Information processing device, information processing method, and program

Abstract

This invention provides an information processing device, an information processing method, and a program that contribute to the visualization of analysis results. [Solution] A processing server 200 according to one embodiment includes an embedding unit 203 that embeds location information data of one or more entities into a Poincaré disk, and a rendering unit 204 that uses time information data corresponding to the location information of one or more entities to render the location information data embedded in the Poincaré disk as the trajectory of one or more entities.

Description

Technical Field

[0001] The present disclosure relates to an information processing apparatus, an information processing method, and a program.

Background Art

[0002] Various methods for analyzing processes have been studied. For example, Patent Document 1 discloses a method for performing process mining on a multi-instance process including one or more multi-instance subprocesses. In this method, the event log of the multi-instance process is divided into a main log and one or more sub-logs. For each of the main log and the one or more sub-logs, a process graph is generated. The generated process graphs are combined into a combined process graph.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the method according to Patent Document 1, when many objects are analyzed simultaneously, it may be difficult to visualize the analysis results so that the user can perceive them.

[0005] The present disclosure is for solving such problems, and provides an information processing apparatus, an information processing method, and a program that contribute to visualization of analysis results.

Means for Solving the Problems

[0006] An information processing device according to an exemplary aspect of the present disclosure includes an embedding unit that embeds location information data of one or more entities into a Poincaré disk, and a rendering unit that uses time information data corresponding to the location information of one or more entities to render the location information data embedded in the Poincaré disk as the trajectory of one or more entities.

[0007] An information processing method according to an exemplary aspect of the present disclosure is a computer-based information processing method that embeds location data of one or more entities into a Poincaré disk and uses time data corresponding to the location data of one or more entities to depict the location data embedded in the Poincaré disk as the trajectory of one or more entities.

[0008] A program according to an exemplary aspect of the present disclosure causes a computer to embed location data of one or more entities into a Poincaré disk and to use time data corresponding to the location data of one or more entities to depict the location data embedded in the Poincaré disk as the trajectory of one or more entities. [Effects of the Invention]

[0009] This disclosure provides an information processing device, an information processing method, and a program that contribute to the visualization of analysis results. [Brief explanation of the drawing]

[0010] [Figure 1] This is a block diagram showing an example configuration of the analysis system according to Embodiment 1. [Figure 2] This is a diagram showing the event log in 3D spacetime. [Figure 3] This is a top view of the spacetime domain in Figure 2. [Figure 4] This figure shows the event log within the Poincaré disk. [Figure 5] This is an example of event node aggregation. [Figure 6] This is a block diagram showing an example of the hardware configuration of the information processing device relating to this disclosure. [Modes for carrying out the invention]

[0011] Embodiment 1 Embodiments of this disclosure will be described below with reference to the drawings. Note that the following description and drawings have been omitted and simplified as appropriate for clarity of explanation. Each referenced drawing is merely illustrative to illustrate one or more embodiments. Not all features or processes shown in any one of the drawings are essential to illustrating an exemplary embodiment, and some features or processes may be omitted.

[0012] [Explanation of the structure] Figure 1 is a block diagram showing an example configuration of an analysis system. The analysis system S comprises a DB (Database) 100 and a processing server 200. The DB 100 stores logs (hereinafter also referred to as event logs) indicating the location and time of events that have occurred, and map information indicating the location. An event indicates that an arbitrary object moves within space as time progresses. The processing server 200 selects a predetermined event log from the DB 100 and displays events based on the selected event log. The events to be analyzed are events within an arbitrary spatial area (for example, inside a factory). The processing server 200 has a log selection unit 201, an event processing unit 202, an embedding unit 203, a rendering unit 204, an output unit 205, and a resolution specification unit 206. The processing of each unit will be described below.

[0013] The log selection unit 201 specifies the spatial region of the events to be selected by referring to the map information in DB100. The log selection unit 201 also specifies the temporal region of the events to be selected. The log selection unit 201 may automatically specify the spatial and temporal regions, or it may do so based on user instructions. The log selection unit 201 selects event log data existing in the specified spatial and temporal regions by referring to DB100. In the following example, a two-dimensional region (x,y) is assumed as the spatial region. However, the assumed spatial region is not limited to a two-dimensional region; for example, it may be a three-dimensional region (x,y,z). Furthermore, the log selection unit 201 may limit the event logs to be selected by limiting the types of entities of the events to be selected. Entities are the objects that constitute the main subject of the event, such as humans, mobile objects, tools, parts, etc. The number of entities to be analyzed is arbitrary. In the following example, multiple entities are analyzed, but a single entity may also be the target of analysis. Furthermore, the log selection unit 201 may perform labeling processing to enable user search for information from one or more event logs to be analyzed (for example, information about entities).

