Abstract: Provided is a method for creating a 3-D curved surface by using corresponding curves in a plurality of images. The method includes performing an NURBS fitting curve with respect to one image in a plurality of images having camera calibration and extracted camera parameter by using control points designated in a curve characterizing a subject shape. When the curve fitting is performed with respect to the curve that commonly exists in more than two images, a 3-D curve is created by using a camera calibration information, or a 3-D curved surface is created by creating a plurality of 3-D curves or straight lines. Therefore, a 3-D curved surface model can be easily and quickly created by simplifying a complex modeling process for an actual object modeling into an actual image-based modeling process.

Abstract: An apparatus and method for rendering a smooth circular point using polygons on a computer graphics display. The circular point is approximated by a polygon and the selection of the polygon depends on the diameter of the point. The polygon is enclosed in a bounding area that is divided into a plurality of tiles. The tiles are classified into different sections depending on their location relative to the center of the point. The tiles in each section are processed according to an algorithm to generate a mask that is used to render the circular point.

Abstract: When a fixed polygonal plane patch is called a polygonal plane patch of level 0 and when each vertex of such polygonal plane patch is called a shape composition point of level 0, a normal line of level 0 is set on each shape composition point of level 0, and each normal line of level 0 is decomposed on an equivalent tangent plane to the normal line of level 0. Moreover, a tangent line of level 0 is set by a decomposition in a direction equal to or in the vicinity of the edge of the polygonal plane patch of level 0; and based upon two tangent lines of level 0, a normal line is set on a shape composition point and on a shape composition point of level 1. A plane shape is formed by repeated controls of the above one after another.

Abstract: The tessellating elements are in sets and comprise (a) at least one curve element comprising a semi-circle of diameter x; (b) at least one wave element having a perimeter which is three-sided, including a first side which is straight and of length x, a second side which comprises a concave curve forming a semi-circle of diameter x, and a third side which comprises a convex curve forming a quarter circle of radius x; (c) at least one corner element having a perimeter which is three-sided, including two sides of length x at right angles to one another and a third side which is concave and comprises a quarter circle of radius x; and, optionally, (d) one or more lozenge elements having at least one shaped face with a perimeter comprising two arcuate edges, each said arcuate edge having a radius of curvature x. The elements have a wide range of applications, from building tiles and children's toys, to screen-filling of computer screens or the like.

Abstract: Methods and apparatus for facilitating detection of a presence or an absence of at least one underground facility within a dig area. Source data representing one or more input images of a geographic area including the dig area is electronically received at a first user location, which may be remote from the dig area. The source data is processed so as to display at least a portion of the input image(s) on a display device at the first user location. One or more indicators are added to the displayed input image(s), via a user input device associated with the display device, to provide at least one indication of the dig area and thereby generate a marked-up digital image. In one example, the indicator(s) is/are markings that indicate a point, line, and/or path. The indicator(s) may provide a reference for a locate operation or an area of planned excavation.

Abstract: A method is provided for converting a template creation input corresponding to an image into a sketch template. This method may include minimizing stroke data cost and converting the resulting contour into a curve approximation based around landmark points. After the sketch template is created, it may be personalized using various styles which alter the parameters of the curve approximation and/or the landmark points. The sketch template may be used to practice drawing skills. A tracing algorithm may provide feedback as to how far a tracing line deviates from the sketch template, and may also provide overall feedback for all the tracing lines combined, relating to factors such as closeness to the sketch template, speed, and completion percentage.

Abstract: A method, apparatus, and computer readable storage medium provides the ability to stabilize a series of two or more still images (i.e., a clip). The clip of image data is obtained. The clip is then analyzed to produce a set of source curves that represent a global movement detected in the clip. Each of the source curves is filtered to compute result curves. The source and result curves are then exposed and displayed to the user who may modify/tweak the curves as desired. Automatically, without additional user input, and without reanalyzing the original clip, the result curves are recomputed based on the user's changes. The original clip is then transformed into a result clip/series based on the source and result curves.

