Abstract: There is described a method of rasterizing a computer model. One or more non-linear expressions of code are identified in a fragment shader. The one or more non-linear expressions of code are transformed into one or more linear expressions of code. The one or more linear expressions of code are transferred from the fragment shader to a vertex shader. The computer model is then rasterized by executing, on the computer model, code comprised in the vertex shader, including the transferred one or more linear expressions of code.

Abstract: One or more stereoscopic images are generated based on a single monoscopic image that may be obtained from a camera sensor. Each stereoscopic image includes a first digital image and a second digital image that, when viewed using any suitable stereoscopic viewing technique, result in a user or software program receiving a three-dimensional effect with respect to the elements included in the stereoscopic images. The monoscopic image may depict a geographic setting of a particular geographic location and the resulting stereoscopic image may provide a three-dimensional (3D) rendering of the geographic setting. Use of the stereoscopic image helps a system obtain more accurate detection and ranging capabilities. The stereoscopic image may be any configuration of the first digital image (monoscopic) and the second digital image (monoscopic) that together may generate a 3D effect as perceived by a viewer or software program.

Abstract: A method for processing a touch signal includes: detecting, through an event dispatch process, a full-screen gesture touch signal, determining whether the full-screen gesture touch signal conforms to a full-screen gesture trajectory determination rule; and sending, based on a result of the determining, the full-screen gesture touch signal or a part of events of the full-screen gesture touch signal to a gesture processing process or an application processing process.

Abstract: A tool path compensation device according to an aspect of the present disclosure includes: a tool path acquisition unit which acquires tool path information that specifies a tool path on which a tool machining a workpiece moves by way of a plurality of command points through which the tool should pass; a tool shape acquisition unit which acquires tool shape information that specifies a shape of the tool; a target shape acquisition unit which acquires target shape information specifying a target shape after machining of the workpiece; and a density adjustment unit which adjusts a density of the command points, so that the density of the command points becomes larger as curvature of the target shape increases.

Abstract: A touch input device includes: a position detector that determines an input range in a touch input produced with an inputter on a touch panel and that detects, as a touch position, any position within the input range; a line information generator that generates line information which is information of a line connecting a plurality of the touch positions detected with the position detector; a smoothing level setter that sets, based on the area of the input range, a smoothing level indicating the degree of smoothing; and a smoothing processing processor that executes, on the line of the line information generated by the line information generator, smoothing corresponding to the smoothing level set by the smoothing level setter.

Abstract: A method is provided for modifying an image. The method comprises displaying an image, the image comprising a portion of an object; and determining if an edge of the object is in a location within the portion. The method further comprises detecting movement, in a member direction, of an operating member with respect to the edge. The method still further comprises moving, if the edge is not in the location, the object in an object direction corresponding to the detected movement; and modifying, if the edge is in the location, the image in response to the detected movement, the modified image comprising the edge in the location.

Abstract: A biometric information display device includes a display controller configured to display a morphological image indicative of a morphology of a subject, on a display, an input controller configured to receive a designation of a specified position on the morphological image, a pathway generating section configured to generate a pathway based on the specified position on the morphological image, and a current extracting section configured to extract current components at a plurality of positions along the pathway, based on current information reconstructed based on magnetic field measurement data generated by the subject. The display controller displays the current components extracted along the pathway on the display.

Abstract: A computer displays data sources associated with tables of data. The computer also displays data object icons, each representing a logical combination of tables. While displaying the data sources and the data object icons, the computer detects a portion of an input on a table. In response, the computer generates a candidate data object icon corresponding to the table. The computer also detects another portion of the input on the candidate data object icon. In response, the computer moves the candidate object icon towards the data object icons, while providing a visual cue connecting the candidate object icon to a neighboring data object icon. The computer detects yet another portion of the input, and, in response, displays a connection between the candidate object icon and the neighboring data object icon, and updates the tree of the one or more data object icons to include the candidate data object icon.

Abstract: In implementations of systems for generating indications of perceptual linear regions of vector objects, a computing device implements a linear region system to receive input data describing an outline of a vector object. The linear region system determines differences between sequential points of the outline and linear approximation lines projected through the sequential points. The linear region system combines a first linear group and a second linear group of the linear groups into a combined group based on a linearity constraint. An indication of a perceptual linear region of the vector object is generated for display in a user interface based on the combined group.

