarchies can be formed based on leaf nodes of internal trees included in the first internal tree hierarchies.

[0010] In one embodiment of the present invention, the depth of nodes included in each of the internal trees may be less than or equal to the maximum subtree depth.

[0011] In one embodiment of the present invention, the leaf trees may form one leaf tree hierarchy.

[0012] In one embodiment of the present invention, the leaf trees can be formed based on leaf nodes of internal trees included in the Nth internal tree hierarchy.

[0013] In one embodiment of the present invention, the depth of nodes included in the internal trees and the leaf trees may be less than or equal to the maximum augmented tree depth.

[0014] In one embodiment of the present invention, the number of faces of a polygon mesh included in each of the spaces generated based on the internal trees may be less than or equal to the maximum number of faces of a lift tree space.

[0015] In one embodiment of the present invention, parent nodes and child nodes are formed based on the internal nodes and the leaf nodes, and each of the parent nodes can have two child nodes.

[0016] In one embodiment of the present invention, the internal trees and the leaf trees form parent trees and child trees, and each of the parent trees can have at least two child trees.

[0017] In one embodiment of the present invention, the internal trees may be generated by a working stealing algorithm.

[0018] In one embodiment of the present invention, the work stealing algorithm is performed by workers, and the workers can perform work on at least one internal tree.

[0019] In one embodiment of the present invention, each of the workers performs the task in the task stealing queue of each of the workers, and a worker that has completed one task can steal another task and perform the other task.

[0020] In one embodiment of the present invention, the polygon mesh may be a polygonal surface.

[0021] In one embodiment of the present invention, when the space is two-dimensional, the space can be divided by a two-dimensional straight line.

[0022] In one embodiment of the present invention, when the space is three-dimensional, the space can be divided by a three-dimensional plane.

[0023] According to one embodiment of the present invention, a method for representing an object using binary space partitioning for realizing another object expressed as a polygon mesh includes the steps of creating internal trees for dividing a space including the object, and the steps of creating leaf trees for representing the shape of the object in spaces created based on the internal trees. Each of the internal trees and the leaf trees includes internal nodes and leaf nodes.

[0024] In one embodiment of the present invention, the depth of nodes included in each of the internal trees may be less than or equal to the maximum subtree depth.

[0025] In one embodiment of the present invention, the number of polygon meshes included in each of the spaces generated based on the internal trees may be less than or equal to the maximum number of lifttree space faces.

[0026] In one embodiment of the present invention, a method for representing the dental object using the binary space division and a program for executing the method for representing the object using the binary space division on a computer can be recorded on a computer-readable recording medium.

[0027] According to a method for representing a dental object using binary space partitioning according to the present invention, a method for representing an object using binary space partitioning, and a computer-readable recording medium having recorded thereon a program for executing the same on a computer, a space including a dental object (or objects) including a polygon mesh can equally include the number of polygons included in each of the spaces generated based on the internal trees by internal trees. Therefore, since the operations performed in each of the spaces generated based on the internal trees can be equally performed, the operations can be efficiently parallelized.

[0028] Additionally, the internal trees can be generated using a task-stealing algorithm. Therefore, workers can perform tasks efficiently.

[0029] Figure 1 is a diagram explaining the concept of binary space partitioning.

[0030] FIG. 2 is a flowchart illustrating a method for representing a dental object using binary space division according to one embodiment of the present invention.

[0031] Figures 3 and 4 are drawings explaining the internal trees and leaf trees of Figure 2.

[0032] Figures 5 and 6 are drawings explaining spaces created based on internal nodes.

[0033] Figure 7 is a diagram illustrating a work stealing algorithm.

[0034] FIGS. 8 and 9 are drawings showing a dental object in which a method of representing a dental object using binary space division according to one embodiment of the present invention is performed.

[0035] With respect to the embodiments of the present invention disclosed in the text, specific structural and functional descriptions are merely illustrative for the purpose of explaining the embodiments of the present invention, and the embodiments of the present invention may be implemented in various forms and should not be construed as being limited to the embodiments described in the text.

[0036] The present invention is susceptible to various modifications and takes various forms. Specific embodiments are illustrated in the drawings and described in detail herein. However, this is not intended to limit the present invention to specific disclosed forms, but rather to encompass all modifications, equivalents, and alternatives falling within the spirit and technical scope of the present invention.