Abstract: This specification describes technologies relating to creation of shadow effects in a two-dimensional (2D) imaging space. In general, one aspect of the subject matter described in this specification can be embodied in a method that includes obtaining shadow orientation and length information of a source object in a 2D imaging space. The method also includes creating a shadow effect in the 2D imaging space based on the shadow orientation and length information. The shadow effect resembles a shadow falling on a perceptual three-dimensional (3D) background in the 2D imaging space. Other embodiments of this aspect include corresponding systems, apparatus, and computer program products.

Abstract: A method is provided for approximating a quadratic Bezier curve represented by two anchor points and a control point that are fixed-point binary numbers. If a first flatness of a line formed between the two anchor points of the Bezier curve is less than a threshold, the method includes replacing the Bezier curve with an edge between the two anchor points. If the first flatness is not less than the threshold, the method includes subdividing the Bezier curve into halves and determining a second flatness of one of the halves. The first flatness is approximated by a triangular area formed by the two anchor points and the control point, and the triangular area is approximated by multiplication and subtraction operations. The second flatness of the half is approximated as the triangular area divided by 8, where the division by 8 is determined by shifting 3 bits to the right.

Abstract: The advantageous embodiments provide a computer implemented method, apparatus, and computer program product for constructing a computer aided design model. User input is received that contains a callback function and a required accuracy. The callback function prescribes a procedurally defined geometry and the required accuracy specifies the degree of accuracy needed for the computer aided design model. The callback function is sampled at a number of points to form sampled points and a candidate curve is constructed that approaches the sampled points. A determination is made as to whether the candidate curve meets the required accuracy.

Abstract: A method of rendering an image described by a list of graphical objects includes the steps of assigning objects in the list to at least one of a first set of objects and a second set of objects, and rendering the first set of objects to an image store using a first rendering method that determines whether a portion of an object of the first set contributes to a rendered output of the first set of objects and, if so, the first rendering method renders each pixel of the portion in sequence. The second set of objects to the image store are rendered using a second rendering method that renders each object in the second set in sequence and independently of the other objects in the second set.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: Monitoring events triggered by a computer network. Each event being provided with attribute values allocated to a given set of attributes, and providing an event display, determining a primary attribute and a corresponding display label of the events selected from the given set of attributes presented with attribute values on a cross plot, providing a pattern algorithm to detect whether an arrived event is part of a given pattern, providing a mapping algorithm to map attribute values on the cross plot, allocating a second display label to the events indicating the attributes uncovered as part of the given pattern, plotting events arriving and including an attribute value allocated to a primary attribute into the cross plot, and plotting events arriving within the time period and detected by the pattern algorithm as part of the given pattern into the cross plot with the second display label indicating the given pattern.

Abstract: A pen-based system allows users, such as artists, graphic designers and illustrators, and the like, to create accurate curve models by sketching. A tool set implemented in software that runs on a computer system combines paper sketch metaphors and a minimalist gesture set. This tool set provides an environment where the artists can focus on the creative task at hand rather than the details of operating software. A pen-based drawing method and system allows users to create and edit three dimensional (“3D”) objects by sketching.

Abstract: In the cabling work aiding system, the RFID reader reads the RFID attached to at least one of the terminal, its terminal block, and cable member. A cabling work terminal device is connected to the RFID reader. The device is comprised of: a data base that records a template connection diagram containing the terminal-side RFID region constituted by RFID data as to the terminal and a cable-side RFID region constituted by RFID data as to the cable member; a relating part that relates the RFID read by the RFID reader to the terminal-side RIFD region and the cable-side RIFD region defined in the template connection diagram; a terminal-cable member correspondence table preparing part that prepares a correspondence table for leading correspondence between the RFID data as to the terminal and RFID data as to cable member from correspondence between the terminal-side RIFD region and the cable-side RFID related by the RFID read by the RFID reader.

Abstract: A client device receives a user interface event corresponding to a spline curve associated with an object displayed on a mobile device. The user interface triggers creation of a new spline curve based on computation of a new spline tangent associated with the spline curve and phase space-based dynamics of a new state. A scene graph having state information associated with the new state is maintained. A rendering event triggers repainting of the object associated with the spline curve suing the scene graph.

