Patent Grant
11189083
The disclosed embodiments generally relate to techniques for displaying polygons. More specifically, the disclosed embodiments relate to an efficient polygon-clipping technique that facilitates clipping polygons to reduce the data that needs to be processed to display a set of polygons within a moveable viewport.
Many applications may require clipping of polygons that have large point counts. An example is a web-based choropleth map in which the user “drags” the map. This has the effect of repositioning a clip rectangle defined by the screen's viewport. When the user releases the drag event, the server responds by sending a portion of the geometry that is clipped out of the entire map geometry to fit just the viewport. This reduces the amount of data that must be transferred. Used in conjunction with a generalization technique such as the Ramer-Douglas-Peucker technique, the map can be viewed in sufficient detail for any desired clip.
One popular polygon-clipping technique is the Greiner-Hormann technique (GH). The GH polygon-clipping technique begins by finding all the points at which two polygons intersect. Given n vertices for the subject polygon and m vertices for the clip polygon, the step of finding the intersections requires O(m*n) time. This means that using the GH polygon-clipping technique can be time-consuming for choropleth maps that have large point counts, which can cause the clipping operation to introduce a noticeable lag when a user drags a choropleth map.
Hence, what is needed is an efficient polygon-clipping technique to facilitate re-positioning a screen's viewport.
The disclosed embodiments relate to a system, a method and instructions embodied on a non-transitory computer-readable storage medium that display a set of polygons. During operation, the system obtains a set of line segments that defines the set of polygons. Next, the system forms a horizontal index that keeps track of where line segments in the set of line segments vertically project onto a horizontal reference line. The system also forms a vertical index that keeps track of where line segments in the set of line segments horizontally project onto a vertical reference line. The system then obtains a clip rectangle that defines a view into the set of polygons. Next, the system uses the horizontal index to determine intersections between vertical borders of the clip rectangle and the line segments, and also uses the vertical index to determine intersections between horizontal borders of the clip rectangle and the line segments. The system then uses the determined intersections to clip polygons that intersect the clip rectangle. Finally, the system transfers the clipped polygons, and also unclipped polygons that fit completely within the clip rectangle, to a display device that displays the view into the set of polygons.
In some embodiments, the system subsequently obtains a new clip rectangle from a user that defines a new view into the set of polygons. The system then uses the horizontal and vertical indexes to determine intersections between the new clip rectangle and the line segments. Next, the system uses the new intersections to clip polygons that intersect the new clip rectangle. Then, the system transfers the new clipped polygons, and also unclipped polygons that fit completely within the new clip rectangle, to a display device that displays the new view into the set of polygons.
In some embodiments, the system maintains a storage grid to keep track of the line segments with respect to a tiled grid, wherein the tiled grid divides a region occupied by the polygons into a set of tiles, and wherein each entry in the storage grid identifies line segments with endpoints that fall within a corresponding tile in the tiled grid. Then, prior to determining the intersections, the system winnows the set of line segments by: (1) identifying tiles in the set of tiles that intersect with or are contained within the clip rectangle; (2) looking up the identified tiles in the storage grid to identify line segments having endpoints that fall within the identified tiles; and (3) redefining the set of line segments to comprise the identified line segments.
In some embodiments, while using the determined intersections to clip the polygons, the system performs as follows: for each polygon intersected by the clip rectangle, the system maintains a polygon list including vertices of the polygon, and also maintains a clip rectangle list including vertices of the clip rectangle. Next, the system inserts polygon-specific intersections between the polygon and the clip rectangle, obtained from the determined intersections, into both the polygon list and the clip rectangle list, and also maintains a bidirectional neighbor link between each instance of an intersection in the polygon list and a corresponding instance of the same intersection in the clip rectangle list. Then, the system sorts the intersections and the vertices in the polygon list in either clockwise or counter-clockwise order and also sorts the intersections and the vertices in the clip rectangle list in either clockwise or counter-clockwise order. The system then marks each intersection as an entry or an exit from the polygon by using a point-in-polygon test to determine whether an initial vertex in the clip rectangle list is inside or outside the clip rectangle, and then while traversing the clip rectangle list, marks intersections alternately as an entry or an exit. Finally, the system generates one or more clipped polygons by emitting vertices starting at an intersection in the polygon list and navigating back and forth between the polygon list and the clip rectangle list as intersections are encountered, and proceeding backward or forward in the polygon list or the clip rectangle list based upon whether the intersection is an entry or an exit.
In some embodiments, the set of polygons defines regions of a choropleth map wherein each region is shaded, patterned or colored in proportion to a number of data points that fall into the region.
Table 1 illustrates sorted point structures in accordance with the disclosed embodiments.
Table 2 illustrates sorted point structures with corresponding lists of open segments in accordance with the disclosed embodiments.
Table 3 illustrates how non-final rows can be struck out in accordance with the disclosed embodiments.
Table 4 illustrates y-ranges and corresponding open segments in accordance with the disclosed embodiments.
Table 5 illustrates how non-final rows can be struck out in accordance with the disclosed embodiments.