[0014] The event processing unit 202 stores the event log data selected by the log selection unit 201 in a three-dimensional spacetime. In other words, the event log data is represented in a three-dimensional spacetime. A three-dimensional spacetime is represented by a two-dimensional space, which is Euclidean space, and a one-dimensional time. If the spatial domain of the event log is a three-dimensional domain, the event processing unit 202 stores the selected event log data in a four-dimensional spacetime. A four-dimensional spacetime is represented by a three-dimensional space and a one-dimensional time. The processing of the processing server 200 in a three-dimensional spacetime is described below, but the processing server 200 can perform similar processing in other dimensions of spacetime, such as a four-dimensional spacetime.

[0015] Figure 2 shows an event log in three-dimensional spacetime. The position in three-dimensional spacetime is represented by two-dimensional space and time. The spatial region SR indicates the spatial region specified by the log selection unit 201. Also, the log selection unit 201 designates, as the time region, the region from time t1 to t2 (t2 > t1). In Figure 2, the spatial region SR in the region from time t1 to t2 in three-dimensional spacetime is represented as the spacetime region DR. The log selection unit 201 selects the data of the event log shown in Figure 2 by referring to the DB100.

[0016] Also, Figure 3 is a top view of the spacetime region DR in Figure 2. Figure 3 is a diagram for more clearly showing the event log existing within the spacetime region DR. Hereinafter, the event log will be described while referring to Figures 2 and 3.

[0017] In Figures 2 and 3, as entities of the event log selected by the log selection unit 201, Person H1, Person H2, Mobile M1, and Tool T1 are shown. The Mobile M1 is, in this example, an Automatic Guided Vehicle (AGV), but is not limited thereto. In Figure 2, as each event log, the movement trajectory of each entity is shown.

[0018] In Figures 2 and 3, Person H1 enters the spacetime region DR at position P1 and leaves the spacetime region DR at position P2. The time at position P2 is later than the time at position P1. Person H2 enters the spacetime region DR at position P3 and leaves the spacetime region DR at position P4. The time at position P3 is later than the time at position P4. The Mobile M1 enters the spacetime region DR at position P5 and leaves the spacetime region DR at position P6. The time at position P5 is later than the time at position P6. Also, within the spacetime region DR, the trajectory of Person H2 intersects with the trajectory 1 of the Mobile M1 at position P11, and the trajectory of Person H1 intersects with the trajectory of the Mobile M1 at position P12. In other words, Person H2 overlaps with the Mobile M1 at position P11, and Person H1 overlaps with the Mobile M1 at position P12. The time at position P12 is later than the time at position P11.

[0019] Also, FIGS. 2 and 3 show the following situation. Person H2 carries tool T1 from position P3 to position P11 and passes tool T1 to moving body M1 at position P11. Moving body M1 carries tool T1 from position P11 to position P12. Person H1 receives tool T1 from moving body M1 at position P12 and carries it to position P2.

[0020] The event processing unit 202 can clarify the relationships between the above-described entities by storing the data of the event log in the three-dimensional space-time. The relationships between entities indicate, for example, at which positions the entities overlapped or which entities accompanied each other from which position to which position. However, the spatio-temporal region DR is a region that extends in space and time. The larger the spatio-temporal region DR extends, the more laborious it is to track the trajectories of each entity in the spatio-temporal region DR. Also, when a large number of entities exist in the spatio-temporal region DR, the labor of tracking the trajectories of each entity further increases. Therefore, it is assumed that it takes time for the user to analyze the data of the event log. To suppress the occurrence of such a situation, the processing server 200 executes the following processing.