Abstract: In some implementations, a computing device can perform multi-display alignment through observed user interactions. The computing device can receive user input aligning a first alignment object on a first display device with a second alignment object on a second display device. The computing device can align the display buffers for each display device based on the positions of the alignment objects in each display buffer corresponding to each display device. The computing device can align display buffers based on observed movements of graphical objects between multiple display devices. When display buffers corresponding to the display devices are misaligned, the user may correct the path of a graphical object when moving the graphical object between display devices. The computing device can detect the correction and align the display buffers of the display devices so that graphical objects are presented at the appropriate locations when moved between the display devices.

Abstract: A robotic motion control method provided by the present disclosure includes: obtaining a position and orientation of a starting point where the robot is currently located through a positioning sensor, and obtaining a position and orientation of a preset target point where the robot is moved to; determining an arc path and a straight path of the robot according to the position and orientation of the starting point, the position and orientation of the preset target point, and a preset arc radius; and moving the robot to the preset target point according to the determined arc path and straight path. Because there are only pure circular motion and pure linear motion which are simple during the movement of the robot, it is beneficial to improve the precision of the motion control of the robot and enable the robot to reach the target position in a reliable manner.

Abstract: A programmatic arbitrary distribution of items in a modeling system may be provided. To perform the distribution, a surface may be received, and a point count of application points associated with locations on the surface may be determined. A density map may be applied over the surface to assign a density to portions of the surface for the point count. Application points are then assigned to locations on the surface according to the density map and a scattering function of the point count, where the scattering function is based on one or more repulsion forces between neighboring points. The one or more repulsion forces are treated as pushing each of the neighboring point apart. Thereafter, the surface may be provided having the application points scattered across the surface based on the one or more repulsion forces.

Abstract: Graphical interactive model selection is provided. A response variable vector for each value of a group variable and an explanatory variable vector are defined. A wavelet function is fit to the explanatory variable vector paired with the response variable vector defined for each value of the group variable. Each fit wavelet function defines coefficients for each value of the group variable. A curve is presented for each value of the group variable and is defined by the plurality of coefficients of an associated fit wavelet function. An indicator is received of a request to perform functional analysis using the coefficients for each value of the of the group variable based on a predefined factor variable. A model is trained using the coefficients for each value of the group variable and a factor variable value associated with each observation vector of each plurality of observation vectors as a model effect.

Abstract: A method for smoothing coordinates, a touch chip, and an electronic terminal are provided. The method includes: acquiring touch point coordinates of a current data frame on a touch screen, and touch point coordinates of N consecutive data frames prior to the current data frame, the N is a natural number greater than or equal to 2; performing a Bessel interpolation iteration on the touch point coordinates of N+1 data frames including the current data frame with the touch point coordinates of the N+1 data frames as initial iteration values; and acquiring an iteration result of the Bessel interpolation iteration, and implementing coordinate smoothing according to the iteration result. According to the embodiments of the present disclosure, the cost of smoothing coordinates is lowered, and the effect of smoothing coordinates is improved.

Abstract: An image generator generates images of a set of virtual fibers and effects thereon by processing representations of the set of fibers and computing representation of a virtual surface for a fiber clump in the set of virtual fibers from an artist parameter representing a desired artist effect, computing correlations of the vertices from a set of vertices based on associations of the vertices corresponding to the artist parameter, computing a set of relevant vertices using the correlations of the vertices, computing orthogonal gradients to produce a plurality of gradients using a selected vertex and the set of relevant vertices for the fiber clump, and computing the virtual surface of the fiber clump from the plurality of gradients.

Abstract: Artificial intelligence is introduced into an electronic meeting context to perform various tasks before, during, and/or after electronic meetings. The tasks may include a wide variety of tasks, such as agenda creation, participant selection, real-time meeting management, meeting content supplementation, and post-meeting processing. The artificial intelligence may analyze a wide variety of data such as data pertaining to other electronic meetings, data pertaining to organizations and users, and other general information pertaining to any topic. Capability is also provided to create, manage, and enforce meeting rules templates that specify requirements and constraints for various aspects of electronic meetings.