Table 6 illustrates how the data structure can be modified for modulo 3 storage in accordance with the disclosed embodiments.
The disclosed embodiments relate to a system, a method and instructions embodied on a non-transitory computer-readable storage medium code that facilitate displaying a set of polygons in a viewport. (Note that throughout this specification and the attached claims we refer to “the system,” “the method” and “the instructions embodied on a non-transitory computer-readable storage medium” collectively as “the system.”) We describe a solution to the point-in-polygon (PIP) problem, before we finally describe a technique for clipping a set of polygons for a view port.
Modern data centers often comprise thousands of host computer systems that operate collectively to service requests from even larger numbers of remote clients. During operation, these data centers generate significant volumes of performance data and diagnostic information that can be analyzed to quickly diagnose performance problems. In order to reduce the size of this performance data, the data is typically pre-processed prior to being stored based on anticipated data-analysis needs. For example, pre-specified data items can be extracted from the performance data and stored in a database to facilitate efficient retrieval and analysis at search time. However, the rest of the performance data is not saved and is essentially discarded during pre-processing. As storage capacity becomes progressively cheaper and more plentiful, there are fewer incentives to discard this performance data and many reasons to keep it.
This plentiful storage capacity is presently making it feasible to store massive quantities of minimally processed performance data at “ingestion time” for later retrieval and analysis at “search time.” Note that performing the analysis operations at search time provides greater flexibility because it enables an analyst to search all of the performance data, instead of searching pre-specified data items that were stored at ingestion time. This enables the analyst to investigate different aspects of the performance data instead of being confined to the pre-specified set of data items that was selected at ingestion time.
However, analyzing massive quantities of heterogeneous performance data at search time can be a challenging task. A data center may generate heterogeneous performance data from thousands of different components, which can collectively generate tremendous volumes of performance data that can be time-consuming to analyze. For example, this performance data can include data from system logs, network packet data, sensor data, and data generated by various applications. Also, the unstructured nature of much of this performance data can pose additional challenges because of the difficulty of applying semantic meaning to unstructured data, and the difficulty of indexing and querying unstructured data using traditional database systems.
These challenges can be addressed by using an event-based system, such as the SPLUNK® ENTERPRISE system produced by Splunk Inc. of San Francisco, Calif., to store and process performance data. The SPLUNK® ENTERPRISE system is the leading platform for providing real-time operational intelligence that enables organizations to collect, index, and harness machine-generated data from various websites, applications, servers, networks, and mobile devices that power their businesses. The SPLUNK® ENTERPRISE system is particularly useful for analyzing unstructured performance data, which is commonly found in system log files. Although many of the techniques described herein are explained with reference to the SPLUNK® ENTERPRISE system, the techniques are also applicable to other types of data server systems.
In the SPLUNK® ENTERPRISE system, performance data is stored as “events,” wherein each event comprises a collection of performance data and/or diagnostic information that is generated by a computer system and is correlated with a specific point in time. Events can be derived from “time series data,” wherein time series data comprises a sequence of data points (e.g., performance measurements from a computer system) that are associated with successive points in time and are typically spaced at uniform time intervals. Events can also be derived from “structured” or “unstructured” data. Structured data has a predefined format, wherein specific data items with specific data formats reside at predefined locations in the data. For example, structured data can include data items stored in fields in a database table. In contrast, unstructured data does not have a predefined format. This means that unstructured data can comprise various data items having different data types that can reside at different locations. For example, when the data source is an operating system log, an event can include one or more lines from the operating system log containing raw data that includes different types of performance and diagnostic information associated with a specific point in time. Examples of data sources from which an event may be derived include, but are not limited to: web servers; application servers; databases; firewalls; routers; operating systems; and software applications that execute on computer systems, mobile devices, and sensors. The data generated by such data sources can be produced in various forms including, for example and without limitation, server log files, activity log files, configuration files, messages, network packet data, performance measurements and sensor measurements. An event typically includes a timestamp that may be derived from the raw data in the event, or may be determined through interpolation between temporally proximate events having known timestamps.
The SPLUNK® ENTERPRISE system also facilitates using a flexible schema to specify how to extract information from the event data, wherein the flexible schema may be developed and redefined as needed. Note that a flexible schema may be applied to event data “on the fly,” when it is needed (e.g., at search time), rather than at ingestion time of the data as in traditional database systems. Because the schema is not applied to event data until it is needed (e.g., at search time), it is referred to as a “late-binding schema.”
During operation, the SPLUNK® ENTERPRISE system starts with raw data, which can include unstructured data, machine data, performance measurements or other time-series data, such as data obtained from weblogs, syslogs, or sensor readings. It divides this raw data into “portions,” and optionally transforms the data to produce timestamped events. The system stores the timestamped events in a data store, and enables a user to run queries against the data store to retrieve events that meet specified criteria, such as containing certain keywords or having specific values in defined fields. Note that the term “field” refers to a location in the event data containing a value for a specific data item.
