Abstract: An image processing apparatus and an image processing method reconstruct a three-dimensional image of an object which expresses a texture, glossiness, and three-dimensionality with realism. The image processing apparatus produces, from a physical object, data representing a shape and a surface feature of the physical object, holds the data as a three-dimensional model, and presents a three-dimensional image under conditions of an illumination environment and line of sight designated by a user when the three-dimensional image is reconstructed. To present the three-dimensional image at a high speed with realism, the apparatus and method use new and particularly advantageous features in a generation process and in a data format used in the three-dimensional model.

Abstract: A method for extracting from an image a shape descriptor which describes shape features of the image is provided. The shape descriptor extracting method includes: (a) extracting a skeleton from an input image, (b) obtaining a list of straight lines by connecting pixels based on the extracted skeleton, and (c) determining the regularized list of straight lines obtained by normalizing a list of straight lines as the shape descriptor. A shape descriptor extracted according to the shape descriptor extracting method possesses information of a schematic feature of a shape included in an image. Therefore, the shape descriptor extracting method effectively extracts a local motion in the data collection of the same category, and the number of extracted shapes is not limited to the number of objects.

Abstract: A method for rapid rendering of a desired line in a volumetric display having a rotatable screen includes stepping the rotatable screen through a sequence of angular positions and, at each angular position, rendering, on the rotatable screen, a rasterized approximation of a line segment containing an intersection of the desired line and the rotatable screen.

Abstract: Automatic interpretation processing operations, such as character recognition, require a binary image of information-bearing image elements and a background. Digital image data produced by scanning a color-containing document frequently contain many different colors so that a division into information-bearing image elements and background is not evident. The invention divides connected components (contiguous pixels with the same color) in the digital image into background and other connected components, whereafter the other connected components are allocated, in accordance with a predetermined criterion, either to the background or to a foreground. The foreground connected components are combined into information elements suitable for the automatic interpretation processing. The division into information-bearing image elements and background can be preceded by a color quantisation processing of the digital image data.

Abstract: In one embodiment, selecting a screen region on a screen of a monitor of a computer graphics display system to activate in rendering a straight line segment. Steps of aligning a rectangular grid to screen region boundaries, wherein the screen includes a screen space divided into at least one screen region, locating a first and second endpoints of the straight line segment on the screen space, defining a rectangular bounding box in the screen space having vertices at the first and second endpoints, identifying each screen region that at least partially overlaps the bounding box, and selecting each identified screen region through which the straight line segment passes to activate for rendering the straight line segment on the screen are disclosed.

Abstract: A graphics system and method for displaying lines on a display device. The system may comprise a sample buffer, a rendering unit and a sample-to-pixel calculation unit. The rendering unit may (a) generate a plurality of sample positions in a two-dimensional space, (b) determine a sample normal distance for each of the sample positions with respect to a line defined by the line-draw command, (c) assign sample values to the sample positions based on the sample normal distance of each of the sample positions, and (d) store the sample values in the sample buffer. The sample-to-pixel calculation unit may read sample values from the sample buffer, filter them to determine a pixel value, and transmit the pixel value to the display device. The rendering unit may render the line sample values with a narrower width to pre-compensate for the line-expanding effect of the filtering performed by the sample-to-pixel calculation unit.

Abstract: A method corrects an adaptively sampled distance field of a model. The adaptively sampled distance field includes a multiple of cells. Each cell stores distance values at vertices of the cell. The cells include interior cells, surface cells, and exterior cells, and neighboring cells have a common edge. Selected cells are marked as unprocessed cells, and the surface cells as marked as processed cells. A particular vertex of each unprocessed cell is marked as a minimum vertex if it has a minimum absolute value distance value. The unprocessed cells in an ascending order of the minimum vertices are further processed by appending, for each common edge of each unprocessed cell, distance values of neighboring processed cells to the common edge, adjusting the distance values of the vertices of the unprocessed cell according to the appended distance values of the edges and the distance values of the vertices, and marking the unprocessed cell as processed.