Abstract: Exemplary apparatus, method, and system embodiments provide for accelerated hardware processing of an action script for a graphical image for visual display. An exemplary apparatus comprises: a first memory to store corresponding data; a first processor to separate the action script from other data; and a second processor to convert a plurality of descriptive elements of the action script into a plurality of operational codes, and to perform an operation corresponding to an operational code of the plurality of operational codes using the corresponding data to generate pixel data for the graphical image. In exemplary embodiments the second processor further is to parse the action script into the plurality of descriptive elements and the corresponding data, and to extract data from the action script and to store the extracted data in the first memory as a plurality of control words having the corresponding data in predetermined fields.

Abstract: Exemplary apparatus, method, and system embodiments provide for processing an action script for a graphical image for visual display. An exemplary apparatus comprises: a first memory; first circuitry configured to convert a plurality of descriptive elements of the action script into a plurality of operational codes; and second circuitry configured to execute the plurality of operational codes using corresponding data stored in the first memory to generate pixel data for the graphical image. Exemplary embodiments may further include third circuitry configured to parse the action script into the plurality of descriptive elements and the corresponding data, and fourth circuitry configured to extract data from the action script and to store the extracted data in the first memory as a plurality of control words having the corresponding data in predetermined fields.

Abstract: This disclosure describes techniques for removing vertex points during two-dimensional (2D) graphics rendering using three-dimensional (3D) graphics hardware. In accordance with the described techniques one or more vertex points may be removed during 2D graphics rendering using 3D graphics hardware. For example, the techniques may remove redundant vertex points in the display coordinate space by discarding vertex points that have the substantially same positional coordinates in the display coordinate space as a previous vertex point. Alternatively or additionally, the techniques may remove excess vertex points that lie in a straight line. Removing the redundant vertex points or vertex points that lie in a straight line allow for more efficient utilization of the hardware resources of the GPU and increase the speed at which the GPU renders the image for display.

Abstract: A method for drawing pie charts illustrating comparative data on the display of a client computer in a client-server environment with horizontal parallel lines each having a height of one pixel. A circular or elliptical pie is first defined in an array of endpoints of a set of horizontal lines from which the pie is constructed. Each slice of the pie is assigned a start angle and a stop angle as a function of the datum that it represents and its proximity to other slices. Pixels on the horizontal lines forming the pie are then tested to define segments of the horizontal lines for inclusion in the slices. The pixels of each line segment are illuminated on the display to form an image of a pie with each slice proportional in area to its respective datum.

Abstract: A method of identifying semantic units in an electronic document includes the steps of: providing an electronic document being described in a page description language, the document having at least one page having a plurality of text fragments, each text fragment including a plurality of glyphs that have not been identified as semantic units, the document further including geometric information and page description language parameters; determining strips of at least one glyph by comparing the geometric position of subsequent glyphs; determining zones of at least one strip wherein a zone is defined by the combined area of strips, the geometrical areas of which overlap with each other; determining a boundary between two semantic units in a zone based on the geometric properties of the glyphs; sorting the identified semantic units in the zone in a sorted list; and, combining subsequent semantic units in the sorted list according to geometric considerations.

Abstract: An input stroked curve 1 that is received by a graphics processing system can be rendering using at least two, and preferably more, rendering processes that are available for use by the system. The process or processes that are used for rendering the received stroked curve 1 are selected based on whether the input stroked curve comprises one or more regions having a particular characteristic or characteristics, e.g. whether the input stroked curve 1 comprises one or more self-overlapping regions. Preferably, the at least two rendering processes are each capable of correctly rendering different sets of stroked curves. Furthermore, the least two rendering process preferably differ in the processing burden that they place on the graphics processing system.

Abstract: When rendering a stroked curve for display in a graphics processing system, an input stroked curve 1 defined in user space 2 is received by the system. The portion of a canonical space 5 that corresponds to the received stroked curve 1 is determined by determining the portion of a canonical curve 12 defined in the canonical space 5 that corresponds to the received stroked curve 1. Then, for each of a plurality of sampling points within one or more primitives 4 that are generated to cover the received stroked curve 1? following its projection into surface space 3, it is determined whether a corresponding location in canonical space 5 (to the sampling point in surface space 3) is within the portion of the canonical space that corresponds to the received stroked curve, e.g. by looking up suitable information that has been stored (in advance) in one or more graphics textures. Data for rendering the received stroked curve 1 (e.g.