As noted above, the SPLUNK® ENTERPRISE system facilitates using a late-binding schema while performing queries on events. A late-binding schema specifies “extraction rules” that are applied to data in the events to extract values for specific fields. More specifically, the extraction rules for a field can include one or more instructions that specify how to extract a value for the field from the event data. An extraction rule can generally include any type of instruction for extracting values from data in events. In some cases, an extraction rule comprises a regular expression, in which case the rule is referred to as a “regex rule.”
In contrast to a conventional schema for a database system, a late-binding schema is not defined at data ingestion time. Instead, the late-binding schema can be developed on an ongoing basis until the time a query is actually executed. This means that extraction rules for the fields in a query may be provided in the query itself, or may be located during execution of the query. Hence, as an analyst learns more about the data in the events, the analyst can continue to refine the late-binding schema by adding new fields, deleting fields, or changing the field extraction rules until the next time the schema is used by a query. Because the SPLUNK® ENTERPRISE system maintains the underlying raw data and provides a late-binding schema for searching the raw data, it enables an analyst to investigate questions that arise as the analyst learns more about the events.
In the SPLUNK® ENTERPRISE system, a field extractor may be configured to automatically generate extraction rules for certain fields in the events when the events are being created, indexed, or stored, or possibly at a later time. Alternatively, a user may manually define extraction rules for fields using a variety of techniques.
Also, a number of “default fields” that specify metadata about the events rather than data in the events themselves can be created automatically. For example, such default fields can specify: a timestamp for the event data; a host from which the event data originated; a source of the event data; and a source type for the event data. These default fields may be determined automatically when the events are created, indexed or stored.
In some embodiments, a common field name may be used to reference two or more fields containing equivalent data items, even though the fields may be associated with different types of events that possibly have different data formats and different extraction rules. By enabling a common field name to be used to identify equivalent fields from different types of events generated by different data sources, the system facilitates use of a “common information model” (CIM) across the different data sources.
During operation, the forwarders 101 identify which indexers 102 will receive the collected data and then forward the data to the identified indexers. Forwarders 101 can also perform operations to strip out extraneous data and detect timestamps in the data. The forwarders next determine which indexers 102 will receive each data item and then forward the data items to the determined indexers 102.
Note that distributing data across different indexers facilitates parallel processing. This parallel processing can take place at data ingestion time, because multiple indexers can process the incoming data in parallel. The parallel processing can also take place at search time, because multiple indexers can search through the data in parallel.
System 100 and the processes described below with respect to
Next, the indexer determines a timestamp for each event at block 203. As mentioned above, these timestamps can be determined by extracting the time directly from data in the event, or by interpolating the time based on timestamps from temporally proximate events. In some cases, a timestamp can be determined based on the time the data was received or generated. The indexer subsequently associates the determined timestamp with each event at block 204, for example by storing the timestamp as metadata for each event.
Then, the system can apply transformations to data to be included in events at block 205. For log data, such transformations can include removing a portion of an event (e.g., a portion used to define event boundaries, extraneous text, characters, etc.) or removing redundant portions of an event. Note that a user can specify portions to be removed using a regular expression or any other possible technique.
Next, a keyword index can optionally be generated to facilitate fast keyword searching for events. To build a keyword index, the indexer first identifies a set of keywords in block 206. Then, at block 207 the indexer includes the identified keywords in an index, which associates each stored keyword with references to events containing that keyword (or to locations within events where that keyword is located). When an indexer subsequently receives a keyword-based query, the indexer can access the keyword index to quickly identify events containing the keyword.
In some embodiments, the keyword index may include entries for name-value pairs found in events, wherein a name-value pair can include a pair of keywords connected by a symbol, such as an equals sign or colon. In this way, events containing these name-value pairs can be quickly located. In some embodiments, fields can automatically be generated for some or all of the name-value pairs at the time of indexing. For example, if the string “dest=10.0.1.2” is found in an event, a field named “dest” may be created for the event, and assigned a value of “10.0.1.2.”
Finally, the indexer stores the events in a data store at block 208, wherein a timestamp can be stored with each event to facilitate searching for events based on a time range. In some cases, the stored events are organized into a plurality of buckets, wherein each bucket stores events associated with a specific time range. This not only improves time-based searches, but it also allows events with recent timestamps that may have a higher likelihood of being accessed to be stored in faster memory to facilitate faster retrieval. For example, a bucket containing the most recent events can be stored as flash memory instead of on hard disk.
Each indexer 102 is responsible for storing and searching a subset of the events contained in a corresponding data store 103. By distributing events among the indexers and data stores, the indexers can analyze events for a query in parallel, for example using map-reduce techniques, wherein each indexer returns partial responses for a subset of events to a search head that combines the results to produce an answer for the query. By storing events in buckets for specific time ranges, an indexer may further optimize searching by looking only in buckets for time ranges that are relevant to a query.
Moreover, events and buckets can also be replicated across different indexers and data stores to facilitate high availability and disaster recovery as is described in U.S. patent application Ser. No. 14/266,812 filed on 30 Apr. 2014, and in U.S. patent application Ser. No. 14/266,817 also filed on 30 Apr. 2014.