Abstract: A graphics system and method with which thick graphic primitives are efficiently drawn by minimizing dependence on drawing algorithms that require appreciable setup time. The method contemplates drawing a thick primitive in which an offset or displacement value is first calculated, based upon the thickness of the graphic primitive. The offset is approximately one half of the thickness of the primitive. Following calculation of the offset value, line drawing parameter values are determined for a line that is parallel to the origin line and displaced from the origin line in a minor axis direction by the displacement or offset value. A loop is then repeated for each grip point in the major axis range of the line. The loop includes an initial step in which a boundary pixel of the thick graphic primitive is drawn using the line drawing algorithm and the line drawing parameter values calculated for the offset line.

Abstract: A method and system for the extraction of linear features from digital imagery is described herein. The proposed methodology is based on the tridimensional Radon transformation and on the generation of a multi-layer database having separate layers containing different types of information to allow the reconstruction of an output image where the linear features of the input image are restored.

Abstract: A method, apparatus, article of manufacture, for implementing a relative polar angle snap tool. The relative polar angle snap tool allows the user to define lines and shapes that are at pre-settable angles relative to existing lines and shapes, and at pre-settable lengths.

Abstract: Apparatus and methods for dynamically rendering digital ink strokes of arbitrary stroke width while a user is drawing the ink strokes. An ink rendering system may receive sampled pen tip positions associated with a stylus or pen on a digitizer. The ink rendering system may further determine pen tip instances having particular shapes, sizes, and/or rotations, and may determine connecting shapes, preferably quadrangles, that connect between the pen tip instances. Smoothing techniques may also be used for existing digital ink.

Abstract: The present invention provides a method and apparatus for rendering images on a computer screen. Under the invention, a portion of a base image is described using a path. The path is then transformed using a non-affine transform to produce a transformed path. The transformed path is then rendered onto the computer screen. Another aspect of the present invention is a method and apparatus for rendering curves of any order and any dimension. In particular, the present invention provides a means for converting a function of any order and any dimension that describes one segment of a curve into a function that describes a different sized segment or an adjoining segment.

Abstract: The minimum number of rectangles required to fill a particular polygon and which meet input parameters including minimum stripe width, maximum stripe width, stripe overlap amount, maximum number of borders, and whether or not to merge adjacent borders, is determined by: (1) bordering, including computing a border width which is wide as possible, bordering all non-orthogonal polygons with one or more borders, merging borders when appropriate, halting bordering as soon as the interior can be efficiently filled using orthogonal fill rectangles; (2) filling, including filling the interior of the bordered non-orthogonal polygon or the unbordered orthogonal polygon with orthogonal paint stripes, filling, if possible, the uncovered area with a single least encompassing rectangle, otherwise generating orthogonal stripes using the minimum stripe width and where practical merging them with a previous adjacent stripe; and (3) processing, including locating any and all unfilled portions of the original polygon, applying

Abstract: The object of the invention is to provide a method, a program and a device that can set accurately and easily the origin of the coordinate system of a workpiece based on the result obtained by a surface texture measuring machine scanning over a feature area on the surface of the workpiece. The device comprises a data inputter for inputting data obtained by scanning a feature area including at least a feature point area and a non-feature point area of the surface of a workpiece, a feature point selector for extracting the feature points of the data by statistically processing the data inputted into the data inputter and an origin setter for setting the origin of a workpiece coordinate system relative to an origin setting target point of the workpiece based on the coordinate values of the feature point obtained by the feature point selector.

Abstract: A graphing calculator (10) having manual line drawing capability. The calculator (10) is programmed to receive data representing the begin point and end point of a line (FIGS. 7 and 8), and to then draw a line that includes these points (FIG. 9). The display includes a display of the line equation (FIG. 9). The slope and y-intercept of the line may be adjusted using cursor direction keys. As the line is adjusted, it is redrawn and the line equation is re-calculated and displayed (FIG. 10).

Abstract: A method of rasterizing a line on a display having pixels with locations defined by a polar coordinate system uses the sign of a discriminant to choose which of two candidate pixels is to be the next pixel on the rasterized line. The discriminant, which is derived from the desired line, is evaluated at a point in the neighborhood of the candidate pixels. The discriminant value depends on the local slope of the line in polar coordinates. The method divides the line into segments having selected ranges of slope and rasterizes the desired line along each segment.