[0037] While terms like "first" and "second" may be used to describe various components, these components should not be limited by these terms. These terms may be used to distinguish one component from another. For example, without departing from the scope of the present invention, a first component could be referred to as a "second component," and similarly, a second component could also be referred to as a "first component."

[0038] When a component is referred to as being "connected" or "connected" to another component, it should be understood that it may be directly connected or connected to that other component, but that there may be other components in between. Conversely, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there are no other components in between. Other expressions that describe the relationship between components, such as "between" and "directly between" or "adjacent to" and "directly adjacent to", should be interpreted similarly.

[0039] The terminology used in this application is only used to describe specific embodiments and is not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly indicates otherwise. In this application, it should be understood that the terms "comprise" or "have" indicate the presence of a described feature, number, step, operation, component, part, or combination thereof, but do not preclude the possibility of the presence or addition of one or more other features, numbers, steps, operations, components, parts, or combinations thereof.

[0040] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by those of ordinary skill in the art to which this invention pertains. Terms defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology, and shall not be construed in an idealized or overly formal sense unless explicitly defined herein.

[0041] Meanwhile, if a particular embodiment can be implemented differently, the functions or operations specified within a particular block may occur in a different order than specified in the flowchart. For example, two consecutive blocks may actually be executed substantially simultaneously, or, depending on the related functions or operations, the blocks may be executed in reverse order.

[0042] Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the attached drawings. Identical components in the drawings are designated by the same reference numerals, and redundant descriptions of identical components are omitted.

[0043] Figure 1 is a diagram explaining the concept of binary space partitioning.

[0044] Referring to Fig. 1, space can be represented by binary space partitioning. The binary space partitioning is a method of recursively partitioning Euclidean space into hyperplanes. For example, when the Euclidean space is two-dimensional, the Euclidean space can be partitioned into two-dimensional straight lines. For example, when the Euclidean space is three-dimensional, the Euclidean space can be partitioned into three-dimensional planes. Fig. 1 is an example of partitioning the two-dimensional space. The left drawing of Fig. 1 shows an example of partitioning the two-dimensional space into the two-dimensional straight lines, and the right drawing of Fig. 1 shows the example as a binary space partitioning tree.

[0045] Referring to the left drawing of Fig. 1, the two-dimensional space can be divided into + space and - space based on straight line a. Referring to the right drawing of Fig. 1, straight line a can correspond to node a, the + space of straight line a can correspond to the OUT of node a, and the - space of straight line a can correspond to the IN of node a.

[0046] Referring to the left drawing of Fig. 1, the - space of the a straight line can be divided into + space and - space based on the b straight line. Referring to the right drawing of Fig. 1, the b straight line can correspond to the b node, the + space can correspond to OUT, and the - space can correspond to IN.

[0047] Referring to the left drawing of Fig. 1, the - space of the b straight line can be divided into + space and - space based on the c straight line. Referring to the right drawing of Fig. 1, the c straight line can correspond to the c node, the + space can correspond to OUT, and the - space can correspond to IN.

[0048] Referring to the left drawing of Fig. 1, the - space of the c straight line can be divided into + space and - space based on the d straight line. Referring to the right drawing of Fig. 1, the d straight line can correspond to the d node, the + space can correspond to OUT, and the - space can correspond to IN.

[0049] The above space may include an object represented by a polygonal mesh. The polygonal mesh may be a polygonal surface. For example, the polygonal mesh may be a triangular surface or a quadrilateral surface. The object may be represented using the binary space partitioning. A method for representing an object using binary space partitioning according to one embodiment of the present invention provides a binary space partitioning that effectively parallelizes operations.

[0050] FIG. 2 is a flowchart illustrating a method for representing an object using binary space division according to one embodiment of the present invention.

[0051] Referring to FIG. 2, a method for representing an object using binary space partitioning according to one embodiment of the present invention may include a step (S100) of generating internal trees for dividing a space including a dental object represented by a polygon mesh, and a step (S200) of generating leaf trees for representing the shape of the dental object in spaces generated based on the internal trees. Each of the internal trees and the leaf trees may include internal nodes and leaf nodes.

[0052] The method of representing a dental object using binary space division according to one embodiment of the present invention can be performed by a computing device.

[0053] Figures 3 and 4 are drawings explaining the internal trees (IT) and leaf trees (LT) of Figure 2.

[0054] Referring to FIG. 3, a method for representing a dental object using binary space partitioning according to one embodiment of the present invention may include the step (S100) of generating internal trees (IT) that partition the space including the dental object represented by the polygon mesh.