Abstract: An image scaling method based on a linear extension/contraction mode, includes step I: compressing an original image matrix composed of image pixels in a row by row manner with a Linearlization or OptimalPLR compression method to obtain a line segment segmentation form; step II: lengthening the line segments under Policy I or shortening the line segments under Policy II by resampling at a upscaling or downscaling factor, to obtain an upscaled or downscaled image in the row direction; and step III: upscaling the data upscaled in the row direction in the step II in a column by column manner through the process in the step II, to obtain an image upscaled in the column direction. The method which is an image scaling technique directly based on PLA for data compression, not only can compress static image data, but also can compress image data of dynamic data streams.

Abstract: The present invention provides a method that includes accepting a plurality of positional data with corresponding times of the motion, determining one or more continuous positional functions that together represent an approximation of path of the positional data, and determining, for each positional function, one or more time functions that together represent an approximation of the times for the positional data corresponding to the positional functions.

Abstract: Methods and apparatuses for compressing drive curves for scanning devices and corresponding computer programs are provided. In this case, a drive curve is decomposed into segments. Segments which are not yet present in a library are stored in the library. Moreover, for each segment a pointer to a corresponding segment in the library is stored in a list.

Abstract: Techniques are disclosed for tracing a vector image over at least a part of a raster image. One or more edges of the raster image (e.g., bitmap or photograph) are identified, and an edge model is generated. The edge model is a vector image including a plurality of Bezier curves that overlap with the edges of the raster image. One or more user inputs are received, which identify a first and second path point on the edge model. A subset of the plurality of Bezier curves that are between the first and second path points and on the edge model are selected. The subset of the plurality of Bezier curves are displayed, without displaying Bezier curves that are not within the subset. In an example, the subset of the Bezier curves traces edges of a section of the raster image between the first and second path points.

Abstract: The present disclosure relates to systems, methods, and non-transitory computer readable media for removing an anchor point from a Bezier spline while preserving the shape of the Bezier spline. For example, the disclosed systems can replace adjacent input segments of an initial Bezier spline that are connected at an anchor point with a new contiguous segment that does not include an anchor point and that spans the portion of the spline covered by the adjacent segments. The disclosed systems can utilize an objective function to determine tangent vectors that indicate locations of control points for generating the new segment to replace the adjacent segments. In addition, the disclosed systems can generate a modified Bezier spline that includes the new segment in place of the adjacent segments of the initial Bezier spline.

Abstract: Computer-implemented methods and apparatus are provided for annotating digital images of line plots with ground truth labels. For each digital image, such a method includes supplying image data defining the image of a line plot to a machine-learning model trained to generate a set of control points defining a spline corresponding to the line plot. The method further comprises displaying the spline, and the set of control points, superimposed on the image in a graphical user interface and, in response to user manipulation via the graphical user interface of one or more control points, dynamically adjusting the displayed spline in accordance with manipulated control points whereby the displayed spline can be adjusted for conformity with the line plot. The set of control points for the adjusted spline is then stored as a ground truth label for the image.

Abstract: It is an object of the present invention to provide a technique capable of reducing a difference between a three-dimensional shape represented by map data, using approximation, and a real three-dimensional shape. A map data generating apparatus is a map data generating apparatus capable of generating map data representing a three-dimensional shape, using approximation, the map data generating apparatus including: an acquisition part that acquires a shape point sequence indicating the three-dimensional shape, and a control part that generates an arc passing three object points, based on the three object points in the shape point sequence acquired by the acquisition part, and determines whether an approximation division point that should not be approximated in the three-dimensional shape is included in the three object points, based on the arc.

Abstract: An activity recognition method includes steps of obtaining a plurality of embedded feature values, converting a data set obtained by at least one sensor into an activity feature value, comparing the activity feature value with the embedded feature values to generate a comparison result, and performing an activity recognition according to the comparison result. Therefore, the present invention achieves the advantages of precisely recognizing activities.

Abstract: A method for rendering an object is provided. The method may include obtaining tile information associated with a region of interest (ROI) from a database. The method may include extracting, from the tile information, one or more links along a center line of an overpass in the ROI. The method may include determining at least one intersection of the one or more links. The method may include performing a topology analysis on the one or more links and the at least one intersection to generate a link chain of the one or more links. The method may include constructing a model of the overpass based on the link chain of the one or more links. The method may further include rendering the model of the overpass.

