Abstract: A system for providing information on a computer map display indicates symbol and data components associated with one or more map display symbols. The system provides a symbol expansion display that can be applied to various map display symbols, including normal, cluttered, and de-cluttered.

Abstract: An image processing apparatus is provided for accurately recognizing an edge direction to perform an accurate image interpolation. A direction determining unit recognizes an edge direction of a remarked pixel and outputs it with information on its position to a reliability ranking unit and a directional distribution generating unit. A direction interpolating unit interpolates the remarked pixel in terms of directional interpolation. The reliability ranking unit determines whether or not a interpolated pixel is properly interpolated by the direction interpolating unit, ranks its reliability, and outputs a result to a directional distribution generating unit. This directional distribution generating unit generates directional distribution based on directional information and reliability information. A direction selecting unit recognizes an edge direction based on the directional distribution generated by the directional distribution generating unit.

Abstract: A sample-to-pixel calculation unit in a graphics system may comprise an adder tree. The adder tree includes a plurality of adder cells coupled in a tree configuration. Input values are presented to a first layer of adder cells. Each input value may have two associated control signals: a data valid signal and a winner-take-all signal. The final output of the adder tree equals (a) a sum of those input values whose data valid signals are asserted provided that none of the winner-take-all signals are asserted, or (b) a selected one of the input values if one of the winner-take-all bits is asserted. The selected input value is the one whose winner-take-all bit is set. The adder tree may be used to perform sums of weighted sample attributes and/or sums of coefficients values as part of pixel value computations.

Abstract: In an information processing apparatus for conducting an affine transformation representative of ( x ? y ? z ? ) = A ? ( x y z ) + ( t 1 t 2 t 3 ) , a matrix A ? = ( a 11 ? a 12 ? a 13 ? a 21 ? a 22 ? a 23 ? a 31 ? a 32 ? a 33 ? ) = ? ? ? ? A = ( ? ? ? ? a 11 ? ? ? ? a 12 ? ? ? ? a 13 ? ? ? ? a 21 ? ? ? ? a 22 ? ? ? ? a 23 ? ? ? ? a 31 ? ? ? ? a 32 ? ? ? ? a 33 ) obtained by multiplying a matrix A for the affine transformation by ?(?0) is stored in a memory section in advance.

Abstract: Multi-thread video data processing for use in a computer video display system. The parameters of vertex data are grouped into a plurality of groups. The computation needs of each group are broken down into several arithmetic operations to be performed by corresponding arithmetic units. The units concurrently process the vertex data.

Abstract: An imaging or other sensory reproduction system efficiently converts image or other sensory data between a perceptual color space (e.g., the sRGB color space) and a physical color space (unity gamma) or other perceptual/physical sensory models that are related by an expression involving a computationally expensive exponential function. The imaging system calculates exponential functions that can be composed from computationally inexpensive operations, such as square root, square, reciprocal, as well as multiplications and/or additions and subtractions. These computationally less expensive functions are then combined, such as in a weighted and/or offset mean, summation or difference to approximate the computationally expensive exponential function. The imaging system evaluates the expression using the approximation to efficiently yield the converted image data.

Abstract: Pixel clock frequency and optimum sampling phase adjustment is an important requirement in Flat panel display monitors (FPDM) with an analog video interface. This invention proposes a new and more advanced method for frequency an optimum sampling phase determination. It is based on analyzing the content of the image to arrive at an optimum value of phase and frequency by directly optimizing image quality. The method differs from exsisting methods on two counts. First, no assumptions are needed about the precise value of expected frequency. Second, instead of following a two step approach of first determining frequency and then phase, this invention makes possible a single pass phase-frequency optimization.

Abstract: An image processor includes: a color conversion unit for converting an input signal to color signals of at least four colors; a gamma correction unit for performing gamma correction on the color signals; a binarization unit for binarizing the color signals through comparison with a threshold value; a superimposing unit for superimposing a color signal of at least one color but of the binarized color signals on another color signal to convert the signals to a superimposed color signal; logical operation unit for performing a logical operation previously defined for an image of three or fewer colors on the superimposed color signal; and a separator for separating color signals as an output of the logical operation unit into separated color signals of at least four colors.

