Abstract: Computer graphic method is used to transform a irregular hand drawing into a regular shape, such as a circuit, a rectangle, or a curve. First step of the computer graphic method is inputting the hand drawing to a computer. Then, identify at least one characteristic of the hand drawing, and creating a regular shape based on the characteristic. Finally, replacing the hand drawing with the regular shape.

Abstract: A method, apparatus, and article of manufacture provide the ability to update a filleted curve in a computer graphics application. A drawing having a first input curve and a second input curve is displayed. The first and second input curves are selected. A fillet curve is calculated, created, and displayed between the two input curves. A property of the first input curve is modified. Automatically, without additional user input, the fillet curve is recalculated based on the modified property. The recalculated fillet curve is displayed.

Abstract: A computer-implemented method for displaying animation splines includes receiving a source spline formed of paths between a sequence of knots to define a path between a first and a second end knot, where the knots are mapped to first second axes, identifying one or more pose knots and one or more timing knots between the first and the second end knot, thereafter producing a modified spline wherein second axes through at least one of the one or more pose knots are reversed, and displaying the modified spline evaluation and to allow adjustment of the source spline.

Abstract: A method for filling closed regions in a drawing using a region filling tool. Rather than selecting individual regions to fill, or filling based on style-by-layer techniques, the user creates a path or an area boundary to identify the regions to be filled. A graphics application may then fill each region that intersects the path or area boundary with a selected color or graphical style. In this manner, multiple regions in the drawing may be identified using one interaction with the region filling tool, allowing the user to more efficiently and intuitively fill regions in the drawing with the selected color or graphical style.

Abstract: A shape defined partially be a Bézier curve is rendered through a GPU-implemented technique which determines for various screen points which side of the curve the points lie on. This is done in the particular case of cubic Bézier curves for shapes defined by the Bézier control points of the curves. The type of the curve is identified through an analysis of an inflection point polynomial based on the curve. The curve is then projected to a canonical implicit form in a canonical texture space, allowing computation to be efficiently performed on a simple canonical form of the curve.

Abstract: Methods, systems, and apparatus, including computer program products, for presenting location information. A first geographic area in which a device is currently located is estimated using a first positioning system. A second geographic area in which the device is currently located is estimated using a second positioning system. A first map view including an indication of the first geographic area on the first map view is presented if the first geographic area is contained within the second geographic area. A second map view including an indication of the second geographic area is presented if the first geographic area is not contained within the second geographic area.

Abstract: The gamma curve generation method of the invention selects each set of three consecutive control points among multiple consecutive control points, forms a cubic curve passing through the selected three consecutive control points, and combines all formed cubic curves to generate a gamma curve. The selected three consecutive control points are set to a first control point, a second control point, and a third control point in a sequential order. Each cubic curve is formed to pass through the first control point, the second control point, and the third control point and have a tangent of a certain gradient at the second control point, which is internal division at an inverse ratio of a gradient of a straight line connecting the first control point with the second control point and a gradient of a straight line connecting the second control point with the third control point. This arrangement of the invention demands the less amount of computation and desirably reduces the required circuit scale.

Abstract: The graphic elements which constitutes a graphic data created by a CAD system for processing the graphic data displaying a graphic formed by combining the graphic elements are sorted into separate attributes consisting of graphic type, color, line type, line width, and the like while are represented by coordinate which indicates the position to be located and configuration as well as by a range coordinate and recorded in comparison files which include tables where each attribute is assigned with the coordinate data. Accordingly, the comparison files can be used with higher effectiveness for comparing the graphic data between the different formats. Also, as the identity of graphic data is judged through the comparison in the number of tables and the number of graphic elements with respect to the attributes, the number of items to be compared will be decreased.

