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: The invention relates to a technical field of graphic image processing, especially to a technology for simplifying a complex path. The invention provides a method and a device for simplifying a complex path, to accomplish simplification of any complex path into a simple path of a region described by the complex path. The method for simplifying a complex path comprises: parsing the complex path into a vector linked-list consisted of linked monotonic vectors; dividing each vector in the vector linked-list into vector segments according to intersection points of the vector with other vectors in the vector linked-list; and extracting from all vector segments the vector segments located on a boundary of a region defined by the complex path, and connecting the extracted vector segments according to their location to obtain a simple path.

Abstract: A computer-implemented method can provide compression of a digital representation of an object. The digital representation can include a graphical data structure with graphical data defining the object in terms of a definition of respective faces of the object. Each face can be defined in terms of a surface for the face and each edge of the face on that surface. The method can include, for respective faces of the object, accessing the definition of the face in the graphical data structure, generating a compressed definition of the face and replacing the definition of the face in the graphical data structure by the compressed definition of the face.

Abstract: A drawing apparatus includes a reception unit, a first holding unit and a drawing processing unit. The reception unit receives graphic information. The first holding unit holds a plurality of first data which is a part of the graphic information received by the reception unit, in association with identification numbers assigned to the first data. The drawing processing unit draws a graphic on the basis of the first data held in the first holding unit. The drawing processing unit uses the plurality of the first data in a same task to draw the graphic. The reception unit records the identification numbers of the first data and a synchronization flag in order of reception. The synchronization flag is set for the first data received first among the plurality of first data processed by the same task in the drawing processing unit.

Abstract: Improving on the waveform viewing technology can advantageously address the industry's need for speedup and capacity of existing solution. As described herein, making data manipulation local and bounded can facilitate tremendous speedup. The waveform viewer can process data on-demand where the user explicitly specifies signals and a desired window (i.e. range). Operations including, but not limited to, zoom, pan, scan, etc. on the waveform viewer can be sent to the waveform servers in the form of a query containing the visualization parameters (e.g. number of pixels), which in turn compute bitmaps (or other waveform images) that are sent back to be displayed.

Abstract: A visualization system that preserves, augments or increases resolution of images within an industrial automation environment is provided. A reference component identifies, determines, or maps level of zooming or panning in connection with an image within an industrial automation environment, the image data located at a first source. A resolution component retrieves image data from a second sources that is different from the first source, the retrieved image data corresponding to specific portions of the image, the resolution component retrieving the image data from the second source as a function of the level of zooming or panning. A visualization component generates a visualization of the image, and receives the retrieved image data from the resolution component to preserve, augment, or enhance resolution of the image as a function of the zooming or panning.

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: A method of determining a distance of a source point to a surface of an object in three-dimensional space, wherein the object is represented by a decision rule and a plurality of volume elements arranged in slices comprising rows and columns, wherein each volume element carries at least one value, and wherein the decision rule determines membership of each volume element to the object in accordance with the at least one value of the volume element, the method comprising: determining a contour of a representation of the object within each slice; locating on the contour of each slice a homing point closest to the source point; fitting a curve to the located homing points; determining a distance from the source point to the fitted curve; and equating the determined distance as the distance of the source point to the surface of the object.

Abstract: Techniques are disclosed for accounting for features of computer-generated dynamic or simulation models being at different scales. Some examples of dynamic or simulation models may include models representing hair, fur, strings, vines, tails, or the like. In various embodiments, features at different scales in a complex dynamic or simulation model can be treated differently when rendered and/or simulated.

Abstract: In one embodiment, a method for encoding source data includes defining a source polygon using a parametric representation associated with the source data, and identifying one or more portions of the source polygon. The method further includes passing a filter throughout the entire sequence of the samples representing the source polygon, and performing a piecewise, portion by portion, re-parameterization of the source polygon using the corresponding portions of the filtered polygon to obtain an updated sequence of samples representing the source polygon. The passing of the filter and the performance of the piecewise re-parameterization are then iteratively repeated until a convergence condition is satisfied, to provide encoded data.