[0055] The step (S100) of generating the internal trees (IT) that divide the space including the dental object expressed by the polygon mesh may be performed until the number of polygon meshes included in each of the spaces generated based on the internal trees (IT) becomes less than or equal to the maximum number of lift-tree space faces. Accordingly, since the operations performed in each of the spaces generated based on the internal trees (IT) may be equal, the operations may be effectively parallelized. The generated internal trees (IT) may form first to Nth (wherein N is a natural number greater than or equal to 1) internal tree hierarchies.

[0056] For example, second to fifth internal trees (IT2 to IT5) may be generated based on a first internal tree (IT1). In this case, the first internal tree (IT1) may be a parent tree, and the second to fifth internal trees (IT2 to IT5) may be child trees. Here, the first to fifth internal trees (IT1 to IT5) may form a first internal tree hierarchy (IT_T1) and a second internal tree hierarchy (IT_T2). The first internal tree (IT1) may form the first internal tree hierarchy (IT_T1), and the second to fifth internal trees (IT2 to IT5) may form the second internal tree hierarchy (IT_T2).

[0057] A method for representing a dental object using binary space partitioning according to one embodiment of the present invention may include the step (S200) of generating leaf trees (LT) representing the shape of the dental object in the spaces generated based on the internal trees (IT). The generated leaf trees (LT) may form one leaf tree hierarchy (LT_T).

[0058] For example, the first to sixteenth leaf trees (LT1 to LT16) may be generated based on the second to fifth internal trees (IT2 to IT5). In this case, the second to fifth internal trees (IT2 to IT5) may be parent trees, and the first to sixteenth leaf trees (LT1 to LT16) may be child trees. Here, the first to sixteenth leaf trees (LT1 to LT16) may form the leaf tree hierarchy (LT_T).

[0059] In this way, the internal trees (IT) and the leaf trees (LT) can form parent trees and child trees, and each of the parent trees can have at least two child trees.

[0060] Referring to FIG. 4, the internal trees (IT) and the leaf trees (LT) may form an augmented binary space partition tree together. Each of the internal trees (IT) and the leaf trees (LT) may form a binary space partition tree. Therefore, each of the internal trees (IT) may include internal nodes and leaf nodes. As described in FIG. 1, each of the internal nodes and the imaginary leaf nodes may mean dividing a space. The space partitioning may be performed so that the number of faces of the polygon mesh is halved. For example, a median splitting technique may be performed in the space partitioning.

[0061] The depth of the nodes included in each of the internal trees (IT) may be less than or equal to the maximum subtree depth (PTD_MAX). Therefore, when the depth of the nodes included in each of the internal trees (IT) becomes the maximum subtree depth (PTD_MAX), internal trees or leaf trees corresponding to child trees may be newly generated. Accordingly, the operations performed in each of the spaces generated based on the internal trees (IT) may be uniform.

[0062] Even if the above operations performed in each of the spaces generated based on the above internal trees (IT) are equal, if the overall amount of operations is too large, the operation speed may actually decrease.

[0063] To prevent this, the depth of the nodes included in the augmented binary space partition tree (i.e., the internal trees (IT) and the leaf trees (LT)) may be less than or equal to the maximum augmented tree depth (ATD_MAX). Accordingly, the overall amount of computation may be reduced.

[0064] For example, the maximum partial tree depth (PTD_MAX) may be 3, the first internal tree (IT1) may form the first internal tree hierarchy (IT_T1), and the first internal tree (IT1) may include a first internal node (IT1_IN1). A second internal node (IT1_IN2) and a third internal node (IT1_IN3) may be generated based on the first internal node (IT1_IN1). In this case, the first internal node (IT1_IN1) may be a parent node, and the second internal node (IT1_IN2) and the third internal node (IT1_IN3) may be child nodes. A first leaf node (IT1_LN1) and a second leaf node (IT1_LN2) may be generated based on the second internal node (IT1_IN2). In this case, the second internal node (IT1_IN2) may be a parent node, and the first leaf node (IT1_LN1) and the second leaf node (IT1_LN2) may be child nodes. A third leaf node (IT1_LN3) and a fourth leaf node (IT1_LN4) may be generated based on the third internal node (IT1_IN3). In this case, the third internal node (IT1_IN3) may be a parent node, and the third leaf node (IT1_LN3) and the fourth leaf node (IT1_LN4) may be child nodes.