Abstract: A smooth curve is represented in a graphics texture by setting the texels that are inside the curve 1 to a value greater than a predetermined threshold value and the texels that are outside the curve 1 to a value less than the threshold value (or vice-versa). The texture value returned for a sampled position can thus be used to determine whether the sampled position should be treated as being inside the curve 1 or not. The texture is optimised for sampling using bi-linear filtering.

Abstract: A pen-based system allows users, such as artists, graphic designers and illustrators, and the like, to create accurate curve models by sketching. A tool set implemented in software that runs on a computer system combines paper sketch metaphors and a minimalist gesture set. This tool set provides an environment where the artists can focus on the creative task at hand rather than the details of operating software. A pen-based drawing method and system allows users to create and edit three dimensional (“3D”) objects by sketching.

Abstract: Apparatus and methods of generating a curved baseline for a map labeling include receiving a polyline P={p1,p2, . . . ,pn} of n points, generating a supporting polyline Q={q1,q2, . . . , qm} (m?n) of m points at an expected distance d between polyline P and a curved base line L. A predetermined number of B-Spline points is generated based upon supporting polyline Q. The B-Spline points are then connected to form a curved baseline L for displaying a label.

Abstract: Compact and accurate piecewise parametric representations of implicit curves may be achieved by iteratively selecting ranges of parameterizing regions and testing each for satisfying an intervalized super convergence test. In one aspect, the implicit curves is represented as a compact form of one or more representations of such convergence regions. For memory and bandwidth constrained applications, starting points of convergence regions may not be stored but instead calculated at runtime prior to rendering a point on the implicit curve. Furthermore, not all endpoints relevant convergence regions of a selected implicit curve need be stored. Instead, based on at least one endpoint, the other endpoints can be derived via Newton iterations. To further reduce memory and bandwidth costs, coordinates can be stored in a quantized format and the points reflecting floating point accuracy can be derived at runtime again by Newton iteration.

Abstract: A graphics processing unit implemented method for fiber tract mapping from diffusion tensor magnetic resonance imaging data includes providing a diffusion tensor magnetic resonance brain image volume, initializing a set of fiber positions in a 3D set of points, fiber displacements, and a posterior distribution for an updated fiber displacement in terms of the initial displacements and diffusion tensors, randomly sampling a set of updated fiber displacements from said posterior distribution, computing a new set of fiber positions from said initial fiber positions and said updated fiber displacements, wherein a fiber path comprises a set of fiber points connected by successive fiber displacements, accumulating connectivity values in each point of said 3D set of points by additive alpha-blending a scaled value if a fiber path has passed through a point and adding zero if not, and rendering said connectivity values.

Abstract: Simulating dynamics (e.g., physical effects of inertia, forces, wind) on strands (e.g., hair) during computer based animation requires quick and accurate approximations of mathematical curves. Each strand is initially represented as a B-spline curve. Line segments approximating the curve are created by using affine combinations based on the curve's control vertices. Dynamics simulation is performed on the line segment approximation. Once an approximated strand is simulated, it is converted back into a B-spine curve representation for downstream processes, such as rendering. The rendering process displays the simulated strand to the animator.

Abstract: A method, apparatus, and article of manufacture provide the ability to display a stroked fill for an object. A computer-generated rendering is obtained that consists of vector geometry. Closed geometry is obtained in the computer-generated rendering. Lastly, a fill is automatically created. The fill consists of a series of two or more curves, wherein each curve in the series crosses an interior of the closed geometry.

Abstract: A method of animating feather elements includes: specifying initial positions for a skin surface and for feather elements; specifying positions for the skin surface at an animated time; determining a feather-ordering sequence for placing the feather elements on the skin surface; determining positions for skirt elements that provide spatial extensions for the skin surface at the animated time; determining positions for feather-proxy elements that provide spatial extensions for the feather elements at the animated time; and determining positions for the feather elements at the animated time by extracting the feather elements from the feather-proxy elements. The feather-proxy elements are determined from the skirt elements according to the feather-ordering sequence, and the feather-proxy elements satisfy a separation criterion for avoiding intersections between the feather-proxy elements.