Abstract: A method for modifying an object design using a computer comprises the steps of: selecting a first sub-design of the object design comprising a first free form deformation geometry and a first free deformation control volume that is variable and adaptive; choosing a second sub-design comprising a second free form deformation geometry; and replacing the first geometry with the second geometry.

Abstract: The present invention discloses an image processing method for feature retention associated with averaging processes. The image processing method comprises: scaling and aligning a plurality of image data for acquiring feature information; determining a plurality of two-dimensional feature label points according to the feature information for generating at least one Bezier curve; utilizing the at least one Bezier curve to generate at least one Bezier tube and performing Bezier tube fitting for generating result of Bezier tube fitting; deforming the plurality of image data according to the Bezier tube or the result of Bezier tube fitting for generating a plurality of deformed image data; and averaging the plurality of deformed image data for generating feature-preserved average image data. The present invention also provides an image processing system, a computer readable storage medium, and a computer program product, for implementing the image processing method.

Abstract: A Bezier curve drawing device is configured as follows. A control point coordinate acquiring unit (10) acquires the coordinates of a plurality of control points of a Bezier curve. An inter-control point distance calculation unit (11) selects, using the minimum distance of a resolution for displaying the Bezier curve as a unit, either the horizontal distance or the vertical distance of adjacent control points of the Bezier curve, whichever is greater, adds up thus selected distances between adjacent control points, the added-up value being calculated as an indicator of the length of the Bezier curve. A division number setting unit (12) sets, based on the indicator of the length, the number of divisions to be used when the Bezier curve is divided and drawn. A Bezier division apex calculation unit (16) calculates, according to the number of divisions set by the division number setting unit (12), the coordinates of the end points of each interval obtained by dividing the Bezier curve.

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 resamples the curves [104], and spatially modulates the curves according to the evolution parameters [106]. The spatial modulation includes computing sample point displacements by calculating distances between each of the sample points and neighboring points using a surface distance metric that estimates a geodesic distance metric in a two-dimensional non-Euclidean evolution space. The evolved labyrinth curves are may be processed [110] for use in various applications. The evolved curves can also be triangulated and projected to a plane to create patterns for manufacturing developable surfaces.

Abstract: A user's watch list comprising stocks and stock market indices is organized into a browsing sequence using a computer. The computer provides a sequential browsing feature to sequentially browse, in an order according to the browsing sequence, the stocks and the indices in the user's watch list. The computer provides a visible representation feature to display regions to visibly represent the stocks and the indices in the user's watch list. Each region is user-selectable, is bordered by a respective color that is based on a change in price of its represented one of the stocks and the indices, and has an interior color that is not based on the change in price. In response to a user selection of a region from a touch screen, the computer retrieves a chart associated with the respective one of the stocks and the indices in the user's watch list represented by the region.

Abstract: A method of coronary vessel segmentation and visualization includes providing a digitized coronary image, placing a plurality of seed points along an estimated centerline of a coronary vessel, selecting a seed point and constructing a cyclic graph around the seed point in a plane perpendicular to the centerline at the seed point, performing a multi-scale-mean shift filtering in the perpendicular plane to estimate image gradient values, detecting a vessel boundary using a minimum-mean-cycle optimization that minimizes a ratio of a cost of a cycle to a length of a cycle, constructing a sub-voxel accurate vessel boundary about a point on the centerline, and refining the location of the centerline point from the sub-voxel accurate boundary, where the steps of constructing a sub-voxel accurate vessel boundary and refining the centerline point location are repeated until convergence.

Abstract: A curved surface importing device and method imports character strings of graphic parameters and graphic attributes of graphs from an initial graphic exchange specification (IGES) document, and analyzes the character strings of each of the graphs to generate a graphic model. The curved surface importing device converts the graphic model to a plurality of free-form curves and a free-form curved surface, connects each of the free-form curves to generate a closed boundary curve, and cuts out a contour surface from the free-form curved surface according to the closed boundary curve. The curved surface importing device further meshes the contour surface using a plurality of triangles, and determines an approximate poly-line of a boundary of the contour surface. The plurality of triangles and the approximate poly-line of a boundary of the contour surface are displayed on a display screen.