Abstract: A method (2500) of converting a monotonic curve into edge information is disclosed. A method (2800A) of determining an integer edge crossing value, Xi, for a new edge crossed by a scanline (i.e., an inactive edge being crossed by the scanline for the first time) is also disclosed. Further, a method (2800B) of determining an integer edge crossing value, Xi, for an active edge crossed by a scanline, is also disclosed. The disclosed methods have general application in the representation of monotonic curves. The described methods allow monotonic curves to be accurately represented in terms of edges where the original curve can be reconstructed from the edges. Furthermore, the methods allow edge tracking to be performed such that any resulting error is restricted to a fixed-point division error. At transition points between adjoining segments, an original edge crossing point may be determined to avoid accumulated error.

Abstract: A method and system for determining a number of samples used in rendering a Bezier curve, defined by first, second, third and fourth sequential Bezier control points. The method and system determines: a visual significance of a curve by measuring a characteristic of the curve, a curvature estimation factor of the curve based on a length of the curve and a distance between first and last control points of the curve, and the number of samples for a predetermined accuracy depending on the visual significance of the curve and the curvature estimation factor.

Abstract: A curve is created in a computer-aided design system, based on a set of points inputted by the user. A polyline is computed and the curvature envelope along said polyline is computed to determine particular points (A0, A1, A2, A3, A4, A5) on thepolyline, which are extrema of curvature. Segmenting points (M0,1, M1,2, M2,3, M3,4, M4,5) are selected between pairs of particular points. A curve passing through the particular segmenting points is computed and is fitted to thepolyline. The process provides a curve that is well fitted to the set of points and does not require high skills from the user.

Abstract: A wipe pattern generation apparatus that can generate wipe patterns of various shapes at high speed and moreover can be miniaturized. is provided.

Abstract: Four related but independent aspects are described: (1) a method and a system to derive mesh surface descriptions (also called connectivity-wireframes) and material properties from objects represented as a scalar field (e.g. discrete multi-dimensional data), scalar functions (e.g. implicit surfaces) or any other surface description, (2) a compact, optionally multi-scalable, optionally view-dependent, optionally animation-friendly, multi-dimensional surface representation method and system comprising a combination of a surface mesh description and material properties associated with a reference grid, (3) a digital coding and decoding method and system of a combined surface mesh representation with connectivity information and material properties and a reference grid, and (4) a method and system for conversion of other surface descriptions to the combined surface mesh representation and reference grid.

Abstract: A method is provided of processing digital image data representing an image of an object to determine data representing a boundary for said object, the method comprising: inputting said image data; initializing a level set function representation of an interface for approximating said boundary; determining a motion of said interface subject to a combined cost function comprising a first cost comprising a signed distance constraint on said interface level set function representation and a second cost comprising a measure of said interface responsive to a density or metric of said image; modifying said level set function representation of said interface in accordance with said determined motion; repeating said determining and modifying such that said interface converges on said boundary; and determining boundary data representing said boundary from said converged level set function interface representation.

Abstract: According to one aspect of exemplary embodiments of the present invention, a method is provided for modeling a transition between adjoining surfaces. The method includes determining a curve of intersection of two adjoining surfaces, where the curve includes a plurality of points. For each of at least some of the points, the method includes selecting a point of the curve of intersection, and determining end points of a section of the transition located at the selected point, where each end point is located on a respective one of the adjoining surfaces. The method also includes determining a shape of the section of the transition, where the shape of the section for each of at least some of the points models the transition between the adjoining surfaces. The transition is curvature continuous with a first curvature at the end points and a second, different curvature at a portion therebetween.

Abstract: A user interface allows a user to freehand draw a probability density curve, or to select from predetermined probability densities, such as a normal distribution. The probability density represents the user's opinion regarding the probability of occurrence for different outcomes of a future event. The user can easily manipulate the shape of the probability density by dragging portions of the curve using an input device, such as to change the mean or standard deviation. Further, a scoring rule is applied to the probability density so that an updated score is displayed as the probability density is manipulated. The probability density can be input to an estimate contest or a prediction market, for instance. The user interface can also allow the user to freehand draw a scoring curve from which a probability density can be computed based on a scoring rule.