Abstract: An integer arithmetic graphic line scan-conversion procedure sub-divides a pixel grid into a 1/N sub-pixel grid, where N is a positive integer selected to provide a desired precision. A line segment is defined by a pair of vertices relative to the sub-pixel grid. The vertices are ordered such that the line segment is in one of the first and the second quadrants, depending upon the slope of the line segment. An integer estimate is made of the slope of the line segment relative to the sub-pixel grid. The scan progresses along a major axis at pixel intervals, while best-fit integer projections of the line segment are made along an orthogonal axis relative to the sub-pixel grid. A resulting array of integer line-scan points relative to the sub-pixel grid are used to adjust color and brightness attributes of display pixels, and the resulting adjusted pixels are output to a display device to create an image of the scanned line segment. In a preferred embodiment, N is a positive power of 2.

Abstract: The present invention provides a systematic automated procedure for routing connections in display applications such as a network topology interface. In one embodiment, the invention first creates an “ideal routing” between two given nodes. The ideal routing includes three segments that join the nodes. If any obstructions exist on the original segments of the ideal routing then the procedure systematically reroutes the appropriate segments to achieve an efficient, visually cohesive and organized routing. The routing procedure operates at different layers, groups and subgroups of nodes. By using the procedure with a layered design it is possible to achieve fast, uniform and effective routing in very complex systems with many nodes and inter-node connections.

Abstract: A system for aiding to make a medical care map includes: a plurality of files for including individual medical care data; a date and time measuring device for measuring a present date and time; a display controlling device for (i) generating main display data to display the medical care data, (ii) selecting one of condition marks set in advance, (iii) generating first sub display data to display the selected condition mark on the care map, (iv) calculating a present position on the care map, and (v) generating second sub display data to display a present mark at the calculated present position on the care map; and a display device for displaying the medical care data on the care map together with the condition mark and the present mark, on the basis of the main display data, the first sub display data and the second sub display data.

Abstract: The invention improves the appearance of freehand drawn lines and shapes in an electronic document by first recognizing freehand drawn lines and shapes and generating a line made up of sequential straight line segments for the freehand drawn line when the line does not form a closed line and generating a multiple straight-line-segment shape when the line forms a closed line. If a multiple segment shape is being reshaped, a basic shape is selected from reference ideal shapes as the basic shape of the multiple segment shape. The basic shape is adjusted to provide a specific shape as an improved shape for the freehand drawn shape. The recognition of the freehand drawn lines and shapes is accomplished by comparing source segments of a source freehand drawn line to a straight line and substituting a straight line segment for a source segment if the deviation between the source segment and the straight line is below a predetermined value.

Abstract: An image processing application employs the concept of integral pre-multiplied alpha channel, and combines the techniques of multi-resolution representation, graph-structured representation, and automatic and intelligent data type conversion in order to permit a computer user to mix and manipulate both raster and vector based images in a single user interface while remaining unaware of the different data types underlying the images.

Abstract: An inventive line-drawing apparatus draws a line that connects a start point to an end point. The start and end points are both presented on a display and represented by mutually different sets of coordinates. The apparatus includes first and second FIFO memories, an adder and a shifter. Each of the first and second FIFO memories accepts a plurality of input coordinate data and sequentially outputs one of these data after another on a first in, first out basis. The adder receives and adds together the respective coordinate data output from the first and second memories and outputs added data. And the shifter divides the added data by two and outputs divided data. The coordinate data output from the first and second memories are input to the first memory. The divided data is input from the shifter to the second memory. The line connecting the start and end points together is drawn on the display in accordance with the divided data output from the shifter.