Abstract: According to one embodiment of the invention, a computerized method for computing a transversal derivative field along a curve on a surface includes receiving data defining the surface, the surface represented in terms of parameters u and v as S(u,v), and receiving data defining the curve, the curve represented in terms of a parameter t as c(t). The method also includes receiving a number equal to N constraint conditions for the derivative field, wherein N is a positive integer and determining the transversal derivative L(t) field according to the formula L ? ( t ) = ? S ( u ? ( t ) , v ? ( t ) ) ? w , where i is an index identifying a particular one of N numbers of constraint conditions and L(ti) is the value of the transversal derivative field at the ith constraint condition and w is a scalar function of u and v that satisfies ? S ( u ? ( t i ) , v ? ( t i ) ) ? w = L ? ( t i ) .

Abstract: A method of comparing two rectangles of a circuit design structure for overlap is provided. The two rectangles being compared are modified conceptually in such a way as to reduce the amount of computation necessary to determine if the two rectangles overlap. In one embodiment, a first rectangle is reduced in both x- and y-directions to a single point residing in the center of that rectangle, while the size of the second rectangle is expanded in both x- and y-directions by the same amount, resulting in an enlarged rectangle. A determination of whether the single point resides within the enlarged rectangle thus indicates if the two original rectangles overlap. Similarly, in another embodiment, a first rectangle is reduced in the x-direction only, resulting in a y-directed line segment, while a second rectangle is reduced in the y-direction, resulting in an x-directed line segment.

Abstract: A method of processing image data for display on a pixelated imaging device is disclosed. The method comprises: pre-compensation filtering an image input to produce pre-compensation filtered pixel values, the pre-compensation filter having a transfer function that approximates the function that equals one divided by a pixel transfer function; and displaying the pre-compensation filtered pixel values on the pixelated imaging device. In another disclosed method, the method further comprises: pre-compensation filtering an image input for each of a plurality of superposed pixelated imaging devices, at least two of which are unaligned, to produce multiple sets of pre-compensation filtered pixel values; and displaying the multiple pre-compensation filtered pixel values on the plurality of superposed pixelated imaging devices.

Abstract: The present invention provides a method for approximating zeros (roots) of polynomials using an iterative technique and displaying graphical images based on the results of that technique. The science of polynomiography is based on the use of at least one of an infinite number of iteration functions designed for the purpose of approximation of roots of polynomials.

Abstract: An apparatus for line drawing using a plurality of pixels to display a line, including a first parameter generating module, a second parameter generating module, a storage module, a retrieving module, and a calculating module. In this case, the first parameter generating module generates a first parameter according to a slope of the line. The second parameter generating module generates a second parameter according to the distance between one of the pixels and the line in axial directions. The storage module stores an index table, which records at least a blending factor and the correlations between the first parameter, second parameter, and blending factor. Therefore, the retrieving module searches for the blending factor from the index table according to the first and second parameter. Finally, the calculating module determines the color of this pixel according to the blending factor.

Abstract: Systems and methods provide a more efficient and effective gradient computation. Specifically, in one embodiment, a method is provided for calculating a texture-mapping gradient, which comprises calculating constant values for use in a gradient-calculating equation, passing the constant values to logic configured to calculate the gradient, and computing the gradient using barycentric coordinates and the calculated constant values. In accordance with another embodiment, an apparatus is provided for calculating a texture-mapping gradient, which comprises logic for calculating constant values for use in a gradient-calculating equation, and logic for computing the gradient-calculating equation using barycentric coordinates and the calculated constant values. In accordance with another embodiment, a computer-readable medium is also provided that contains code (e.g., RTL logic) for generating the computational logic mentioned above.

Abstract: An image processing apparatus draws an image, stores the drawn image in a memory, reads image data from the memory along a raster direction, and executes a processing operation required for a display with respect to the read image data to output the processed image data to a display device. A display processing unit executes a processing operation including a coordinate calculation with respect to the image data read out along the raster direction. As a result, the image can be formed at high speed even under transition state of displayed images.

Abstract: A tolerance display system allows workers to easily obtain accurate size information at actual worksites. The tolerance display system includes a tolerance display device which has a storage device storing standards data/files related to general tolerance, an information input device for inputting information, an operation unit for reading out standards data related to a general tolerance from the storage device based on data input by the information input device and calculating limits of size, and an output device for displaying the standards data, the limits of size and other information. The information input device includes an industry type menu input portion for selecting and inputting a product name of a desired industry type, a specified condition input portion for inputting specified conditions such as a special item, a tolerance class, a basic dimension, and a numerical value/arithmetic operator input portion for inputting a numerical value/arithmetic operator.