Abstract: Implementations of the present disclosure relate to methods, systems, and computer program products for multimedia object management. In one implementation, a computer-implemented method is disclosed and the method may be implemented by one or more processors in a computer. In the method, a graphic pattern indicating a request for searching in a repository for at least one target object may be received. A search condition may be obtained from the received graphic pattern by a graphical analysis. Based on an association model indicating associations between the search condition and at least one feature of one or more objects in the repository, at least one target object may be found according to the obtained search condition. In other implementations, a computer-implemented system and a computer program product for searching for at least one target object is disclosed.

Abstract: In processing to thicken a white thin line, the application range thereof is controlled to as to prevent a white thin line not intended by a user from being thickened. The thickening processing is performed for a line that has a density less than or equal to a predetermined density and includes a pixel having attribute information of a drawing object; and not performed for a line that has a density less than or equal to the predetermined density and includes a pixel not having attribute information of the drawing object.

Abstract: Stroke operation prediction techniques and systems for three-dimensional digital content are described. In one example, stroke operation data is received that describes a stroke operation input via a user interface as part of the three-dimensional digital content. A cycle is generated that defines a closed path within the three-dimensional digital content based on the input stroke operation and at least one other stroke operation in the user interface. A surface is constructed based on the generated cycle. A predicted stroke operation is generated based at least in part on the constructed surface. The predicted stroke operation is then output in real time in the user interface as part of the three-dimensional digital content as the stroke operation data is received.

Abstract: Techniques for intuitive modifications of digital graphics in a digital media environment are described. For example, a digital graphics creation system accesses vector artwork including a vector object, such as a Bezier curve. The digital graphics creation system receives user inputs, including a user input defining handles on the vector object and a user input interacting with the handles indicating a desired change to the vector object. The digital graphics creation system modifies the vector artwork, including the vector object, by accounting for topology of the vector object and maintaining connections between connected segments of the vector object. The digital graphics creation system outputs the modified vector artwork, including the vector object, such as in a user interface.

Abstract: Systems and techniques are described herein for generating a triangle mesh for an image represented by curves (e.g., Bezier segments). An outline of an image is determined and reduced to a set of connected polylines that are efficiently represented in an edge list. A triangle mesh is generated based on the edge list, rather than by directly sampling the curves of the image and using the samples as vertices of triangles. Thus, the triangle mesh is generated with a number of triangles independent from a number of curves representing the image. Samples of the curves are bound to the triangle mesh by representing the samples with barycentric coordinates with respect to a triangle in the mesh. Hence, once a mesh is deformed, locations of the samples are determined from the barycentric coordinates and triangles in the deformed mesh, and used to reconstruct the curves of the deformed image.

Abstract: Photorealistic image stylization concerns transferring style of a reference photo to a content photo with the constraint that the stylized photo should remain photorealistic. Examples of styles include seasons (summer, winter, etc.), weather (sunny, rainy, foggy, etc.), lighting (daytime, nighttime, etc.). A photorealistic image stylization process includes a stylization step and a smoothing step. The stylization step transfers the style of the reference photo to the content photo. A photo style transfer neural network model receives a photorealistic content image and a photorealistic style image and generates an intermediate stylized photorealistic image that includes the content of the content image modified according to the style image. A smoothing function receives the intermediate stylized photorealistic image and pixel similarity data and generates the stylized photorealistic image, ensuring spatially consistent stylizations.

Abstract: Techniques of generating curves in drawing applications involve generating rational interpolating curves in response input points being specified on a display such that the rational interpolating curves have an adjustable sharpness at each of the input points. Along these lines, a user specifies control points of a curve in a drawing application by, e.g., moving these control points on a display. In response, a computer running the drawing application generates a rational interpolating curve that intersects the input points such that the curvature of each curve at its input point is a local maximum and such that the user's sharpness values change the roundness of the curve around corresponding control points.

Abstract: A numerical controller that creates a tool path from a plurality of command points includes: a command point sequence acquisition unit that acquires an existing command point sequence; a command point creating unit that creates at least one additional command point, based on the existing command point sequence; and an interpolation processing unit that interpolates the existing command point sequence and the additional command point to create the tool path. The command point creating unit outputs, as the additional command point, an intersection point Q1 between an arc C1 passing through consecutive three command points, P0, P1 and P2, in the existing command point sequence and a perpendicular bisector of a line segment whose end points are P1 and P2.