Abstract: To easily form curves preferable for design (beautiful curves or aesthetic curves).

Abstract: In one embodiment, a method for curve generation includes forming an initial interpolation polygon using samples within input data as interpolation knots, and upsampling the interpolation polygon by inserting extra samples in each segment between interpolation knots. A filter is then passed throughout a sequence of samples representing the upsampled interpolation polygon. Next, the interpolation polygon is substituted with the filtered polygon converted into a next interpolation polygon using segment-by-segment transformations, where segments of the filtered polygon are delimited by consecutive samples corresponding to interpolation knots, and each segment is transformed to fit between respective interpolation knots. Further, the passing of the filter and the substitution of the current interpolation polygon are repeated until a predefined condition is satisfied, to provide fitting curves.

Abstract: A three-dimensional object modeling tool is described that can derive the 2D cross sections of one or more lofted or unlofted surfaces, allowing those surfaces to be modified instantly. The modeling tool (loft tool) includes sub-tools for selecting a surface, moving a 2D section, editing a 2D section, creating a 2D section, and removing a 2D section. By analysis of the selected lofted surface and its faces, the loft tool can derive an appropriate number of 2D cross section to present to the user for manipulation. When deriving the 2D cross section the modeling tool operates by simplifying the curves making up the lofted surface, and from these can generate 2D cross section that can be easily manipulated and used to instantly update the lofted surface and redisplay it for further user modification.

Abstract: The invention is directed to a computer program product, a computer system, computer apparatus and a computer-implemented method for creating a parametric surface. The invention provides a base mesh having a plurality of outer or inner vertices with valence greater than two. The vertices define faces and at least one of the vertices is an extraordinary vertex. The invention converts faces of the base mesh into parametric elementary surfaces and trims at least one of said parametric elementary surfaces located in the vicinity of the extraordinary vertex. Trimming is performed according to: (i) at least two parametric elementary surfaces adjacent to a subject parametric elementary surface; and (ii) the base mesh. Next the invention constructs at least one parametric elementary surface, adjacent to the trimmed parametric elementary surface, wherein the resulting parametric elementary surfaces form the parametric surface.

Abstract: Fluctuations of cumulative delay value and delay dispersion in a path of a circuit are displayed graphically. Cumulative delay values of circuit elements in the path are obtained from delay analysis results of the circuit and dispersion is obtained from a probability density distribution of the delay of the circuit elements. Corresponding to the location of the circuit element in the path, the former and the latter are plotted on a coordinate plane.

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: The present disclosure relates to music composition devices and methods. A system is provided which allows composers of all skill levels to easily create music that is pleasurable to the ear. The system may also assist more advanced composers in creating complex musical arrangements based off of partially completed compositions. The system also streamlines composition and arrangement in multi-instrument environments. The user is able to select from a variety of available music visualizations and instrument views, allowing comparison therebetween. The system may comprise composition error checking functions, free-play performance abilities, and recording and playback features. Certain embodiments incorporate remote access for collaboration between users.

Abstract: A graphical production system produces pixel bar charts, in various embodiments. In an embodiment, a pixel bar chart is constructed that may include multiple bars with substantially equal widths and potentially variable heights to enable visual data analysis. A bar may include a number of pixel units corresponding to a volume of data records represented within the bar. Selected visual indicators are displayed within the pixel units of the bar, where a selected visual indicator represents a value of an attribute of a data record represented by the pixel unit. In an embodiment, the pixel units may be ordered within a bar in a particular sequence (e.g., ascending, descending or some other order). Further, in an embodiment, the bar width is determined to minimize the amount of padding. In an embodiment, a visual indicator scale is displayed to indicate values associated with each visual indicator.