Abstract: A vehicle navigation apparatus is provided which can reliably guide a vehicle along a guidance route when the vehicle approaches an intersection of interest at which it is to make a turn even if another intersection exists between a vehicle position and the intersection of interest. A controller determines whether or not another intersection exists between the vehicle position and the next guidance intersection (an intersection at which the vehicle is to make a turn) when the vehicle reaches a predetermined distance from the guidance intersection. If another intersection is determined to exist, an intersection guidance map with an arrow indicative of the guidance route colored in a predetermined color is displayed on a display device. In one embodiment, if another intersection does not exist between the vehicle and the guidance intersection, the color of the arrow displayed is changed to a different color.

Abstract: A system and method is provided for analyzing and imaging three-dimensional volume data sets. In one embodiment of the invention, a ribbon section is produced which may include a plurality of planes projected from a polyline. The polyline may include one or more line segments preferably formed within a plane. The projected planes intersect the three-dimensional volume data set and the data located at the intersection may be selectively viewed. The polyline may be edited or varied by editing or varying the control points which define the polyline. In another embodiment of the present invention, a method is provided for quickly tracking a physical phenomena represented within the three-dimensional volume data set. A plurality of planes may be successively displayed in the three-dimensional volume data set from which points are digitized related to the structure of interest to create a spline curve on each plane.

Abstract: Techniques for assigning a region attribute to a region in a drawing are disclosed. One technique includes editing the drawing to define a current region, associating the current region with a previous region having a previous region attribute, and assigning the previous region attribute to the current region. Another technique includes deriving a previous path attribute and a relation for a previous path, editing the drawing to define a current set of paths having current regions, and assigning the previous path attribute to at least one current region based on the relation of the previous path.

Abstract: The present invention employs the notion of a Chinese writing brush in moving a geometric figure to produce a style of calligraphy, where the area of the geometric figure is large or small, then the strokes of a character are thick or thin. Hence the purpose is that the variance of the strokes of a character can be achieved using the present invention. The present invention only decides a moving path for the strokes of a character and the size of a geometric figure at starting points and end points, and then moves the geometric figure along the moving path, where the area the geometric figure passes is the style of calligraphy.

Abstract: A plurality of representative points are selected from a group of points obtained as results of shape measurement of an object, respective principal curvatures are calculated at the representative points on the basis of positional relationships between the representative point and a plurality of points existing around the representative point, a line of curvature is created on the basis of the principal curvatures of the representative points and a curved surface is generated using this line of curvature.

Abstract: Plane position coordinates indicating a position of a player object in a plane game field is updated based on an action which is performed by the player object on the plane game field and is determined according to an input signal. The plane position coordinates in a coordinate system based on the plane game field are converted into coordinates in a coordinate system based on a game field of a curved surface, thereby obtaining curved surface position coordinates. Based on the curved surface position coordinates, the player object is positioned in the game field of the curved surface and displayed on a display screen.

Abstract: A method of varying the relationship between a scalar input parameter and a scalar output parameter, by: displaying a relationship between an input parameter and an output parameter as a curve on a computer screen; selecting at least one control point on the curve; and moving at least one handle associated to the at least one control point to vary the shape of the curve as the curve passes through the at least one control point, thereby varying the relationship between the input parameter and the output parameter.

Abstract: To enable the drawing of a curve which is made to have an appropriate width to display scanning through a simple calculation process without using a frame buffer. A coordinate calculating unit 2 calculates a coordinate to be drawn from an expression of an original curve inputted thereinto. A horizontal broadening unit 4 performs a calculation for horizontal broadening that is implemented on the original curve. A vertical broadening unit 5 performs a calculation for vertical broadening that is implemented on the original curve and conversion to a horizontal vector. A selecting unit 6 switches between the usage of a result of a calculation by the horizontal broadening unit 4 and the usage of a result of a calculation by the vertical broadening unit 5 based on an inclination of a tangent which is calculated in an inclination calculating unit 3. An output unit 8 outputs an image signal of each pixel to scanning of a display screen.