[0021] Returning to Figure 1, let's continue the explanation. The embedding unit 203 embeds all or part (one or more) of the event log location data stored by the event processing unit 202 into the Poincaré disk. Embedding the event log location data into the Poincaré disk means mapping the event log location data onto the Poincaré disk. The Poincaré disk is exactly what the term means in mathematics' non-Euclidean geometry. The hyperbolic metric is used in the Poincaré disk. The mapped event log location data shows the trajectory of movement of each entity within the Poincaré disk. The embedding unit 203 may automatically select the event logs to be embedded into the Poincaré disk from the event logs stored by the event processing unit 202. Alternatively, the embedding unit 203 may select the event logs to be embedded into the Poincaré disk from the event logs stored by the event processing unit 202 based on user instructions.

[0022] The rendering unit 204 renders the positional data of one or more entities embedded in the Poincaré disk as the trajectory of one or more entities. Specifically, the rendering unit 204 renders the trajectory of an entity by using the time information data corresponding to the positional information of one or more entities embedded in the Poincaré disk. In this example, one entity is selected as the target of rendering, but multiple entities may be the target of rendering.

[0023] Figure 4 shows the event log of tool T1 within the Poincaré disk. The arcs in the Poincaré disk PD represent geodesics. The spatial region PR is the spatial region SR in 3D spacetime shown in Figure 2, displayed within the Poincaré disk PD. Positions P1 to P4, as well as positions P11 and P12, shown in Figure 2, are also shown within the Poincaré disk PD.

[0024] The embedded section 203 embeds the location information data from the event log of tool T1, as shown in Figures 2 and 3, into the Poincaré disk PD. As a result of embedding the location information data, as shown in Figure 4, it can be seen that tool T1 passes along the line connecting positions P3, P11, P12, and P2 (hereinafter also referred to as line LT).

[0025] However, at the stage when the embedding unit 203 embeds the location information data from the event log of tool T1 into the Poincaré disk PD, it is not clear which direction tool T1 moves in as time progresses within the Poincaré disk PD. Therefore, the rendering unit 204 uses the time information data from the event log of tool T1 to determine the direction in which tool T1 moves along line LT as time progresses. The determined direction of movement is shown as an arrow in Figure 4. In this way, the location information data of tool T1 is depicted in Figure 4 as a trajectory indicated by line LT accompanied by an arrow.

[0026] The output unit 205 outputs the trajectories of one or more entities drawn by the drawing unit 204 to a display unit such as a display or touch panel. The output unit 205 may also output positional information within the Poincaré disk PD to the display unit. The positional information may include, for example, information indicating the spatial region PR, positions P1 to P6, and positions P11 and P12 within the Poincaré disk PD. By outputting this information, the user can understand the trajectory of the tool T shown in Figure 4 by viewing the display unit. On the display unit, positions P3, P11, P12, and P2 on the trajectory are shown as event nodes where events occur. The edges connecting each position indicate the movement path of the entity.

[0027] The resolution specification unit 206 analyzes the event logs of one or more entities rendered by the rendering unit 204 to identify information indicating the characteristics of each event log (hereinafter also referred to as characteristic information). The characteristic information indicates, but is not limited to, at least one of the following: the frequency of occurrence of the event log (i.e., the number of occurrences), information regarding the movement path of the entity within the Poincaré disk PD (e.g., the amount of movement), or the quantity of goods carried by the entity. The quantity of goods indicates, for example, at least one of the number of items or the weight of the items. The resolution specification unit 206 outputs the characteristic information of the event log, along with the trajectory of one or more entities rendered by the rendering unit 204 corresponding to the event log, from the output unit 205.

[0028] Furthermore, the resolution specification unit 206 may aggregate at least one of the entity trajectories output by the output unit 205 based on at least one of the trajectories of each entity or the characteristic information of the event log of each entity that has been depicted. Figure 5 shows an example of aggregated entity trajectories. Figure 5 shows the trajectories corresponding to the event logs of entities M11, M12, and M13 within the Poincaré disk. Entities M11 to M13 represent moving objects. Moving object M11 reaches position P25 via position P22 from position P21. Moving object M12 reaches position P25 via position P23 from position P21. Moving object M13 reaches position P25 via position P24 from position P21. Here, the trajectory of moving object M11 is denoted as K11, the trajectory of moving object M12 as K12, and the trajectory of moving object M13 as K13. Locations P21 through P25 are event nodes on the trajectory.

[0029] The resolution specification unit 206 can choose whether to output the trajectories of each entity shown in Figure 5 directly to the output unit 205, or to aggregate them and output them to the output unit 205. The resolution specification unit 206 can perform one of the following processes.