Then, at block 304, the indexers to which the query was distributed search their data stores for events that are responsive to the query. To determine which events are responsive to the query, the indexer searches for events that match the criteria specified in the query. This criteria can include matching keywords or specific values for certain fields. In a query that uses a late-binding schema, the searching operations in block 304 may involve using the late-binding scheme to extract values for specified fields from events at the time the query is processed. Next, the indexers can either send the relevant events back to the search head, or use the events to calculate a partial result, and send the partial result back to the search head.
Finally, at block 305, the search head combines the partial results and/or events received from the indexers to produce a final result for the query. This final result can comprise different types of data depending upon what the query is asking for. For example, the final results can include a listing of matching events returned by the query, or some type of visualization of data from the returned events. In another example, the final result can include one or more calculated values derived from the matching events.
Moreover, the results generated by system 100 can be returned to a client using different techniques. For example, one technique streams results back to a client in real-time as they are identified. Another technique waits to report results to the client until a complete set of results is ready to return to the client. Yet another technique streams interim results back to the client in real-time until a complete set of results is ready, and then returns the complete set of results to the client. In another technique, certain results are stored as “search jobs,” and the client may subsequently retrieve the results by referencing the search jobs.
The search head can also perform various operations to make the search more efficient. For example, before the search head starts executing a query, the search head can determine a time range for the query and a set of common keywords that all matching events must include. Next, the search head can use these parameters to query the indexers to obtain a superset of the eventual results. Then, during a filtering stage, the search head can perform field-extraction operations on the superset to produce a reduced set of search results.
Upon receiving search query 402, query processor 404 sees that search query 402 includes two fields “IP” and “target.” Query processor 404 also determines that the values for the “IP” and “target” fields have not already been extracted from events in data store 414, and consequently determines that query processor 404 needs to use extraction rules to extract values for the fields. Hence, query processor 404 performs a lookup for the extraction rules in a rule base 406, wherein rule base 406 maps field names to corresponding extraction rules and obtains extraction rules 408-409, wherein extraction rule 408 specifies how to extract a value for the “IP” field from an event, and extraction rule 409 specifies how to extract a value for the “target” field from an event. As is illustrated in
Next, query processor 404 sends extraction rules 408-409 to a field extractor 412, which applies extraction rules 408-409 to events 416-418 in a data store 414. Note that data store 414 can include one or more data stores, and extraction rules 408-409 can be applied to large numbers of events in data store 414, and are not meant to be limited to the three events 416-418 illustrated in
Next, field extractor 412 applies extraction rule 408 for the first command Search IP=“10*” to events in data store 414 including events 416-418. Extraction rule 408 is used to extract values for the IP address field from events in data store 414 by looking for a pattern of one or more digits, followed by a period, followed again by one or more digits, followed by another period, followed again by one or more digits, followed by another period, and followed again by one or more digits. Next, field extractor 412 returns field values 420 to query processor 404, which uses the criterion IP=“10*” to look for IP addresses that start with “10”. Note that events 416 and 417 match this criterion, but event 418 does not, so the result set for the first command is events 416-417.
Query processor 404 then sends events 416-417 to the next command “stats count target.” To process this command, query processor 404 causes field extractor 412 to apply extraction rule 409 to events 416-417. Extraction rule 409 is used to extract values for the target field for events 416-417 by skipping the first four commas in events 416-417, and then extracting all of the following characters until a comma or period is reached. Next, field extractor 412 returns field values 421 to query processor 404, which executes the command “stats count target” to count the number of unique values contained in the target fields, which in this example produces the value “2” that is returned as a final result 422 for the query.
Note that query results can be returned to a client, a search head, or any other system component for further processing. In general, query results may include: a set of one or more events; a set of one or more values obtained from the events; a subset of the values; statistics calculated based on the values; a report containing the values; or a visualization, such as a graph or chart, generated from the values.
After the search is executed, the search screen 600 can display the results through search results tabs 604, wherein search results tabs 604 includes: an “events tab” that displays various information about events returned by the search; a “statistics tab” that displays statistics about the search results; and a “visualization tab” that displays various visualizations of the search results. The events tab illustrated in
The above-described system provides significant flexibility by enabling a user to analyze massive quantities of minimally processed performance data “on the fly” at search time instead of storing pre-specified portions of the performance data in a database at ingestion time. This flexibility enables a user to see correlations in the performance data and perform subsequent queries to examine interesting aspects of the performance data that may not have been apparent at ingestion time.
However, performing extraction and analysis operations at search time can involve a large amount of data and require a large number of computational operations, which can cause considerable delays while processing the queries. Fortunately, a number of acceleration techniques have been developed to speed up analysis operations performed at search time. These techniques include: (1) performing search operations in parallel by formulating a search as a map-reduce computation; (2) using a keyword index; (3) using a high performance analytics store; and (4) accelerating the process of generating reports. These techniques are described in more detail below.