[0065] Child trees can be generated based on the first internal tree (IT1). Since the number of leaf nodes (IT1_LN1, IT1_LN2, IT1_LN3, IT1_LN4) of the first internal tree (IT1) is 4, the number of child trees of the first internal tree (IT1) can be 4. That is, the second to fifth internal trees (IT2 to IT5) can be generated based on the first internal tree (IT1). The second to fifth internal trees (IT2 to IT5) can form the second internal tree hierarchy (IT_T2).

[0066] For example, the second internal tree (IT2) may include a first internal node (IT2_IN1). A second internal node (IT2_IN2) and a third internal node (IT2_IN3) may be generated based on the first internal node (IT2_IN1). In this case, the first internal node (IT2_IN1) may be a parent node, and the second internal node (IT2_IN2) and the third internal node (IT2_IN3) may be child nodes. A first leaf node (IT2_LN1) and a second leaf node (IT2_LN2) may be generated based on the second internal node (IT2_IN2). In this case, the second internal node (IT2_IN2) may be a parent node, and the first leaf node (IT2_LN1) and the second leaf node (IT2_LN2) may be child nodes. A third leaf node (IT2_LN3) and a fourth leaf node (IT2_LN4) can be created based on the third internal node (IT2_IN3). In this case, the third internal node (IT2_IN3) can be a parent node, and the third leaf node (IT2_LN3) and the fourth leaf node (IT2_LN4) can be child nodes.

[0067] As described above, the step (S100) of generating the internal trees (IT) that divide the space including the dental object expressed by the polygon mesh may be performed until the number of polygon meshes included in each of the spaces generated based on the internal trees (IT) becomes less than or equal to the maximum number of liftree space faces. Therefore, the spaces divided by each of the first to fourth leaf nodes (IT2_LN1 to IT2_LN4) of the second internal tree (IT2) may be less than or equal to the maximum number of liftree space faces.

[0068] Child trees can be generated based on the second to fifth internal trees (IT2 to IT5). When the number of leaf nodes of the second to fifth internal trees (IT2 to IT5) is 16, the number of child trees of the second to fifth internal trees (IT2 to IT5) can be 16. That is, the first to sixteenth leaf trees (LT1 to LT16) can be generated based on the second to fifth internal trees (IT2 to IT5). The first to sixteenth leaf trees (LT1 to LT16) can form a leaf tree hierarchy (LT_T).

[0069] For example, the first leaf tree (LT1) may include a first internal node (LT1_IN1). A second internal node (LT1_IN2) and a third internal node (LT1_IN3) may be generated based on the first internal node (LT1_IN1). In this case, the first internal node (LT1_IN1) may be a parent node, and the second internal node (LT1_IN2) and the third internal node (LT1_IN3) may be child nodes. A first leaf node (LT1_LN1) and a second leaf node (LT1_LN2) may be generated based on the second internal node (LT1_IN2). In this case, the second internal node (LT1_IN2) may be a parent node, and the first leaf node (LT1_LN1) and the second leaf node (LT1_LN2) may be child nodes. A third leaf node (LT1_LN3) and a fourth leaf node (LT1_LN4) can be created based on the third internal node (LT1_IN3). In this case, the third internal node (LT1_IN3) can be a parent node, and the third leaf node (LT1_LN3) and the fourth leaf node (LT1_LN4) can be child nodes.

[0070] In this way, the internal nodes and the leaf nodes can form parent nodes and child nodes, and each of the parent nodes can have two child trees.

[0071] Figures 5 and 6 are drawings explaining spaces created based on internal nodes.

[0072] Referring to FIGS. 5 and 6, a space may include an object. The space may be a two-dimensional space, and the two-dimensional space may be divided into two-dimensional straight lines, and the shape of the object may be a triangle. The two-dimensional space may be divided into a P0 straight line. The P0 straight line may correspond to a P0 node. A space on one side of the P0 straight line may be divided into a P1 straight line. The P1 straight line may correspond to a P1 node. A space on the other side of the P0 straight line may be divided into a P2 straight line. The P2 straight line may correspond to a P2 node.

[0073] As can be seen from Figures 5 and 6, the shape of the object can be evenly divided in the generated spaces. Therefore, the operations performed in each of the generated spaces can be evenly performed, and the operation speed can be improved.

[0074] Figure 7 is a diagram illustrating a work stealing algorithm.