Abstract: A mobile device and method of editing an image in the mobile device are disclosed. The method of editing an image includes dividing the image into an uncertain region, an object region, and a background region along the boundary line which is input through a touch interface and displayed on the image, determining a last object region by determining the uncertain region as one of the object region and the background region through color comparison of the uncertain region with neighboring blocks, and post-correcting an error included in the last object region.

Abstract: A technique for editing is disclosed. The technique includes generating a path definition for a path, generating a plurality of subpath definitions of subpaths of the path based on an intersection of the path, associating the subpath definitions with the path definition, modifying the intersection of the path using an editing tool, and generating a plurality of modified subpath definitions of subpaths of the path based on the modified intersection of the path.

Abstract: Disclosed herein is an apparatus and method for deforming a curved surface using a three-dimensional target curve. The curved surface deformation apparatus of the present invention includes object curved surface selection means, sample vertex extraction means, basis function calculation means, target curve input means, control point variation calculation means, and object curved surface deformation means. The object curved surface selection means selects all or part of the curved surface of the NURBS model. The sample vertex extraction means extracts a plurality of vertexes from the object curved surface. The basis function calculation means calculates a basis function of the object curved surface. The target curve input means inputs a target curve, composed of a plurality of target. The target curve projection means projects the target curve onto the object curved surface.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: The rendering parameters including the position coordinate, the color information and the transparency in a vector definition space are calculated for each pixel occupied by a curved surface model projected on a screen. Plural primitive data are generated and stored from the vector data. By judging whether the plural primitive data include the position coordinate or not, a rendering judgment variable is determined, and in the case where the rendering judgment variable is added an odd number of times, the raster data of the pixel corresponding to the position coordinate is generated based on the rendering parameters.

Abstract: Techniques for assigning a subpath attribute to a subpath in a drawing are disclosed. One technique includes editing the drawing to define a current path having a current subpath, matching a previous vertex in a previous path with a current vertex in the current path, and assigning a current subpath attribute to the current subpath based on the vertex match. Another technique includes editing the drawing to define a current path having a current subpath, comparing the current subpath with a previous subpath having a previous subpath attribute, and assigning a previous subpath attribute to the current subpath based on the comparison.

Abstract: An animation of a plurality of regions is provided to recap, in under a minute, a respective price action of each of a plurality of stocks over a course of a day. Each of the regions has a respective color that changes during the animation to recap, in under the minute, respective price changes of its respective one of the stocks over the course of the day.

Abstract: The present disclosure relates to a medical image processing method for manipulating a curve using a pointing device. The method includes: (a) accepting a first point on the curve specified by the pointing device; (b) reading a first time; (c) reading a second time when a point specified by the pointing device is moved to a second point from the first point; (d) determining a new curve based on a position of the second point, the second time, and the first time; (e) displaying said new curve; (f) reading a third time and a third point specified by the pointing device; (g) determining a further new curve based on a position of the third point, the third time, and the first time or the second time; and (h) displaying said further new curve.

Abstract: An electronic device for displaying a cursor with a trail is provided. The user may control electronic device operations by navigating the cursor on a display. To assist the user in identifying the current location of the cursor, the electronic device may define and display a trail indicating the prior positions of the cursor. For example, the electronic device may identify previous cursor positions and draw a curve, for example a spline, connecting the previous cursor positions and the current cursor position. The curve may have a varying width, thus forming a trail for which the wider portion is adjacent the cursor, and for which the narrower portion is adjacent the tip of the curve. The electronic device may instead or in addition modify the opacity of the curve, for example based on the instantaneous speed of the cursor. In some embodiments, other trail characteristics (e.g., size, color, opacity, path) may be modified based on prior cursor movements or cursor speed.

Abstract: In an image creating device (201) for creating an image viewably showing the distribution of an environment parameter of the environment around a character in a virtual space, a parameter acquiring unit (202) acquires an environment parameter of the environment around a character in each direction from the character, a reference curve setting unit (203) sets a reference curve surrounding the character, a trajectory point setting unit (204) sets a trajectory point in a position moved in a predetermined direction from each reference point in the reference curve by an amount of move associated with the value of the environment parameter at the reference point acquired in the direction from the character toward the reference point, and an image creating unit (205) creates an image showing the trajectory curve passing through the set trajectory points and the character viewed from the point of view placed in the virtual space.