To facilitate faster query processing, a query can be structured as a map-reduce computation, wherein the “map” operations are delegated to the indexers, while the corresponding “reduce” operations are performed locally at the search head. For example,
During operation, upon receiving search query 501, search head 104 modifies search query 501 by substituting “stats” with “prestats” to produce search query 502, and then distributes search query 502 to one or more distributed indexers, which are also referred to as “search peers.” Note that search queries may generally specify search criteria or operations to be performed on events that meet the search criteria. Search queries may also specify field names, as well as search criteria for the values in the fields or operations to be performed on the values in the fields. Moreover, the search head may distribute the full search query to the search peers as is illustrated in
As described above with reference to the flow charts in
To speed up certain types of queries, some embodiments of system 100 make use of a high performance analytics store, which is referred to as a “summarization table,” that contains entries for specific field-value pairs. Each of these entries keeps track of instances of a specific value in a specific field in the event data and includes references to events containing the specific value in the specific field. For example, an exemplary entry in a summarization table can keep track of occurrences of the value “94107” in a “ZIP code” field of a set of events, wherein the entry includes references to all of the events that contain the value “94107” in the ZIP code field. This enables the system to quickly process queries that seek to determine how many events have a particular value for a particular field, because the system can examine the entry in the summarization table to count instances of the specific value in the field without having to go through the individual events or do extractions at search time. Also, if the system needs to process all events that have a specific field-value combination, the system can use the references in the summarization table entry to directly access the events to extract further information without having to search all of the events to find the specific field-value combination at search time.
In some embodiments, the system maintains a separate summarization table for each of the above-described time-specific buckets that stores events for a specific time range, wherein a bucket-specific summarization table includes entries for specific field-value combinations that occur in events in the specific bucket. Alternatively, the system can maintain a separate summarization table for each indexer, wherein the indexer-specific summarization table only includes entries for the events in a data store that is managed by the specific indexer.
The summarization table can be populated by running a “collection query” that scans a set of events to find instances of a specific field-value combination, or alternatively instances of all field-value combinations for a specific field. A collection query can be initiated by a user, or can be scheduled to occur automatically at specific time intervals. A collection query can also be automatically launched in response to a query that asks for a specific field-value combination.
In some cases, the summarization tables may not cover all of the events that are relevant to a query. In this case, the system can use the summarization tables to obtain partial results for the events that are covered by summarization tables, but may also have to search through other events that are not covered by the summarization tables to produce additional results. These additional results can then be combined with the partial results to produce a final set of results for the query. This summarization table and associated techniques are described in more detail in U.S. Pat. No. 8,682,925, issued on Mar. 25, 2014.
In some embodiments, a data server system such as the SPLUNK® ENTERPRISE system can accelerate the process of periodically generating updated reports based on query results. To accelerate this process, a summarization engine automatically examines the query to determine whether generation of updated reports can be accelerated by creating intermediate summaries. (This is possible if results from preceding time periods can be computed separately and combined to generate an updated report. In some cases, it is not possible to combine such incremental results, for example where a value in the report depends on relationships between events from different time periods.) If reports can be accelerated, the summarization engine periodically generates a summary covering data obtained during a latest non-overlapping time period. For example, where the query seeks events meeting a specified criteria, a summary for the time period includes only events within the time period that meet the specified criteria. Similarly, if the query seeks statistics calculated from the events, such as the number of events that match the specified criteria, then the summary for the time period includes the number of events in the period that match the specified criteria.
In parallel with the creation of the summaries, the summarization engine schedules the periodic updating of the report associated with the query. During each scheduled report update, the query engine determines whether intermediate summaries have been generated covering portions of the time period covered by the report update. If so, then the report is generated based on the information contained in the summaries. Also, if additional event data has been received and has not yet been summarized, and is required to generate the complete report, the query can be run on this additional event data. Then, the results returned by this query on the additional event data, along with the partial results obtained from the intermediate summaries, can be combined to generate the updated report. This process is repeated each time the report is updated. Alternatively, if the system stores events in buckets covering specific time ranges, then the summaries can be generated on a bucket-by-bucket basis. Note that producing intermediate summaries can save the work involved in re-running the query for previous time periods, so only the newer event data needs to be processed while generating an updated report. These report acceleration techniques are described in more detail in U.S. Pat. No. 8,589,403, issued on Nov. 19, 2013, and U.S. Pat. No. 8,412,696, issued on Apr. 2, 2011.
To generate a choropleth map, we first determine which data points fall into each geographic region. This can be accomplished by using a technique that solves the point-in-polygon (PIP) problem. The PIP problem is typically solved using either the known crossing number (CN) technique or the known winding number (WN) technique. For example, the CN technique is depicted in
Because this disclosure focuses on accelerating the CN technique, and because the CN technique has the same computational complexity as the WN technique, we will not describe the WN technique further other than to say that it iterates the vertices of the polygon and counts the number of full turns around the point being tested.