[0075] Referring to Fig. 7, the internal trees (IT) may be generated by a work stealing algorithm. The work stealing algorithm may be performed by workers. The initial task may be assigned to a global shared task queue. The initial task may be implemented as an array, queue, deque, etc. In this case, to satisfy the parallel safety (thread safety) of the tasks provided to the workers, a data structure implementation that guarantees the parallel safety may be used, or the point in time when the take operation of the workers is executed may be designated as a critical zone.

[0076] The initial task may include at least one internal tree (IT). That is, the workers may perform tasks on at least one internal tree (IT). The initial task may be split into multiple parts and assigned to the global shared task queue.

[0077] Each of the above workers can perform the task from its respective task-stealing queue. A worker that has completed one task can steal another task and perform the other task. Accordingly, the workers can perform the task efficiently. At this time, when at least two workers attempt to steal the same task simultaneously, a race condition may occur. To prevent this, the operation to steal the task can be performed by designating a critical zone based on a semaphore or mutex, or by implementing the task-stealing queue as a thread-safe or lock-free data structure.

[0078] FIGS. 8 and 9 are drawings showing a dental object in which a method of representing a dental object using binary space division according to one embodiment of the present invention is performed.

[0079] Referring to FIG. 8, a space may include an object comprising a polygonal mesh. The space may be a three-dimensional space, the polygonal mesh may be triangles, and the shape of the object may be a dental object. For example, the dental object may be a tooth.

[0080] The left drawing illustrates a space generated based on the dental object and internal trees (IT). The center drawing illustrates a portion of the dental object contained in the space generated based on the internal trees (IT). The right drawing illustrates a portion of the dental object expressed based on a leaf tree (LT).

[0081] Referring to FIG. 9, the left drawing illustrates a dental object in which the method for representing a dental object using binary space division according to an embodiment of the present invention has not been performed. The right drawing illustrates a dental object in which the method for representing a dental object using binary space division according to an embodiment of the present invention has been performed.

[0082] Conventional binary space partitioning is not efficiently parallelized, making it unsuitable for complex data such as dental objects or arch mesh models. As illustrated in FIGS. 8 and 9 , a method for representing dental objects using binary space partitioning according to an embodiment of the present invention can be efficiently parallelized even for complex data.

[0083] In this way, according to a method for representing a dental object using binary space partitioning according to one embodiment of the present invention, a space including a dental object including a polygon mesh can equally include the number of polygon meshes included in each of the spaces generated based on the internal trees (IT) by the internal trees (IT). Therefore, since the operations performed in each of the spaces generated based on the internal trees (IT) can be equally performed, they can be efficiently parallelized and require less memory space.

[0084] Additionally, the internal trees (IT) can be generated using a task-stealing algorithm. Therefore, workers can perform tasks efficiently.

[0085] A method for representing a dental object using binary space division according to one embodiment of the present invention enables fast and precise three-dimensional geometric calculations, and thus can be applied to various fields such as CAD / CAM (Computer-Aided Design / Computer-Aided Manufacturing) software, virtual and augmented reality, and 3D printing.

[0086] Meanwhile, the method for representing a dental object using binary space partitioning according to one embodiment of the present invention may not be limited to the dental object. For example, the method for representing a dental object using binary space partitioning according to one embodiment of the present invention may be applied to objects other than the dental object. Therefore, the method for representing a dental object using binary space partitioning according to one embodiment of the present invention may have substantially the same configuration and operation as the method for representing an object using binary space partitioning according to one embodiment of the present invention.

[0087] In one embodiment, a computer-readable recording medium having recorded thereon a method for representing a dental object using binary space partitioning according to an embodiment of the present invention and a program for executing the method for representing an object using binary space partitioning according to an embodiment of the present invention on a computer may be provided. The above-described method can be written as a program that can be executed on a computer, and can be implemented in a general-purpose digital computer that runs the program using a computer-readable medium. In addition, the structure of data used in the above-described method can be recorded on a computer-readable medium through various means. The computer-readable medium may include program commands, data files, data structures, etc., either singly or in combination. The program commands recorded on the medium may be those specially designed and configured for the present invention, or may be known and usable by those skilled in the art in the field of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical recording media such as CD-ROMs and DVDs, magneto-optical media such as floptical disks, and hardware devices specially configured to store and execute program commands such as ROMs, RAMs, and flash memories. Examples of program instructions include not only machine language codes, such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the present invention.