Abstract: A fast line drawing method. First, the coordinates of two end points are received and a current point is assigned to one of the end points. The differences of x and y coordinates (?x and ?y) and the sum of error E are computed, the integer part of ?x over ?y is denoted as Q. The current point is checked to determine whether it has reached the end point. If not and the value of E is negative, a point at the current point is drawn. The y-coordinate of the current point and E are updated by (Y+1) and (E?2?x) respectively if E is non-negative, a span of pixels from (X,Y) to (X+Q?1,Y) are drawn if the coordinate of last of Q points is less than the end point. Otherwise, a span of pixels from (X,Y) to (x2,Y) are drawn.

Abstract: An approach for drawing a straight-line graph with minimal cognitive disruption to the user is disclosed. In one embodiment, information defining a first graph comprising a first vertex set and a first edge set is received. A second vertex set and a second edge set are received. The second edge set is added to the first edge set. A second graph is created based on the first vertex set and the first edge set. For each vertex in the second vertex set, one or more neighboring vertices are determined, a first barycenter is determined based on positions of the neighboring vertices in the second graph, a second barycenter is determined based on positions of the neighboring vertices in the first graph, and a vector directed from the first barycenter to the vertex in the second graph is determined. Coordinates of the vertex in the first graph are modified to a final position equal to a sum of the vector and the second barycenter.

Abstract: An active matrix type EL display device is constructed in such a way that a reverse bias voltage can be effectively applied to an EL element without decreasing the lighting time rate thereof. An EL element E1 constituting one pixel 10 is driven to be lit by a write transistor Tr1 and a driving transistor Tr2 and the lighting time of the EL element is controlled by an erase transistor Tr3 so that a multi-gradation expression is realized. The drain of a reverse bias applying transistor is connected to the anode terminal of the EL element E1, and the gate and the source of the same transistor Tr4 are connected to the respective gates of the erase transistor Tr3 and the write transistor Tr1, respectively. By this structure, an ON operation of the reverse bias applying transistor Tr4 is implemented in synchronization with an ON operation of the erase transistor Tr3 so that a reverse bias voltage can be supplied to the EL element E1.

Abstract: An integer arithmetic graphic line scan-conversion procedure sub-divides a pixel grid into a 1/N sub-pixel grid, where N is a positive integer selected to provide a desired precision. A line segment is defined by a pair of vertices relative to the sub-pixel grid. The vertices are ordered such that the line segment is in one of the first and the second quadrants, depending upon the slope of the line segment. An integer estimate is made of the slope of the line segment relative to the sub-pixel grid. The scan progresses along a major axis at pixel intervals, while best-fit integer projections of the line segment are made along an orthogonal axis relative to the sub-pixel grid. A resulting array of integer line-scan points relative to the sub-pixel grid are used to adjust color and brightness attributes of display pixels, and the resulting adjusted pixels are output to a display device to create an image of the scanned line segment. In a preferred embodiment, N is a positive power of 2.

Abstract: A formatting object according to the present invention conveys information to the reader of a document (such as a table or chart) by associating visual attributes (such as color, fill type, border width, line width, line style, font size, marker size and marker type) to characters or markers within the document. The formatting object may be used to emphasize data within a table or a chart by modifying the structural visual attributes of characters or markers within the table or chart according to pre-defined criteria. Similarly, the formatting object may be used to increase information density within a table or chart, and to elegantly represent the relationships between four or more interrelated variables in a two-dimensional chart. The formatting object accomplishes this by defining at least one format map that comprises one or more mapping segments.

Abstract: A noise reducing method for a radio portable terminal having a radio section for transmitting and receiving radio data, a CPU (Central Processing Unit), connected to the radio section and incorporating a cache, for performing predetermined data processing, and an external memory connected to the CPU, reads an internal operation program runnable only in the CPU from the external memory and stores the internal operation program in the cache prior to reception of the radio data, and then executes only the internal operation program. In this manner, this method suppresses access to the external memory, thereby reducing noise.

Abstract: Disclosed are techniques for determining in a lattice a set of cells of the lattice that are intersected by a line endpoints. The tech-niques employ orders 1 . . . n of runs of lattice cells to make the determination and are usable with lines whose endpoints have coordinates that may be any real number. The techniques include an initialization that derives an error term with a real number value and a structural parameter with a real number value for order 1 using the values of the coordinates of the end points and then determines the error terms and structural parameters for each order i belonging to the orders 2 . . . n using the error term and structural parameter for order i−1. When the first run of any orders 1 . . . n is truncated, the initialization also adds the cells belonging to the truncated run to the set. When the initialization is finished, the remaining cells belonging to the set are determined using full runs of order n.