Abstract: Based on a selected stock market index, a visible representation of a plurality of stock market indices is displayed using a display device. The stock market indices comprise the selected stock market index and a plurality of other stock market indices related to the selected stock market index by a non-unary tree. The visible representation comprises a region to represent the selected stock market index. The visible representation further comprises a plurality of regions to represent the plurality of other stock market indices. The plurality of regions are approximately shaped as a plurality of annulus sectors each having a respective area based on a respective market capitalization associated with its represented one of the plurality of other stock market indices. The visible representation represents pairs of stock market indices that are adjacent in the non-unary tree by radially-adjacent pairs of their representing regions.

Abstract: A method, system, and computer-readable storage medium are disclosed for rendering Bézier curves using a graphics processing unit (GPU). In one embodiment, a triangle representing a quadratic Bézier curve is sent to the GPU, wherein the triangle comprises only one texture coordinate per vertex, and wherein each texture coordinate comprises a first coordinate of the respective vertex in a canonical space. In one embodiment, a second coordinate in the canonical space for each vertex sent to the GPU may be determined based on the first coordinate in the canonical space for the respective vertex. In one embodiment, the quadratic Bézier curve is rendered using the GPU.

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 division number that defines the number of divided straight lines representing a circular graphic pattern is registered beforehand in a division number table in relation to a radius r of the circular graphic pattern. Further, data usable to calculate X-coordinate and Y-coordinate values of endpoints of respective divided straight lines are registered beforehand in an endpoint table in relation to a straight line division number N. Accordingly, if a graphic pattern to be drawn is a circular graphic pattern, it is unnecessary to approximate an outline (curve) with Bezier curves and each division point (endpoint) of divided straight lines can be directly and quickly obtained using the trigonometric function.

Abstract: Systems and methods for identifying asymptotes in approximated geometric forms are provided. One disclosed method includes identifying a set of data points that represent an approximated geometric form. The data points may be organized into segments. The method may further include determining a visible range of the geometric form to display. The method may further include looping through successive segments of the approximated geometric form, and on each loop, for a current segment, making a decision whether to draw the current segment based upon a prediction of whether the current segment traverses an asymptote within the visible range. The method may further include displaying on a graphical user interface of a computing device, a graph of the segments of the geometric form in the visible range, the graph not including those segments that were decided not be drawn.

Abstract: A computer aided design system and a computer aided design program which can greatly increase the utility of a computer aided design model, and can improve the efficiency of design and production processes, by adopting a curved surface theory which ensures the continuity of a free-form line or surface. A computer executes: a point sequence information extraction process for extracting a plurality of point sequences on a curved surface; a dividing process for generating a curved surface from the point sequences and dividing the curved surface into a predetermined number of mesh points; a first fundamental form computing process for computing coefficients of the first fundamental form; a second fundamental form computing process for computing coefficients of the second fundamental form; and a storage process for storing the point sequence information, the coefficients of the first fundamental form and the coefficients of the second fundamental form.

Abstract: A method for effective placement of data for visualization of multidimensional data sets using multiple pixel bar charts. Data is received comprising a plurality of records, each record having a plurality of attributes. From the plurality of attributes, a set of attributes is determined for placement of the plurality of records in a graphically displayable array comprising a plurality of data points, each data point representing one record of the plurality of records. In one embodiment, the graphically displayable array is a pixel bar chart. The plurality of records are arranged to construct the pixel bar chart for presenting the data in a format for detecting relationships between the plurality of records. The present invention provides a pixel visualization technique having a method of optimal data placement to resolve the locality and ordering constraints.

Abstract: A drawing processing apparatus for performing tessellation processing, comprising a pixel shader and a texture unit. An internal division operation part of the pixel shader issues texture load instructions to the texture unit, specifying parametric coordinate values of a patch of a parametric surface, and thereby acquires internal division factors interpolated based on the parametric coordinate values from the texture unit. The internal division operation part issues texture load instructions to the texture unit further, specifying the internal division factors acquired from the texture unit as new interpolation factors, and thereby acquires control points internally divided based on the internal division factors in advance from the texture unit.