[0030] (1) For example, the resolution specification unit 206 refers to the characteristic information of each event log and compares the occurrence frequency of each trajectory K11, K12, and K13 with a predetermined threshold. In this case, the occurrence frequency of trajectory K11 is less than the predetermined threshold, and the occurrence frequencies of trajectories K12 and K13 are equal to or greater than the predetermined threshold. In this case, the resolution specification unit 206 determines that the importance of trajectory K11 is lower than that of the other trajectories, and that trajectory K11 may be consolidated into one of the other trajectories. The resolution specification unit 206 compares the proximity of trajectory K11 to trajectory K12, and the proximity of trajectory K11 to trajectory K13, and determines which of trajectories K12 or K13 is closer to trajectory K11. In this example, trajectory K12 is closer to trajectory K11 than trajectory K13. Therefore, the resolution specification unit 206 is set so that the output unit 205 outputs the trajectory K11 in a format in which the trajectory K12 is aggregated. When the trajectory K11 is aggregated into the trajectory K12, when the user looks at the display unit, they can see the trajectories K12 and K13 in Figure 5, but they cannot see the trajectory K11. As another example, the trajectory K11 may be displayed on the display unit in a less conspicuous format (for example, with a dashed line or a light color) compared to the trajectories K12 and K13. Position P22 may also be displayed on the display unit in a less conspicuous format compared to the other positions.

[0031] (2) The resolution specification unit 206 may refer to the characteristic information of each event log and compare the ratio of the occurrence frequency of each trajectory K11, K12, and K13 to the occurrence frequency of all trajectories in the Poincaré disk with a predetermined threshold. In this example, the ratio of the occurrence frequency of trajectory K11 is less than the predetermined threshold, and the ratio of the occurrence frequencies of trajectories K12 and K13 is greater than or equal to the predetermined threshold. In this case as well, the resolution specification unit 206 determines that the importance of trajectory K11 is lower than that of the other trajectories, and that trajectory K11 may be consolidated into any one of the other trajectories. After the determination, the processing performed by the resolution specification unit 206 is the same as the processing shown in (1).

[0032] (3) The resolution specification unit 206 may refer to the characteristic information of each event log and compare the quantity of goods carried by the entity related to each event log with a predetermined threshold. The quantity of goods may be the number of items or the weight of the items, as described above. In this example, it is assumed that the quantity of goods carried by mobile body M11 is less than the predetermined threshold, and the quantity of goods carried by mobile bodies M12 and M13 is equal to or greater than the predetermined threshold. In this case as well, the resolution specification unit 206 determines that the importance of trajectory K11 is lower than that of the other trajectories, and that trajectory K11 may be consolidated into any one of the other trajectories. After the determination, the processing performed by the resolution specification unit 206 is the same as the processing shown in (1).

[0033] (4) The resolution specification unit 206 may compare the proximity of trajectory K11 and trajectory K12 with a predetermined criterion for proximity. Furthermore, the resolution specification unit 206 may compare the proximity of trajectory K11 and trajectory K13 with a predetermined criterion for proximity. In this example, the resolution specification unit 206 determines that the proximity of trajectory K11 and trajectory K12 is closer than the predetermined criterion, and the proximity of trajectory K11 and trajectory K13 is not closer than the predetermined criterion. At this time, the resolution specification unit 206 can be set so that trajectory K11 is output from the output unit 205 in a format in which trajectory K11 is aggregated into trajectory K12. Alternatively, the resolution specification unit 206 may further perform the comparison processing regarding the frequency of occurrence shown in (1) or (2). If the frequency of occurrence of trajectory K11 is below a predetermined threshold, or if the ratio of the frequency of occurrence of trajectory K11 is below a predetermined threshold, the resolution specification unit 206 can be set to output from the output unit 205 in a format in which trajectory K11 is aggregated into trajectory K12. As another example, the resolution specification unit 206 may refer to the characteristic information of each event log and further compare the amount of goods carried by the entity related to each event log with a predetermined threshold. If the amount of goods carried by mobile body M11 is below a predetermined threshold, and the amount of goods carried by mobile body M12 is equal to or greater than the predetermined threshold, the resolution specification unit 206 can be set to output from the output unit 205 in a format in which trajectory K11 is aggregated into trajectory K12.