Abstract: A method generates a distance field for a region of a shape descriptor representing an object. The distance field includes a set of cells for which cell types are defined. A configuration of a set of cells for the region is generated. Each cell of the configuration includes a cell type and a method for reconstructing the distance field within the cell. The configuration of the set of cells is modified until an optimal configuration is reached. The modification is based on the shape descriptor, the region, and the set of cell types. The optimal configuration of the set of cells is stored in a memory to generate the distance field for the region. Another method generates a two-dimensional distance field within a cell associated with a two-dimensional object. A set of boundary descriptors for the two-dimensional object is determined and partitioned into a set of segments. The segments are delimited by a set of features of the boundary descriptors.

Abstract: In one embodiment, selecting auxiliary screen regions to activate in rendering a straight line segment on a screen of a computer monitor, wherein the straight line segment comprises points defined by an algebraic expression equal to zero, wherein the expression is expressed as a first constant multiplied by a x-axis value plus a second constant multiplied by a y-axis value plus a third constant, wherein the straight line segment has a width.

Abstract: The method for line patterning may include receiving line data for a first line. The line data for the first line may include an original starting point and an original endpoint. The first line may be divided into one or more line segments, which may include generating a new starting point and a new endpoint for one or more of the one or more line segments. The new line segments may then be rasterized from the new endpoint to the new starting point. In other words, each line segment may be rasterized from right to left, thus avoiding problems associated with multiple consecutive accesses of pixel addresses in the pixel buffer. The original or intended line pattern of the line is preserved since the zeros and ones are drawn or rendered in their appropriate locations as if they were being drawn left to right, even though they are actually rasterized from right to left.

Abstract: In one embodiment, selecting a pixel in a screen region on a screen of a monitor of a computer graphics display system to activate in rendering a straight line segment by a rasterizer assigned to the screen region. Steps of aligning a rectangular grid to pixel boundaries, wherein the screen comprises a screen space divided into at least one screen region, wherein the screen region comprises multiple pixels, identifying each pixel in the screen region through which the straight line segment passes, and selecting each identified pixel to activate for rendering the straight line segment on the screen when the straight line segment passes through a diamond shaped area of the pixel whose boundary is defined by the lower, upper, left, and right pixel grid mid-points are disclosed.

Abstract: In one embodiment, selecting a screen region on a screen of a monitor of a computer graphics display system to activate in rendering a straight line segment. Steps of aligning a rectangular grid to screen region boundaries, wherein the screen includes a screen space divided into at least one screen region, locating a first and second endpoints of the straight line segment on the screen space, defining a rectangular bounding box in the screen space having vertices at the first and second endpoints, identifying each screen region that at least partially overlaps the bounding box, and selecting each identified screen region through which the straight line segment passes to activate for rendering the straight line segment on the screen are disclosed.

Abstract: A method and system for processing an image including capturing an image and storing the image as image pixel data. Each image pixel datum is stored in a respective memory location having a corresponding address. Threshold pixel data is selected from the image pixel data and linear spot segments are identified from the threshold pixel data selected. The positions of only a first pixel and a last pixel for each linear segment are saved. Movement of one or more objects are tracked by comparing the positions of first and last pixels of a linear segment present in the captured image with respective first and last pixel positions in subsequent captured images. Alternatively, additional data for each linear data segment is saved such as sum of pixels and the weighted sum of pixels (i.e., each threshold pixel value is multiplied by that pixel's x-location).

Abstract: A method for rasterizing a graphic primitive (120) in a graphics system generates, starting from graphic primitive description data, pixel data for the graphic primitive, the graphics system comprising a memory which is divided up into a plurality of blocks (a, a+1, b, b+1) which are each associated with a predetermined one of a plurality of areas on a mapping screen (114). Each block of the plurality of blocks (a, a+1, b, b+1) is associated with a memory page in the memory. The method includes scanning the pixels associated with the graphic primitive (120) in one of the plurality of blocks (a) into which the graphic primitive extends, repeating the preceding steps until all of the pixels associated with the graphic primitive have been scanned in each of the plurality of blocks into which the graphic primitive extends, and outputting the pixel data.