Abstract: Described is a method for fitting a parametric representation to digital data. A vector distance field is generated to represent a set of objects and a parametric representation for the set of objects is initialized. A fitting error is determined from the vector distance field representation. The fitting error indicates the accuracy of the fit of the parametric representation to the set of objects. The parametric representation is adjusted and the fitting error is again determined in an iterative manner until an acceptable fitting error is achieved. The method has numerous technical advantages such as robustness, speed, simplicity relative to standard approaches, and the ability to manage constraints such as maintaining corners and enforcing continuity.

Abstract: Described is a method for sketching with a digitizing device. A set of digitized points along a path of the digitizing device are acquired and a parametric representation is fit to the path. Fitting includes generating a vector distance field representation of a set of objects corresponding to the set of digitized points and initializing a parametric representation for the set of objects. A fitting error indicating an accuracy of the fit of the parametric representation to the set of objects is determined from the vector distance field representation. The parametric representation is adjusted and the fitting error is again determined in an iterative manner until an acceptable fitting error is achieved. The method has numerous technical advantages such as robustness, speed, simplicity relative to standard approaches, and the ability to manage constraints such as maintaining corners and enforcing continuity.

Abstract: Described is a method for recognizing a shape from a path of a digitizing device. A set of points along a path of the digitizing device is acquired and a parametric representation is fit to the path. The parametric representation is compared to a set of known shapes to determine that the path of the digitizing device represents a particular shape. Fitting the parametric representation to the path includes generating a vector distance field representation of a set of objects corresponding to the set of digitized points, initializing a parametric representation to fit the set of objects, determining a fitting error from the vector distance field representation and adjusting the parametric representation to reduce the fitting error. The fitting error indicates an accuracy of the fit of the parametric representation to the set of objects.

Abstract: A method for generating a scale-dependent rendering of natural media styles in a vector-based graphics application is disclosed. A vector-based graphics drawing may be resized such that certain scale-dependent parameters are scaled proportionately, while other scale-independent parameters are not scaled. The result of such resizing is a scaled rendering of the vector-based graphics drawing that closely resemble hand drawn images created using natural media materials.

Abstract: A recursively partitioned/nested geometric structure is employed to graphically present and/or facilitate analysis of multi-variate data, including functions of multi-dimensional variables. Visual attributes are associated with appropriate ones of the regions within the geometric structure, in accordance with determined graphing values. In one embodiment, the data are normalized, comprising relative coordinate values, and encoded into polynary strings. Processing is advantageously performed using the polynary strings.

Abstract: A plurality of position data are input, which indicate the position of an observation target defined in a three-dimensional space, on its three-dimensional image, which is viewed from a predetermined view point along a predetermined line-of-sight direction. A curved cross-section in the line-of-sight direction is calculated from the plurality of position data and line-of-sight data including the predetermined view point and the predetermined line-of-sight direction. A projection image is generated by projecting the three-dimensional image on the calculated curved cross-section onto a projection surface along the line-of-sight direction. The projection image is then displayed.

Abstract: Complex labyrinth curves are interactively generated by an iterative process that spatially modulates curve evolution by an image or other function defined on the evolution space. After curves and evolution parameters are initialized [100], the iterative process allows the curve and evolution parameters to be interactively modified by a user [102], resamples the curves [104], and spatially modulates the curves according to the evolution parameters [106]. The evolved labyrinth curves are may be processed [110] for use in various applications including animation, maze creation, intricate artistic patterns, and graphical user interfaces that map linearly ordered data to the evolved curve and allow the data to be navigated using the rendered curve. The evolved curves can also be triangulated and projected to a plane to create patterns for manufacturing developable surfaces.