Abstract: A method and apparatus is described to control velocity of object movement in a display device. A path is provided that the object will follow in the display. A plurality of handles are provided along the path and a velocity of the object is controlled by using the handles.

Abstract: A facility for evaluating a spreadsheet cell is described. The facility reads a function call stored in a spreadsheet cell. The function call specifies an arbitrary geometric path and an operation to be performed on the specified path. The facility performs the specified operation on the specified path, and attributes one or more values produced thereby as the evaluated value of the spreadsheet cell.

Abstract: Methods, systems, and apparatus, including computer program products, for processing graphical input. Input that specifies a path is received. The path includes multiple locations ordered along the path. A tracking zone is specified for each of the multiple locations based on the location and a previous location preceding the location along the path, where the tracking zone indicates a direction of the path at the location. A backward motion is detected between a first and a second location in the path if the first location's tracking zone overlaps with the second location's tracking zone. If a backward motion is detected between the first and second locations, a portion of the path connecting the first location to the second location can be replaced.

Abstract: In a method and system to extract data from handwritten information when the information is captured as sequences of strokes, vectors, or marks, temporal data is stored within the color or gray-scale encoding of pixel values within a bitmapped image. A bitmapped image is used to create a derived image suitable for data extraction and a method of analyzing the image, including the encoded temporal data, to yield an adjusted image that better reflects the intent of the person who created the handwriting. While the primary application of the invention is in processing handwritten responses to assessment items, the system and method can be advantageously used to extract data from or to improve the presentation of information from an electronic representation of temporal human marks in many applications. Additionally, the system and method can be advantageously used to store and process other types of data within a bitmapped image.

Abstract: Methods and apparatus implementing a technique for rendering a hinted character for display in grayscale on a grayscale output device in accordance with a hinted stem placement policy. In one embodiment, the policy is a black-edge policy, by which a hinted stem is moved so that at least one of the hinted stem edges aligns with an edge of a device cell (which corresponds to an output device pixel). In another embodiment, the policy is an unbiased-stems policy, by which a hinted stem is moved a minimum distance to have it span a minimum number of device cells.

Abstract: An image generating method comprises the steps of extracting elliptical shape parameters (specifying an elliptical shape), gradation pattern parameters (specifying a gradation pattern to be drawn in the elliptical shape) and drawing area parameters (specifying a drawing area) from an instruction for drawing an elliptical radial gradation, generating a transformation matrix for transforming the elliptical shape into a perfect circular shape based on the elliptical shape parameters, calculating an inverse matrix of the transformation matrix, transforming the gradation pattern parameters using the transformation matrix, transforming a first area containing the drawing area using the transformation matrix, drawing a radial gradation in the perfect circular shape in a second area containing the transformed first area based on the transformed gradation pattern parameters, and generating the elliptical radial gradation for the drawing area by inversely transforming the second area (in which the radial gradation has

Abstract: A system, method, and computer program for editing curves having bidirectional offset constraints, comprising selecting a collection of curves having a set of curve end points to perform an operation; and constraining a set of offset end points to said set of curve end points; whereby end constraints for offset curves are known, and appropriate means and computer-readable instructions.

Abstract: A system, method, and computer program for editing offsets, comprising connecting one or more input curves to a constraint system by constraints; offsetting output curves from said input curves by an operation; and creating a plurality of constraints among said input curves and said output curves; whereby editing said operation transforms said input curves and said output curves in a bidirectional manner, and appropriate means and computer-readable instructions.

Abstract: A system and method for rendering or facilitating the rendering of an attractive dashed path. A dashed path comprises a pattern of alternating stroke and gap segments; different dash patterns employ different lengths of stroke and gap segments and/or repeat the segments with different frequency. A curve to be drawn with a dashed pattern is divided at critical features (e.g., endpoints, vertices, corners, cusps, intersections) into curve sections. For each curve section, the optimal number of times to repeat a dash pattern (a sequence of segments) is determined, and the optimal length of each segment is calculated, based on constraints specified in the segment's definition. The curve section is then broken into sub-curves corresponding to individual segments. After all curve sections are processed, a trailer may be added to the path, and all sub-curves of all curve sections are rendered.