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 method of rendering a stroked curve for display in a graphics processing system in which an input stroked curve 2 to be displayed, such as a character in a computer font or a portion thereof, is defined in user space 4 and projected into a surface space 6 for display. For each of one or more sampling points in the surface space 6, a corresponding sampling position in a projected space 12 is determined, and predetermined information is used to estimate the extent in a defined direction of a projected form of the stroked curve in the projected space 12 at a position along the length of the projected form of the stroked curve corresponding to the position along the length of the projected form of the stroked curve of the sampling position in the projected space 12. The estimated extent is then used to determine whether the sampling position in question falls within the stroked curve or not, thereby allowing suitable rendering data to be assigned to the sampling point.

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 function approximation processing method comprises inputting and binarizing image data, extracting contour from the binarized image data, estimating tangent points in horizontal and vertical directions from the contour, and approximating contour between adjacent tangent points among the estimated tangent points with a predetermined function, thereby an input object such as a character or a figure can be processed at high speed, and outline data with high image quality can be generated with a reduced number of points.

Abstract: A method, system, and computer-readable storage medium are disclosed for rendering Bézier curves using a graphics processing unit (GPU). In one embodiment, a respective set of barycentric coordinates may be assigned to each of the three vertices of a triangle. The triangle may comprise a control triangle for a quadratic Bézier curve, and the quadratic Bézier curve may be a rational quadratic Bézier curve. Each set of barycentric coordinates may comprise three values such as (1,0,0), (0,1,0) or (0,0,1). In one embodiment, the quadratic Bézier curve may be rendered using the GPU. Rendering the quadratic Bézier curve may comprise evaluating a function of the barycentric coordinates using the GPU.

Abstract: Methods and apparatus disclosed herein receive a non-integer star points input parameter value, create a star shape with a number of star points equal to an integer portion of the star points input parameter plus one, and store or render the star shape to an output device. A fractional star point is differentiated from integer star points by a differential radial length between the two. Some embodiments also receive a non-integer polygon sides input parameter value and render a modified polygon shape with a total number of sides equal to an integer portion of the polygon sides input parameter plus one. A number of sides equal to the integer portion of the polygon sides parameter minus one are rendered as regular polygon sides. Two sides are rendered as adjacent symmetrical bezier curves, and the modified polygon shape is stored or rendered to an output device.

Abstract: Generalization of features in a digital map is enabled by performing a simplification of polylines. A set of chords between points on a polyline is selected such that each chord does not violate specified rules such as maximum distance from the original polyline. If a chord is acceptable, a node representing the chord is created, described by the start and end points of the chord. For pairs of nodes created, a transition from the first node to the second node is evaluated to determine whether it is acceptable. In one embodiment, a transition is acceptable if the absolute value of the angle formed by the chords is within a threshold angle from the angle formed by the original polyline at that point. If the transition is acceptable, a link between the two nodes is established. A least-cost path through the graph is chosen, and a simplified polyline is then generated.

Abstract: A method and apparatus for a scalable property viewer for a massively parallel computer system. The property viewer includes a graphical user interface to allow the user to view different properties of the computer system with several different types of views. The different views provide the user with both logical and graphical representations of the properties being monitored and allows the user to link between a logical and physical view of the system. The GUI provides the user with a convenient way to view the elements of a large system and determine elements that are different. Different properties could be placed together in the same view with different colors to allow the user to see the interaction of multiple properties.

Abstract: A method and system for approximating a curve, and a graphic display control method and apparatus are disclosed. The method for approximating a curve comprises the steps of acquiring number information of subdividing points for subdividing a curve needed to be approximated based on coordinate information of control points of the curve, acquiring coordinate information of the subdividing points based on the number information of the subdividing points and the coordinate information of the control points, and connecting the subdividing points with straight lines based on the coordinate information of the subdividing points. The invention could achieve efficient curve approximation and in turn achieve efficient graphic-display control.