Abstract: A method and system for compressing and displaying a digital ink trace. Raw ink data is smoothed, and sharp points of the smoothed line are found. Curve-fitting is then used to generate a mathematical expression that defines the line segments between adjacent sharp points. The ink trace then is represented by a backbone spline that includes the sharp points and the mathematical expressions for the line segments. Thickness information, such as pressure or acceleration information, is combined with the backbone spline to provide a compressed ink file that represents a contour curve of the original ink trace. A display module uses an algorithm to separate the contour curve into a sequence of straight lines. A set of pixels is then generated for the display of each straight line using a novel antialiasing method. The pixels at the ends of adjacent straight lines are aligned using a weighting algorithm.

Abstract: This invention discloses a transforming apparatus, according to a transforming curve, for transforming a first image to a second image. The first image includes a plurality of pixels. The transforming apparatus includes a differentiating module, a first transforming module, an adjusting module and a second transforming module. According a predetermined value, the differentiating module transforms the transforming curve into a plurality of sub-curves. The first transforming module generates a plurality of straight lines corresponding to the sub-curves. According to the sub-curves, the straight lines and a predetermined threshold, the adjusting module adjusts the straight lines to generate a plurality of approximate lines. According to the approximate lines and the pixels of the first image, the second transforming module generates the second image.

Abstract: A method for generating, displaying and manipulating the orientation of three-dimensional vectors on a two-dimensional surface for visualization, statistical analysis and correlation. The method involves collecting vector data, transforming each vector into spherical co-ordinates, then assigning, a unique color related to a position on a spherical color model. A two-dimensional raster image filled with this unique color is centered at the point of measurement for each vector orientation as obtained from calculations or instrumentation capable of measuring this orientation. This methodology offers the user the ability to discriminate the location of specific orientations as well as the ability to define an enhanced full color gamut gradation for a specific range of orientation. This rendering of color-coded vector orientation enables easier understanding by the viewer of large data sets.

Abstract: In-context paint stroke characteristic adjustment, in which a first user input selecting a path of a paint stroke rendered on a display is received, an anchor point on the path is defined based on the first user input, and a characteristic adjustment control is rendered adjacent to the anchor point. A second user input is received via the characteristic adjustment control, and a characteristic of the paint stroke is adjusted at the anchor point based on the second user input.

Abstract: A curved line correction method is provided, which is used when correcting a curved line displayed on an image display device and formed of a plurality of dots by moving a dot selected from the plurality of dots. The method includes the steps of correcting a portion of the trajectory of the curved line such that the trajectory passes those of the plurality of dots located outside of an adjacent region of the selected dot before the dot is moved and a position of the selected dot after moved, and arranging a plurality of new dots on the corrected portion of the trajectory according to the length thereof.

Abstract: Compact and accurate piecewise parametric representations of implicit functions 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 function is represented as a compact form of one or more representations of such convergence regions. In yet another aspect, iteration is begun with applying the intervalized convergence test to an entire pameterization region. In yet another aspect, the range being tested for super convergence is iteratively sub-divided to generate other ranges for testing. In one aspect, such sub-dividing comprises dividing the selected ranges by half. In one further aspect, Newton iterate steps are applied to selected ranges to change such ranges for further testing of super convergence of such ranges.

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: 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: A method for deforming a plurality of shapes is described wherein each of the shapes comprises a set of parametric curves. The method comprises: providing a parametric surface, and forming a deformed shape for each of the shapes by performing a symbolic composition between the parametric surface and each parametric curve from the set of parametric curves comprising the shape being deformed. The parametric surface is defined by two parameters varying over a parametric domain, such that each of the parametric curves comprising the shapes lies in the parametric domain of the surface.