Abstract: A method, apparatus, and system are described for rasterizing a triangle. Pixel parameter values are interpolated by adding or subtracting a vertical delta and/or by adding or subtracting a horizontal delta within a 4×4 tile of 16 pixels.

Abstract: In one embodiment, selecting a screen region on a screen of a monitor of a computer graphics display system to activate in rendering a straight line segment. Steps of aligning a rectangular grid to screen region boundaries, wherein the screen includes a screen space divided into at least one screen region, locating a first and second endpoints of the straight line segment on the screen space, defining a rectangular bounding box in the screen space having vertices at the first and second endpoints, identifying each screen region that at least partially overlaps the bounding box, and selecting each identified screen region through which the straight line segment passes to activate for rendering the straight line segment on the screen are disclosed.

Abstract: A method and apparatus are disclosed for analyzing a boundary of an object. An embodiment for determining defects of a boundary to sub-pixel precision and an embodiment for fast correlation scoring are disclosed. The boundary is analyzed by matching a first boundary, such as a model of an ideal object boundary, to a second boundary, such as the boundary of an object being produced at a factory. The boundaries are represented as a set of indexed vertices, which are generated by parsing the boundaries into a set of segments. One embodiment refines the parse through merging segments and reassigning data points near the endpoints of the segments. The model produced is very accurate and is useful in other applications. To analyze the boundaries, the sets of indexed vertices are matched, and optionally the segmentation of the second boundary is refined to increase the extent of matching.

Abstract: Embodiments of the present invention provide a method and apparatus for determining the zones that a polygon overlaps to minimize the bins that are updated during binning and reduce the number of polygons to be set up in the render phase. The polygons supported include, but are not limited to, points, lines, triangles and rectangles. Each zone has associated with it a batch buffer to which data is written back for the polygons that overlap that zone. This data includes the setting up of state and the indices for those polygons. Since the zones that a polygon overlaps is precisely determined, the data written back is minimized and the polygons to be set up during the render phase is optimally reduced.

Abstract: A line segment detector includes a first weighted average section which calculates the weighted average of pixel values in a first detecting window. The detector also includes a second weighted average section which calculates the weighted average of pixel values in a second detection window. A differentiating section calculates the absolute value of a difference between the outputs of the first and second weighted average sections. A dot detecting section calculates the average of absolute differential values between pixels in a vertical line direction, a horizontal line direction, and diagonal directions set in a detection window in an area containing the target pixel.

Abstract: A computer implemented method cross-fades intensities of a plurality of overlapping images by identifying pixels in a target image that are only produced by a first source image. The weights of all the corresponding pixels in the first source image are set to one. Pixels in a second source images contributing to the target image are similarly identified and set to one. the weight of each remaining pixel in the first and second images is inversely proportional to a distance to a nearest pixel having a weight of one. Then, the first and second source image can be projected to form the target image.

Abstract: A printer forms an approximate of a Bezier curve as a sequence of line segments. Two parametric equations, X(t) and Y(t), are employed. Two methods can be used to evaluate the parametric equations. Both use fixed point integer arithmetic to directly calculate points along the curve which are the values of the X(t) and Y(t) equations. The first method sets the number of steps of the parametric variable are equal to an integral power of 2. This gives a predictable execution time and uses line segments to connect the points as a piecewise straight line approximation to the curve. The number of steps is set as the next higher power of 2 than an estimated length of the curve. The second method allows Y(t), the scan line variable, to change only in predetermined integer steps. The value of X(t) is evaluated for each t corresponding to the integer step in Y(t). This second method has a natural advantage, if a closed path is being decomposed as a run array rather than a collection of trapezoids.