Abstract: This invention relates to as animation authoring system and an animation authoring method, to enable beginners to produce a three-dimensional animation easily and to solve input ambiguity problem in the three-dimensional environment. The animation authoring method according to the invention comprises the steps of: (a) receiving a plane route of an object on a predetermined reference plane from a user; (b) creating a motion window formed along the plane route and having a predetermined angle to the reference plane to receive motion information of the object on the motion window from the user; and (c) implementing an animation according to the received motion information.

Abstract: A makeup part generating apparatus includes a drawing receiver that receives a drawing operation of a makeup part image that is to be overlaid on a facial image, an information acquiring unit that acquires, at each time point in a process of the drawing operation, a progress image that is an image drawn by the time point, and a drawing technique used at the time point, and an information processor that records and outputs makeup part information including, in a time-series manner, image information indicating the progress image, and technique information indicating at least one of the drawing technique and a makeup technique that is an application technique of a cosmetic corresponding to the drawing technique.

Abstract: A method of selection of an object in an environment including a plurality of real and/or virtual objects is described. The environment being displayed to a user through a display device includes an assignment of a gesture path to each object of the plurality of objects and the gesture path includes a series of gestures to be performed by the user to select the object.

Abstract: A method and system for writing trajectory synchronization among multiple clients are disclosed. The method includes: receiving (S10) segmented writing trajectory data of a real-time writing trajectory transmitted in segments by each transmitting end; forwarding (S20) each segment of the segmented writing trajectory data to each receiving end in real time respectively, where the segmented writing trajectory data is received asynchronously and restored into a real-time writing trajectory by each receiving end; receiving (S30) complete writing trajectory data of a complete writing input transmitted by each transmitting end; and forwarding (S40) the complete writing trajectory data transmitted by each transmitting end to each receiving end, where the complete writing trajectory data is received synchronously and inserted into an interface for display by each receiving end.

Abstract: Systems and methods are provided for improving the latency for display of ink during user creation of ink content with an object, such as a stylus, mouse, finger (or other touch input), or other drawing device. In order to reduce or minimize the time for display of ink content created by a user, aspects of the technology described herein generate predictive wet ink that can be displayed with actual wet ink. The predictive wet ink is calculated by extending an active ink segment a predictive distance. The predictive distance is intended to be a distance between a termination ink point for an active wet ink segment and a tip of the writing object. In one aspect, the predictive distance is calculated by determining the current latency period on a touch device and the velocity of the writing object.

Abstract: A display data correction apparatus is provided with: a control circuit responsive to an input gray-level value for initially providing first to N-th control points (N?3) defined in a coordinate system in which a first coordinate axis is associated with the input gray-level value and a second coordinate axis is associated with an output gray-level value to be calculated for the input gray-level value; and a processing circuit obtaining an output gray-level value by repeating an update operation in which the first to N-th control points are updated. The degree (N?1) Bezier curve is used as an approximated curve of the gamma curve. The output gray-level value is finally obtained as the coordinate value of a specific point in the degree (N?1) Bezier curve along the second coordinate axis, where the specific point has the coordinate value closest to the input gray-level value along the first coordinate axis.

Abstract: A numerical control device is a numerical control device that controls a machine tool including a plurality of axes, and includes a reading unit that reads a machining program for machining a workpiece, and when the machining program read by the reading unit is a machining program for simultaneously operating five or more axes of the plurality of axes, controls operation of the five or more axes to be simultaneously operated in the machining program by dividing the operation into a plurality of sets of operation of four or less axes.

Abstract: The formulation of multiple physical flowpaths that fit within a physical space. The formation of physical flowpaths is done by a 3-D printer using a representation of that flowpath that is within a utility flowpath model. The flowpaths are represented in the utility flowpath model so that there is high certainty that the respective physical flowpaths will actual fit into a physical space even if space is limited. Furthermore, the 3-D printing of those physical flowpaths ensures high precision in formulating the physical flowpaths to match the utility flowpath representation.

Abstract: There is provided a technique for arranging characters along a road to improve appearance and readability. A map display system arranges a plurality of characters along a road line which is a polyline representing a road shape, and includes an arranging part that arranges, at a connecting portion where a first road line segment and a second road line segment forming the road line are connected, a third character in a third direction between a first character arranged in a first direction and a second character arranged in a second direction, the first direction being a direction for the first road line segment, the second direction being a direction for the second road line segment, and the third direction being a direction between the first direction and the second direction; and a display control part that displays the road line and the plurality of characters on a display part.