[0034] As described above, the resolution specification unit 206 can function as an aggregation unit that can change the granularity of the display of the event log trajectory. When aggregation is performed, the resolution specification unit 206 controls the output unit 205 to perform the display so that information about less important event logs is aggregated with information about more important event logs.

[0035] Furthermore, depending on the user's operation on the processing server 200, the resolution specification unit 206 may switch the display unit between a state in which the event log is aggregated and a state in which it is not aggregated. Three or more trajectories of an entity may also be aggregated into one trajectory in the same manner as the examples shown in (1) to (4). The predetermined thresholds or criteria used for the determination in (1) to (4) can be changed by the user.

[0036] Furthermore, after performing aggregation, the resolution specification unit 206 may cause the display unit to display at least one of the following: the number of aggregated trajectories across the entire Poincaré disk, or the number of aggregated trajectories for each event node after aggregation. For example, a user inputs information to the processing server 200 that identifies an event node or edge displayed on the display unit. The resolution specification unit 206 then causes the display unit to display the number of aggregated trajectories at the identified event node or edge.

[0037] [Explanation of effects] In the processing server 200 of this disclosure, the embedding unit 203 embeds location information data of one or more entities into a Poincaré disk. The rendering unit 204 uses time information data corresponding to the location information of one or more entities to render the location information data embedded in the Poincaré disk as the trajectory of one or more entities. By rendering the trajectory, the user can track and understand events related to the entities. The user can visually understand the trajectory of each entity and event-related information such as characteristic information. For example, in a manufacturing plant or distribution center, the user can clarify through analysis what kind of entity transported what parts, when, and to where. In this way, the processing server 200 can contribute to the visualization of analysis results related to entities.

[0038] Furthermore, the user may input information from one or more event logs to be analyzed into the processing server 200 to search for that information. The output unit 205 can display the trajectory and characteristic information of entities related to the input event logs on the display unit. As a result, the processing server 200 can more clearly identify situations in which the processes of multiple events influence each other. Situations in which the processes of events influence each other include, for example, situations where the trajectories of entities intersect or where they are closer than a predetermined standard. The user can perform a detailed analysis of the relationships between multiple events extracted through the search using statistical methods such as time series analysis and Granger causal analysis.

[0039] Furthermore, the embedding unit 203 embeds the spatial region to be analyzed in Euclidean space into the Poincaré disk, and the rendering unit 204 can render the trajectories of one or more entities within that spatial region embedded in the Poincaré disk. Compared to the case where the spatial region to be analyzed is stored in normal 3D spacetime, the processing server 200 can reduce the size of the spatial region that the user is analyzing. Therefore, the user can easily visualize the trajectories of entities. This effect is particularly significant when there are many entities and the processes of event logs have complex influences on each other. It also reduces the need for the user to enlarge or reduce the display scale of the entity trajectories. In addition, when the user searches for information on one or more event logs to be analyzed, the processing server 200 can narrow down the search target faster. Therefore, the user can analyze events efficiently.

[0040] Furthermore, the resolution specification unit 206 can aggregate two or more trajectories of multiple entities into one trajectory based on at least one of the trajectories of multiple entities or characteristic information relating to multiple entities. For example, the processing server 200 can aggregate information about complex event logs into information about simpler, more important event logs. As a result, users can easily identify important event logs. Also, the aggregation reduces the number of event logs that the processing server 200 has to process. Therefore, the processing server 200 can reduce processing costs such as computing resources and time. In other words, the processing server 200 can improve its scalability. Users can perform detailed analysis of events by visualizing specific information about the number of aggregated events.

[0041] Furthermore, by allowing the log selection unit 201 to specify the spatial region of the events to be selected, the user can easily grasp information related to the events to be analyzed. In addition, by limiting the event logs to be selected or enabling user search, the log selection unit 201 can make it even easier for the user to grasp information related to events.

[0042] The configuration of the processing server 200 is not limited to the hardware configuration shown above. Processing by the processing server 200 can also be achieved by having a computer program run on a processor within a computer.

[0043] Figure 6 is a block diagram showing an example of the hardware configuration of an information processing device (in other words, a computer) on which the processing server 200 performs its operations. Referring to Figure 6, the information processing device 90 includes a signal processing circuit 91, a processor 92, and memory 93.