Abstract: A graphic module wherein, given a curve P(x,y)=P(x(t), y(t)) between two points P0(x,y)=P0(x(t0), y(t0)) and P1(x,y)=P1(x(t1), y(t1)), in the screen coordinates, a calculating circuit computes a curve mid-point Phalf(x,y)=Phalf(x(thalf), y(thalf)), where thalf=((t0+t1)/2 on the curve, computes a segment mid-point PM(x,y)=(P0(x,y)+P1(x,y))/2 on segment P0P1, computes a distance function d between the curve mid-point and the segment mid-point, and, given two thresholds THR0 and THR1, with THR0<=THR1, if d<THR0, it generates line segment PoP1, and if THR0<=d<THR1, it generates two line segments P0Phalf and PhalfP1, and if d>=THR1, it repeats the previous steps for the curve portions from P0 to Phalf and from Phalf to P1.

Abstract: The invention creates a method for representing moving objects in bit-mapped format on a matrixlike display device, having the following steps: calculation of a plurality of bit maps for a certain number of a various object representations along a predetermined path curve in advance; storage of the plurality of bit maps in memory in advance; and execution of a representation processing with a display sequence of object representations along the path curve by reading and displaying correspondingly memorized bit maps.

Abstract: A method, apparatus, and computer-readable storage medium provide a financial Web site to display, based on a user-selected stock, a plurality of user-selectable elements associated with a respective plurality of stocks that are determined to be related to the user-selected stock. Each stock of the plurality of stocks is determined to be related to the user-selected stock based on a respective correlation between postings of messages for the stock and the user-selected stock. Each respective correlation is between a respective time series of an aggregate level of messaging for its respective stock and a time series of an aggregate level of messaging for the user-selected stock. Each of the plurality of user-selectable elements is user-selectable to retrieve information from a message board associated with its respective one of the plurality of stocks.

Abstract: A distance information generating unit 4 for rasterizing minute line segments divided by a curved line dividing unit 2 through a combination of straight line cells and corner cells to generate distance information corresponding to a pixel 12 of a display and an edge rasterizing unit 7 for rasterizing edge information about the minute line segments divided by the curved line dividing unit 2 are disposed, and a mapping unit 10 determines whether the pixel 12 is located inside or outside by using the edge information rasterized by the edge rasterizing unit 7, and maps the distance information generated by the distance information generating unit 4 onto the antialiasing intensity 11 of a component 13 included in the pixel 12 according to the results of the inside or outside determination.

Abstract: An image measuring system comprises a measurement point acquire, a measurement direction calculator, a synthesized direction calculator operative to calculate a synthesized direction resulted from synthesis of movement directions before and after the measurement point, a fore/aft-running point calculator operative to calculate a forerunning point at a position spaced a certain distance backward in the synthesized direction from the measurement point and to calculate an aft-running point at a position spaced a certain distance forward in the synthesized direction from the measurement point, a way point calculator operative to calculate a plurality of way points arranged on a path smoothly connecting the aft-running point to the forerunning point, and a measurement path setter operative to set a measurement path following the synthesized directions and passing through the calculated way points and the measurement points.

Abstract: A system for interactive computer graphics enables generation of Bezier curves from a series of points based on the relative position of successive points in the series. For example, for successive points in a series, point A, point B, and point C are successive points in the series of points, and wherein a control point corresponding to point B and associated with the segment AB is determined by the equation B+RA*(RA*(B?C)+RC*(A?B)), and a control point corresponding to point B and associated with the segment BC is determined by the equation PBBC=B+RC*(RA*(C?B)+RC*(B?A)), where RA=|AB|/(|AB|+|BC|), and RC=|BC|/(|AB|+|BC|).

Abstract: A image processing apparatus has a first data generation unit which generates triangular data by making straight line contours and curved contours triangles by analyzing the straight line contours and the curved contours with respect to vector format graphic data, a second data generation unit which generates stencil data from the triangular data, and a third data generation unit which generates raster format graphic data with reference to the stencil data.

Abstract: A user identifies an area of a digital canvas. Color gradients are determined based on a corresponding area on a reference. Brush strokes are applied in the area of the digital canvas, the brush strokes having trajectories based on the color gradients.