Abstract: An apparatus and method for supporting editing of a segment displayed on a screen includes: specifying a segment to be edited; extracting attribute information at least containing information on a starting point and an endpoint of the segment; determining the starting point and the endpoint of the segment, or either one of the starting point and the endpoint of the segment, based on the attribute information; and displaying the starting point and the endpoint of the segment, or either one of the starting point and the endpoint of the segment.

Abstract: The middle of line segments may be drawn on a computer display using an iterative method that reduces the number of calculations required. The process is repeated for each column. The first pixel is plotted according to a formula that allows the first pixel to best represent the location of the line in the column. A second pixel is then plotted either above, below, to the left of, or the right of the first pixel depending on the direction of the line. A normalized intensity value between 0 and 1.0 is then assigned to the first pixel according to the amount of area above, below, to the left of, or the right of the line in the first pixel depending on the direction of the line. This value may be assigned using a variable computed in plotting the first pixel. A normalized intensity value for the second pixel equal to 1.0 minus the normalized intensity value of the first pixel may then be assigned. Finally, the first and second pixels are shaded according to the normalized intensity values.

Abstract: Starting and ending caps of smooth line segments may be drawn on a computer display without complicated calculations and avoiding the use of inverse square root calculations by drawing the caps using rectangles. The direction of the line segment may be determined, and using the direction certain pixels in a four-pixel grouping may be selectively illuminated. The normalized intensity values of the illuminated pixels may be determined by computing an x-fraction and a y-fraction, representing the distance in the x-direction and y-direction between a sample origin point in a corner of the four-pixel grouping and the closest corner of a region covered by the mathematical origin or endpoint corrected for the thickness of the line segment. It is generally preferable for only two pixels to be illuminated for each cap, the pixels chosen according to a formula ensuring that there are no perception problems when two smooth line segments share a common mathematical origin or endpoint.

Abstract: Starting and ending caps of smooth line segments may be drawn on a computer display without complicated calculations and avoiding the use of inverse square root calculations by drawing the caps using rectangles. The direction of the line segment may be determined, and using the direction certain pixels in a four-pixel grouping may be selectively illuminated. The normalized intensity values of the illuminated pixels may be determined by computing an x-fraction and a y-fraction, representing the distance in the x-direction and y-direction between a sample origin point in a corner of the four-pixel grouping and the closest corner of a region covered by the mathematical origin or endpoint corrected for the thickness of the line segment. It is generally preferable for only two pixels to be illuminated for each cap, the pixels chosen according to a formula ensuring that there are no perception problems when two smooth line segments share a common mathematical origin or endpoint.

Abstract: A method, apparatus and article of manufacture for generating regularized tangents of curves. The method comprises the steps of bounding a length of the arc, computing a chord vector, where the chord vector corresponds to the bounded length of the arc, generating a tangent vector, where the tangent vector is substantially normal to the chord vector, and regularizing the tangent vector, where the regularized tangent vector approximates a true tangent vector to the arc.

Abstract: A method for mapping a boundary for a multi-pel thickness line into a bitmap image which describes the pel boundary with respect to an orthogonal pel array. The line has thickness T centered around a spine between a start and stop point. The boundaries for the rounded ends of the line are determined by centering a pre-stored T-diameter pel dot boundary with respect to the start and stop points. The rounded end boundaries are tangentially connected by a first pair of sides of a rectangular perimeter whose remaining two sides diametrically intersect the dot boundaries. The start point, the thickness, and line slope are utilized for estimating and mapping four corner points of the rectangular perimeter with respect to the orthogonal pel array. The vertical orientation of the mapped corner points designate up to five sections of the line boundary including two end sections, one of which lies above an uppermost corner point, and the other below a lowermost corner point.

Abstract: A method and system for creating a controllable, shaped, and scalable graphical user interface (“GUI”) object for use in an application program displayed on a computer. An infinite resolution scheme according to the present invention may display a GUI in any shape at any size with minimal or no loss of original image quality. Infinite resolution may be accomplished by storing optimized vector image data (“OVID”), as opposed to raster-type data, for the outline and body of the image to be displayed. When the image is resized or reshaped, the OVID is accessed so that the original quality of the image is captured and maintained.