Abstract: In one aspect, the invention relates to a method for analyzing qualitative data. The method includes the step of providing a plurality of evaluation categories and a respective ranking system. Providing a closed curvilinear graph in which each unit of radius corresponds to a rank in the ranking system is another step of the method. Another step in the method includes placing each evaluation category at a location on the circumference of the closed curvilinear graph. The steps of the method also include providing the evaluation categories and ranking system to an entity being evaluated. The entity selects a rank in response in each respective category according to the method. Plotting the ranking of each respective category as a node in the closed curvilinear graph in response to the ranking by the entity is another step in the method.

Abstract: A computer-implemented graphics program for drawing a spline. The spline is drawn using a first method in the graphics program. Thereafter, the graphics program seamlessly switches from drawing the spline using the first method to drawing the spline using a second method, in response to a first user command. Further, the graphics program may also seamlessly switch from drawing the spline using the second method to drawing the spline using the first method, in response to a second user command.

Abstract: The invention relates to a method for generating a map depiction displaying street courses to travel through, for example in navigation, toll ticketing depiction or in precision applications such as automatic driving. For this purpose a street course consists of stringing together geometrical elements, for example, one or several circle arcs or one or several straight lines, wherein clothoids connect circle arcs and/or straight lines without sharp bends. The clothoids are calculated according to a required resolution from the arc of circle elements approximately approached by values or simply omitted, thereby making it possible to obtain a map depiction particularly reliably and optimal in terms of memory allocations.

Abstract: A rendering device according to the present invention comprises an information acquiring unit for acquiring system information or rendering object information, a control point generating section for setting a curved surface interpolating level serving to determine number of control points for creating a curved surface or a curved line based on the acquired information and thereby generating the control point in accordance with the curved surface interpolating level, and a curved surface creating section for creating the curved surface based on the control point, wherein an operation quantity for rendering the curved surface of a display object is dynamically changed based on the acquired information.

Abstract: A method and a system for image editing are provided. The method includes the following steps: firstly, search for characteristic curves of an image; next, approximate the characteristic curves with spline functions; then, when editing the image, manipulate the characteristic curves through control points of the corresponding spline functions; and then, reconstruct the image according to the manipulated characteristic curves.

Abstract: A curve designing system/method is provided. When similar curves are to be generated by evenly mixing features of given sample curves, the method of the present invention can control the extent of mixing features, smoothness, and size. The technology of the present invention can be applied to designing curve and curved surface in the fields of computer graphics and Computer-Aided Design (CAD).

Abstract: An item editing device, and item editing method, and a program stored on a tangible media enable easily editing items whether the item is rectangle or an arch shape by unifying the item editing operation and reducing the number of steps.

Abstract: A method of adjusting amplification curves in a PCR experiment includes receiving a plurality of amplification curves for a sample and computing a first parameter for each of the plurality of amplification curves. The method also includes computing a second parameter for each of the plurality of amplification curves and computing a third parameter using at least a portion of the first or second parameters. The method further includes computing an offset for each of the plurality of amplification curves. The offset is a function of the first parameter and the third parameter. Moreover, the method includes adjusting at least one of the plurality of amplification curves by subtracting the offset.

Abstract: A system and method for providing a dynamic user interface for a dense three-dimensional scene is presented. Clusters are placed in a three-dimensional scene arranged proximal to each other such cluster to form a cluster spine. Each cluster includes one or more concepts. Each cluster spine is projected into a two-dimensional display relative to a stationary perspective. Controls operating on a view of the cluster spines in the display are presented. A compass logically framing the cluster spines within the display is provided. A label to identify one such concept in one or more of the cluster spines appearing within the compass is generated. A plurality of slots in the two-dimensional display positioned circumferentially around the compass is defined. Each label is assigned to the slot outside of the compass for the cluster spine having a closest angularity to the slot.

Abstract: The present invention is a character image generation system for generating outline font based on character information and displaying the outline font on a display with a prescribed number of pixels. The character image generation system subdivides a curve expressed by character outline information corresponding to inputted character information, calculates the difference between coordinates at each end of the subdivided curve, compares the difference with a predetermined threshold value and sequentially calculates coordinates for each pixel, based on this comparison result.