There are a number of existing approaches to accelerating PIP testing. Perhaps the most common is to insert the polygons into a spatial data structure such as an R-Tree. One example of this is the PostGIS™ database. The R-Tree can be queried to retrieve a set of candidate polygons based on rectangular bounding boxes surrounding each polygon. This eliminates polygons whose bounding boxes do not surround the point in question. Each surviving candidate must then be tested using either CN or WN to determine if the point in question falls inside, outside or on the edge of the candidate. Because candidates may contain large numbers of vertices, and because there may exist many candidates, the CN and WN techniques are still the bottleneck because they are both O(n) where n is the number of vertices in the polygon being tested. More recently, an approach has been proposed that builds an index specifically for PIP testing; however, this approach suffers from an exponential index build complexity of O(n2.6). Both the R-Tree and the above-described index-building approach rely on in-memory tree structures. The performance of these in-memory tree structures when stored on spinning disk media as opposed to RAM depends on the depth of the tree because each link traversal in a tree search requires a seek operation and seek operations are slow on traditional spinning media.
The new indexing technique described in this disclosure involves casting horizontal rays from polygon segments onto a reference line and then storing the set of segments intersected by the rays. For a given point to be PIP tested, the set of intersected segments across all polygons in the index can then be retrieved from the index and fed directly to the CN technique. This obviates the need to iterate the boundaries of the polygons to determine which segments intersect a ray emanating from the point to be tested.
We now describe how to build such an index that comprises sorted y-ranges, and their corresponding set of intersected segments. Consider a point data structure for describing the points as {segmentId, x, y, order}. The “order” field can assume the values O or C for “opening” or “closing”. An “opening” point for a segment corresponds to the point with the smaller y-coordinate. A “closing” point is the segment's point with the larger y-coordinate. For example, the coordinate of S1 with the smaller y-value would be {S1, --, y1, O} (the x-values are shown as “--”). By sorting the point structures based on their y-value from smallest to largest, we obtain the ordering with ascending y-values illustrated in Table 1.
By traversing this sorted set of point data structures from beginning to end, we can create a corresponding list of open segments (that is to say, segments that would intersect a horizontal ray projected from point x,y). As we traverse the listed point structures shown in Table 1, we can perform the following operation: if the order field is “O”, then we add the corresponding segment ID to the list of open segments. If the order field is “C”, then we remove the corresponding segment ID from the list. Hereafter, we call this the “opening and closing technique.” Following this simple procedure, the list of open segments is shown next to each point data structure as is illustrated in Table 2 below.
For the list shown in Table 2, the final list for a given y-value provides the set of open segments between the current y-value and the next y-value. Table 3 illustrates this by striking out the non-final segments.
From the remaining adjacent y-values (those not struck out), we can extract the y-coordinates, and the open lists to create continuous y-ranges, and corresponding lists of open segments, as shown in Table 4, including the ranges from negativity infinity, and to positive infinity on the y-axis.
We can extend the above-described methodology to multiple polygons by including the identity of the polygon in the segmentId field. For example,
We now describe a technique for minimizing the storage of ray intersection lists because the lists themselves can grow large and tend to be duplicative with respect to their neighboring lists. This is accomplished by storing 1 of every K ray intersection lists, and using the point data structure to update a stored intersection list at runtime. That is, the intersection list is stored modulo K. In this variation, the point data structure must be stored for each point and is used at runtime to update a stored ray intersection set to the desired g-range. For example, Table 6 below illustrates polygons of
We now describe the process of determining the set of intersected segments of a horizontal ray at an arbitrary height, given the modulo style of index storage. Given a desired ray height of Y, the sorted point structure is binary searched to determine the point having a stored ray and a y-value less than or equal to the desired y-value. In essence, the system retrieves a ray that is parallel to, but lower than the desired ray. This lower ray is then raised to the desired height using the opening and closing technique. When a point is reached having a y-value greater than the desired height, the technique terminates.
For example, consider a point at location {x,y} for which we want to answer the PIP question. Assume Y falls in the range [y4, y5) of Table 6. Binary searching the point structure yields {S2B, --, y4, O}: [S2A, S3A, S1B, S3B, S2B] because the point structure and ray are lower than or equal to the desired y. Correcting the ray using the following point structure {S1B, --, y4, C} updates the ray to [S2A, S3A, S3B, S2B], which is the correct set of intersections for a ray falling in the range [y4, y5). The next point structure, {S2B, y5, C}, causes the updating to stop, because y5 is greater than the desired height.