[0088] In addition, the method for representing a dental object using binary space division according to one embodiment of the present invention and the method for representing an object using binary space division can also be implemented in the form of a computer program or application executed by a computer and stored in a recording medium.

[0089] The present invention relates to a method for representing a dental object using binary space division, a method for representing an object using binary space division, and a computer-readable recording medium having recorded thereon a program for executing the method on a computer, which can reduce the effort and time for computational processing operations and improve accuracy and productivity.

[0090] Although the present invention has been described above with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various modifications and changes may be made to the present invention without departing from the spirit and scope of the present invention as set forth in the claims below.

Claims

1. A step of generating internal trees that divide a space containing dental objects represented by polygon meshes; and A step of generating leaf trees representing the shape of the dental object in spaces generated based on the internal trees is included. A method for representing a dental object using binary space partitioning, wherein each of the internal trees and the leaf trees includes internal nodes and leaf nodes.

2. A method for expressing a dental object using binary space division, characterized in that, in the first paragraph, when the space is divided, a median division technique is performed so that the number of faces of the polygon mesh is halved.

3. In paragraph 1, A method for representing a dental object using binary space partitioning, characterized in that the internal trees form first to Nth (where N is a natural number greater than or equal to 1) internal tree hierarchies, and internal trees included in the second internal tree hierarchy are formed based on leaf nodes of internal trees included in the first internal tree hierarchy.

4. A method for representing a dental object using binary space partitioning, characterized in that, in the third paragraph, the depth of nodes included in each of the internal trees is less than or equal to the maximum subtree depth.

5. A method for representing a dental object using binary space partitioning, characterized in that in the third paragraph, the leaf trees form one leaf tree hierarchy.

6. A method for representing a dental object using binary space partitioning, characterized in that the leaf trees are formed based on leaf nodes of internal trees included in the Nth internal tree hierarchy in the fifth paragraph.

7. A method for representing a dental object using binary space partitioning, characterized in that the depth of nodes included in the internal trees and the leaf trees in the first paragraph is less than or equal to the maximum augmented tree depth.

8. A method for expressing a dental object using binary space division, characterized in that the number of polygon meshes included in each of the spaces generated based on the internal trees in the first paragraph is less than or equal to the maximum number of lift tree space surfaces.

9. A method for representing a dental object using binary space partitioning, characterized in that in the first paragraph, parent nodes and child nodes are formed based on the internal nodes and the leaf nodes, and each of the parent nodes has two child nodes.

10. A method for representing a dental object using binary space partitioning, characterized in that in the first paragraph, the internal trees and the leaf trees form parent trees and child trees, and each of the parent trees has at least two child trees.

11. A method for representing a dental object using binary space partitioning, characterized in that in the first paragraph, the internal trees are generated by a working stealing algorithm.

12. A method for representing a dental object using binary space partitioning, characterized in that in the 11th paragraph, the work stealing algorithm is performed by workers, and the workers perform work on at least one internal tree.

13. A method for representing a dental object using binary space division, characterized in that in the 12th paragraph, each of the workers performs the task in the task stealing queue of each of the workers, and a worker that has completed one task steals another task to perform the other task.

14. A method for expressing a dental object using binary space division, characterized in that in the first paragraph, the polygon mesh is a polygonal surface.

15. A method for expressing a dental object using binary space division, characterized in that in the first paragraph, when the space is two-dimensional, the space is divided by a two-dimensional straight line.

16. A method for expressing a dental object using binary space division, characterized in that in the first paragraph, when the space is three-dimensional, the space is divided by a two-dimensional plane.

17. A step of generating internal trees that divide a space containing objects represented by polygon meshes; and A step of generating leaf trees representing the shape of the object in spaces generated based on the internal trees is included, A method for representing an object using binary space partitioning, wherein each of the internal trees and the leaf trees includes internal nodes and leaf nodes.

18. A method for representing an object using binary space partitioning, characterized in that, in the 17th paragraph, the depth of nodes included in each of the internal trees is less than or equal to the maximum subtree depth.

19. A method for expressing an object using binary space partitioning, characterized in that the number of polygon meshes included in each of the spaces generated based on the internal trees in the 17th paragraph is less than or equal to the maximum number of lift tree space faces.

20. A computer-readable recording medium having recorded thereon a program for executing the method of any one of claims 1 to 19 on a computer.

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