Abstract: Methods and apparatus reduce data transmission in a wireless client-server navigation system. A request for data representative of a map-related feature is received at a server from a mobile unit. Data describing the feature is obtained in the form of line segments interconnecting points having coordinates. An operation is performed on the data to generate data representing the feature in a data-reduced format, and the reduced-format data is forwarded to the mobile unit. The operation may include receiving map data; partitioning the map into tiles; designating a reference point within each tile; representing data points as offsets from the reference points. Alternatively, the operation may include approximating the feature with a curve. In a further alternative embodiment, the operation may include removing one or more of the points such that the feature is represented with line segments interconnecting the remaining points.

Abstract: An image synthesizer for a driver assisting system includes a receiving module and a combining module. The driver assisting system includes a first camera configured to capture a first image from a first scene and a second camera configured to capture a second image from a second scene, wherein the first scene and the second scene partly overlap in an overlapping region. The receiving module configured to receive the first image from the first camera and the second image from the second camera. The combining module is configured to combine the first image and the second image in the overlapping region using a binary mask.

Abstract: Systems and methods are described herein for controlling playback of a media asset using a touch screen. In some embodiments, a media guidance application may control media playback based on touch screen input positions that are stored before the user removes his finger from the touch screen. In some embodiments, the media guidance application may distinguish between intended touch screen inputs and jitter by analyzing the time it takes to perform a touch screen input, the speed/acceleration of an input, or the orientation of an input.

Abstract: Vector format based computer graphics tools have become very powerful tools allowing artists, designers etc. to mimic many artistic styles, exploit automated techniques, etc. and across different simulated physical media and digital media. However, hand-drawing and sketching in vector format graphics is unnatural and a user's strokes rendered by software are generally unnatural and appear artificial. In contrast to today's hand-drawing and sketching which requires significant training of and understanding by the user of complex vector graphics methods embodiments of the invention lower the barrier to accessing computer graphics applications for users in respect of making hand-drawing or sketching easier to perform. Accordingly, the inventors have established a direct vector-based hand-drawing/sketching entry format supporting any input methodology.

Abstract: Techniques for intuitive modifications of digital graphics in a digital media environment are described. For example, a digital graphics creation system accesses vector artwork including a vector object, such as a Bezier curve. The digital graphics creation system receives user inputs, including a user input defining handles on the vector object and a user input interacting with the handles indicating a desired change to the vector object. The digital graphics creation system modifies the vector artwork, including the vector object, by accounting for topology of the vector object and maintaining connections between connected segments of the vector object. The digital graphics creation system outputs the modified vector artwork, including the vector object, such as in a user interface.

Abstract: In one embodiment, a computing system may determine a pixel area in a display coordinate system and project it into a three-dimensional coordinate system to determine a projected area. Based on the projected area, the system may determine a portion of a data structure that contains an analytical definition of a glyph in a two-dimensional coordinate system. The system may access a portion of the analytical definition associated with the selected portion of the data structure, the portion of the analytical definition defining one or more areas of the glyph. The system may project the portion of the analytical definition into the display coordinate system and compute a coverage proportion of the pixel area that overlaps with one or more areas defined by the projected portion of the analytical definition. Based on the coverage, the system may determine a color for the pixel and render the glyph.

Abstract: A method of analyzing a curved surface is provided. The method includes obtaining a first data point set including data points representative of a distance between points along the curved surface and a reference axis, determining outlier data points in the first data point set, extracting the outlier data points from the first data point set, thereby defining a second data point set. The method also includes determining a fitted curve for the second data point set, wherein the fitted curve defines an approximate true curve of the curved surface.

Abstract: A method of visually interacting with an electronically stored document having a plurality of visual objects. The method includes accessing the document that includes a closed region characterized by an open area boundary surrounding an open area. The method further includes displaying the document on a display. The method further includes receiving a user input of a region of interest within the document and in the open area. The method further includes iteratively, in a time interval of multiple segments, dynamically displaying a fill area in each of the multiple time segments. The fill area is defined by outwardly expanding vertices from the region of interest and bounded by an expanding fill perimeter limited by the open area boundary. The fill area is coextensive with the open area upon the fill perimeter coinciding with the open area boundary.