The preceding disclosure describes how to retrieve a pre-cast ray from the index. Also, for the case of modulo indexing, we showed how to “correct” a stored ray to raise its height to the desired range. We now describe the step of how to apply the CN technique to the ray. The rays retrieved (and possibly corrected) from the index are cast from negative infinity toward positive infinity in the X direction. The intersection sets such as [S2A, S3A, S1B, S3B, S2B] are made of segment IDs that include the polygon identity (for instance “A” and “B”). Therefore, before feeding segments to the CN technique, we must first group them by polygonId. This is illustrated in
Using the data illustrated in
In the technique presented so far, a ray must be retrieved (and corrected as needed) for each point to be tested. In practice, retrieving the ray and correcting it takes substantially longer (by orders of magnitude) than performing the CN technique on the retrieved set. The fact that the intersection set is invariant for a given range [ymin, ymax) allows for amortization of the intersection set retrieval and correction costs when a batch of points needs to be PIP tested. This can be accomplished by first sorting the points to be batch tested based on their y-value. While processing the first point in the now-sorted batch, the corresponding ray can be retrieved and corrected from the index. For the second point, and all subsequent points to be tested, the ray can be incrementally corrected. That is to say, if the subsequent point to be tested still falls within the [ymin, ymax) range of the corrected ray, then no further action is required, and the CN technique is again applied directly to the subsequent point. Subsequent points are processed until a point is encountered whose y-value surpasses the upper extent of the ray's valid range (ymax). At this point, rather than performing a brand new query for a ray (which would require a binary search), one can simply continue to apply correction to the ray which requires forward iteration in the index, but not binary searching.
Note that in addition to determining which points fall within each polygon, the above-described technique can be modified to determine whether a given shape overlaps, intersects or encloses another shape by performing the technique for the points that define the given shape.
Displaying Geographic Data
Next, for each data point in a set of data points to be processed, the system identifies a relevant interval on the reference line that the data point projects onto (step 1308), and performs a crossing number (CN) operation by counting intersections between a ray projected from the data point and open line segments associated with the relevant interval to identify zero or more polygons that the data point falls into (step 1310). The intersections can be detected by performing an intersection test using an equation for the line segment (y=mx+b) to see whether a ray projected from positive infinity to the data point intersects the line segment. If the reference line is the y-axis, the system can perform a simple initial filtering test to see whether both x-coordinates of the line segment are less than the data point's x-coordinate. This enables the system to throw out line segments that are obviously not intersected by the ray. The system then increments a count for each polygon that the data point falls into (step 1312).
Finally, the system displays the set of geographic regions, wherein each polygon that defines a geographic region is marked to indicate a number of data points that fall into the polygon (step 1314).
Next, for a data point to be processed, the system identifies a relevant interval on the reference line that the data point projects onto (step 1408). The system subsequently performs a crossing number (CN) operation by counting intersections between a ray projected from the data point and open line segments associated with the relevant interval to identify zero or more polygons that the data point falls into (step 1410). Finally, the system performs a geofencing operation based on the identified zero or more polygons that the data point falls into (step 1412). For example, the geofencing operation can involve sending a notification to a user when the user's location (obtained from the user's phone) indicates that the user has crossed a geofence boundary associated with a restricted security area.
Next, for each for each data point in a set of data points, the system identifies zero or more geographic regions in the set of geographic regions that the data point falls into (step 1506). Finally, the system displays the set of geographic regions, wherein each polygon that defines a geographic region is marked to indicate a number of data points that fall into the polygon (step 1508).
A known polygon-clipping technique is the Greiner-Hormann technique (GH). The GH technique begins by finding all the points at which two polygons intersect. Given n vertices for the subject polygon and m vertices for the clip polygon, the step of finding the intersections is O(m*n). We will use the PIP index (described above), with a slight modification to reduce the complexity to worst case 4*log(n), thereby greatly improving performance (in comparison to a conventional GH technique) against a large server-side database of polygons.
Let us consider the special case of a clip polygon that is an isothetic rectangle (that is to say, a rectangle whose horizontal edges are parallel to the x-axis, and vertical edges are parallel to the y-axis).
For the horizontal edges, this obviates the need to, for each segment of the clip, check each segment of the subject, thereby avoiding the m*n dominant term of the complexity of GH. However, we have no means to look up the vertical edges of the rectangle. We solve this problem by creating a second PIP index, but in the second PIP index, we project points onto the x-axis, thereby indexing vertical rays as opposed to horizontal rays. This is depicted in
So far we have shown how to efficiently retrieve the intersections between a subject polygon and the clipping rectangle. We also need a means to retrieve and order all the segments of the polygons that fall within the clip rectangle. For instance, looking at
Individual keys are indexed by their minimum coordinate in a (yMin, xMin) tuple. In other words, the minimum (lower left) corner of any tile is used to identify the tile. For instance examining the shaded tile of
Given a clip rectangle and a grid size (for instance tenths of a unit), the key for every tile within the clip rectangle or intersecting its boundary is trivial to calculate. One approach to retrieving the necessary segments is to seek and retrieve the content of each tile using the tile as a key in a key-value database.
In the following technique we use a structure called subject_and_clip that pairs a copy of the clipping rectangle with a particular subject polygon. We refer to a subject_and_clip for a particular polygon id as subject_and_clip(id). Think of subject_and_clip as a global hashmap where the key is a poygonId and the value is SubjectAndClip object. If we attempt to retrieve subject_and_clip(14), for example, and no SubjectAndClip object is present in the map, then a new SubjectAndClip is created, inserted into the map with key 14, and the said SubjectAndClip's clip rectangle is initialized with its 4 corner vertices. The Subject_and_clip has methods by which points or intersections can be added to it, and for implementing the GH technique.