[0044] The signal processing circuit 91 is a circuit for processing signals in accordance with the control of the processor 92. The signal processing circuit 91 may also include a communication circuit for transmitting or receiving signals from other devices.

[0045] The processor 92 is connected to the memory 93 and performs the processing of the system described in the above embodiment by reading and executing computer programs from the memory 93. The processor 92 has one or more processors. Examples of processors 92 may include a CPU (Central Processing Unit), an MPU (Micro Processing Unit), an FPGA (Field-Programmable Gate Array), a DSP (Digital Signal Processor), and an ASIC (Application Specific Integrated Circuit).

[0046] Memory 93 is composed of volatile memory, non-volatile memory, or a combination of volatile and non-volatile memory. Memory 93 is not limited to one unit, but may be provided in multiple units. Volatile memory may be, for example, RAM (Random Access Memory) such as DRAM (Dynamic Random Access Memory) or SRAM (Static Random Access Memory). Non-volatile memory may be, for example, ROM (Read Only Memory) such as PROM (Programmable Random Only Memory) or EPROM (Erasable Programmable Read Only Memory), flash memory, or SSD (Solid State Drive).

[0047] Memory 93 is used to store one or more instructions. Here, one or more instructions are stored in memory 93 as a program. The processor 92 can perform the processing described in the above embodiment by reading the stored program from memory 93 and executing it. Memory 93 may be provided either outside or inside the processor 92.

[0048] As described above, one or more processors in each system or device of the above-described embodiment execute one or more programs including a set of instructions. The set of instructions is a set of instructions for causing the computer to perform the algorithm described with reference to the drawings. By executing the program, the information processing described in the embodiment can be realized.

[0049] The program, when loaded into a computer, includes a set of instructions or software code for causing the computer to perform one or more of the functions described in the embodiments. The program may be stored on a non-temporary computer-readable medium or a physical storage medium. Examples, but not limited to, include memory technologies such as random-access memory (RAM), read-only memory (ROM), flash memory, and solid-state drives (SSDs). The computer-readable medium or physical storage medium may also include optical disc storage such as compact disc read-only memory (CD-ROM), digital versatile disk (DVD), and Blu-ray® discs. Furthermore, the computer-readable medium or physical storage medium may include magnetic cassettes, magnetic tapes, magnetic disk storage, and magnetic storage devices. The program may be transmitted over a temporary computer-readable medium or a communication medium. Examples, but not limited to, include propagating signals in electrical, optical, and acoustic forms. Temporary computer-readable media or communication media can supply programs to a computer via wired communication channels such as electric wires and optical fibers, or via wireless communication channels.

[0050] Although the present disclosure has been described above with reference to embodiments, the present disclosure is not limited to the embodiments described above. Various modifications to the structure and details of the present disclosure can be understood by those skilled in the art within the scope of the present disclosure. [Explanation of Symbols]

[0051] 10 Analysis Systems 100 DB 200 processing servers 201 Log selection section 202 Event processing section 203 Embedded section 204 Image rendering section 205 Output section 206 Resolution specification section

Claims

1. An embedding unit that embeds location data of one or more entities into a Poincaré disk, A rendering unit that uses time information data corresponding to the position information of one or more entities to render the position information data embedded in the Poincaré disk as the trajectory of one or more entities, An information processing device equipped with the following features.

2. The embedded portion embeds a predetermined spatial region in Euclidean space into the Poincaré disk. The rendering unit renders the trajectories of one or more entities within the predetermined spatial region embedded in the Poincaré disk. The information processing apparatus according to claim 1.

3. The system further includes an aggregation unit that aggregates two or more trajectories from a plurality of entities into one trajectory, based on at least one of the trajectories of a plurality of entities or information relating to a plurality of entities. The information processing apparatus according to claim 1 or 2.

4. The location data of one or more entities is embedded in the Poincaré disk. By using time information data corresponding to the position information of one or more entities, the position information data embedded in the Poincaré disk is depicted as the trajectory of one or more entities. The information processing method performed by computers.

5. The location data of one or more entities is embedded in the Poincaré disk. By using time information data corresponding to the position information of one or more entities, the position information data embedded in the Poincaré disk is depicted as the trajectory of one or more entities. A program that causes a computer to perform a task.

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