We implement the clipping technique as follows (virtually all of it constitutes precursor steps leading up to the final application of the GH technique to pairs of subject and clip rectangle):
Now we proceed to examine details of the technique above. The “perturb INTERSECTION” step performs as specified by the GH technique: If the intersection between subject and clip is due to a vertex of one polygon falling exactly on the edge of another polygon, then the perturb method will move the computed intersection by the minimum value of a float, in both the x and y direction.
The “for each TILE covered by CLIP” step retrieves the line segments of the subjects that fall in, or partially in, the clip rectangle. Retrieving these segments from tiles allows us to ignore the many segments of the subjects that fall outside of the clip rectangle. In
With step For each POLYGON surrounding CLIPs centerpoint we account for polygons that totally surround the clip rectangle and have no intersections with it. Such polygons would otherwise appear invisible to the technique due to the fact that they would appear neither in tiles intersecting or contained by the clip nor have any intersections with the clip and such would never be seen by any steps of the technique. Such polygons should be emitted(?) as shapes exactly matching that of the clip (imagine zooming deep inside a given polygon; the edges of the polygon disappear as we zoom in but the rectangular viewport should remain completely filled with the interior color of the polygon). To accomplish this, we simply use the PIP index to lookup all polygonIds, “id” surrounding the center point of the clip rectangle and perform a no-op on subject_and_clip(id) for each id. The meaning of the no-op is for a heretofore non-existent SubjectAndClip in the hashmap, create a new one, whose subject has no vertices, and whose clip is initialized to the four vertices of the clip rectangle. The no-op has the effect of “prodding” the global hashmap to insure that a SubjectAndClip is present even for subjects having no intersection with the clip rectangle, and no vertices falling inside the clip rectangle. For heretofore-existent SubjectAndClip instances, the no-op has no effect.
The step “For each subject_and_clip” indicates that each subject_and_clip consists of two Boundary objects, one for the subject and one for the clip. Once the subject_and_clip pair has been loaded with all its intersections and points, the Boundary objects of the subject_and_clip will sort their list of intersections into their points in accordance with GH. To do this, the intersections are sorted first by their subject segmentID (i.e., sorted first by the identity of the line segment upon which the intersection falls) and second by their alpha value (distance between the tail of the segment on which the intersection falls and the intersection itself). Since the clip rectangle is artificial (it doesn't exist in the index) its segments (edges) are assigned artificial segmentIds at the time the Boundary is initialized for the clip rectangle. The clip's segment Ids are assigned in increasing order beginning with the north edge and proceeding clockwise. In this manner a standard Boundary object can sort intersections into a clip rectangle's vertices as well as into a polygon whose vertices connect “real” segmentIds in the index. Finally, the GH technique is applied to each SubjectAndClip in the global subject_and_clip map, thereby emitting every polygon clipped by the clip rectangle.
The preceding description was presented to enable any person skilled in the art to make and use the disclosed embodiments, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the disclosed embodiments. Thus, the disclosed embodiments are not limited to the embodiments shown, but are to be accorded the widest scope consistent with the principles and features disclosed herein. Accordingly, many modifications and variations will be apparent to practitioners skilled in the art. Additionally, the above disclosure is not intended to limit the present description. The scope of the present description is defined by the appended claims.
The data structures and code described in this detailed description are typically stored on a computer-readable storage medium, which may be any device or medium that can store code and/or data for use by a system. The computer-readable storage medium includes, but is not limited to, volatile memory, non-volatile memory, magnetic and optical storage devices such as disk drives, magnetic tape, CDs (compact discs), DVDs (digital versatile discs or digital video discs), or other media capable of storing code and/or data now known or later developed.
The methods and processes described in the detailed description section can be embodied as code and/or data, which can be stored on a non-transitory computer-readable storage medium as described above. When a system reads and executes the code and/or data stored on the non-transitory computer-readable storage medium, the system performs the methods and processes embodied as data structures and code and stored within the non-transitory computer-readable storage medium.
Furthermore, the methods and processes described above can be included in hardware modules. For example, the hardware modules can include, but are not limited to, application-specific integrated circuit (ASIC) chips, field-programmable gate arrays (FPGAs), and other programmable-logic devices now known or later developed. When the hardware modules are activated, the hardware modules perform the methods and processes included within the hardware modules.
This application is a continuation of U.S. application Ser. No. 16/256,783, filed Jan. 24, 2019, entitled “Clipping Polygons to Fit Within A Clip Region,” which is itself a continuation of U.S. patent application Ser. No. 15/799,569, filed Oct. 31, 2017, now issued as U.S. Pat. No. 10,223,826. U.S. application Ser. No. 15/799,569 is itself a continuation of U.S. Pat. No. 9,836,874, filed Jul. 31, 2015 which is itself is a continuation-in-part of U.S. Pat. No. 9,607,414, filed Apr. 30, 2015, which is itself a continuation-in-part of U.S. Pat. No. 9,767,122, filed Jan. 27, 2015. The entire contents of each of the above-listed applications are hereby incorporated by reference for all purposes as if fully set forth herein.
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