Abstract: A method for modifying the design of a component with regard to one or more criteria using a virtual model of the component, wherein a virtual model of the component is produced by combination of the component from basic objects with the aid of Boolean operators, and each basic object is assigned an information element in which attributes of the basic object are stored. Each basic object is decomposed into primitive objects which are combined with aid of Boolean operators, the primitive objects being surfaces or bodies which can be decomposed into rasters. Each geometrical contact surface is assigned a connecting element in which information for coordinating the objects is stored, and the rastering of the primitive objects is performed by a conventional gridding method. A modification of the geometrical shape of objects is undertaken with the information elements defining the limits of possible modifications.

Abstract: Systems and methods for calculating a modification of a geometrical shape by applying an inverse modification function to an array representing the shape. An array representing the geometrical shape is defined on a multi-dimensional space. A modification function is used to modify the geometrical shape. A user or a programmed computer can select the modification function. The computer applies an inverse of the modification function to the array. The computer deduces a change in the geometrical shape from the modified array. An advantage of the system and method is the ability to compute shape changes in certain situations where a direct computation is cumbersome or otherwise inconvenient.

Abstract: An apparatus for generating an image. The apparatus includes a computer. The apparatus includes a display connected to the computer upon which images from the computer appear. The apparatus includes a mechanism for producing images with texture that do not have visible grid artifacts. The producing mechanism disposed in the computer. A method for generating images. The method includes the steps of producing the images with texture that do not have visible grid artifacts with the computer. There is the step of displaying the images on a display.

Abstract: A dither matrix generator defines a three-dimensional array of pixels referred to as the “cluster array” in which each pixel is designated based on its value as a “cluster pixel” or a “void pixel”. The dither matrix generator also defines a three-dimensional array referred to as the “dither matrix,” and assigns rank values to the dither matrix in two stages. In the first stage, the dither matrix generator identifies the largest cluster in the cluster array, identifies a cluster pixel located in the largest cluster, assigns a rank value to the element in the dither matrix corresponding to the cluster pixel and removes the cluster pixel from the cluster array. The process is repeated until the cluster array contains no cluster pixels.

Abstract: Pixels in a YUV format including a Y component representing luminance and U and V components representing chrominance are converted into a RGB format including R, G, and B components respectively representing red, green, and blue colors in order to display images on a video display device such as a CRT (Cathode Ray Tube) or a LCD (Liquid Crystal Display). The present invention relates to an apparatus and a method for converting the pixels from the YUV format to the RGB format using color look-up tables with a small memory capacity. The R component is obtained from the first and second color look-up tables using the Y and V components as indexes, and the G component is obtained from the first, third, and fourth color look-up tables using the Y, U, and V components as indexes, and the B component is obtained from the first and fifth color look-up tables using the Y and U components as indexes.

Abstract: An image processing device includes a data zone expansion circuit and an image processing circuit. The data zone expansion circuit receives input data, increases a number of data bits of the input data, and provides data with the increased number of data bits. The image processing circuit performs image processing on the data with the increased number of data bits.

Abstract: An approach is described for modifying subobjects of geometry objects based on per-subobject objects. A per-subobject object is associated with a sequence of components, such as a modifier stack, that are used to modify a geometry object. The per-subobject object may take one or more actions with respect to subobjects of the mesh object, such as applying data to specified faces. After a subsequent modification of the geometry object, the per-subobject object reapplies data to the faces that result from the modification. For example, the per-subobject object may specify the data to apply to faces that result from splitting faces during the modification or to faces that result from merging faces during the modification. The data for the faces may be accessed using a data channel that is associated with the per-subobject object.

Abstract: An approach is described for using hardware devices to generate modified geometry objects based on instructions provided by extension objects. An extension object is associated with a sequence of components, such as a modifier stack, that are used to modify a geometry object to generate an initial representation of the geometry object. Instructions that are based on the extension object are associated with the initial representation. A graphics device, such as a hardware shader, is used to generate a final representation of the geometry object based on the instructions and the initial representation. The instructions may be executed by an application program interface to provide instructions to the graphics device for generating the final representation of the geometry object. The instructions may be generated based on the extension object, and a graphics card may execute the instructions to generate the final representation of the geometry object.

Abstract: A technique for expressing an elastic body using computer graphics. The elastic body is expressed by transforming coordinates of shape specific points which specify the shape of an object using a transformation matrix. Each element of the transformation matrix is expressed by a function having time as a variable which converges to a corresponding element of a matrix that represents the motion of the object when the object is assumed to be a rigid body. By substituting a predetermined time into this function, a value of each element of the transformation matrix is determined. The shape of the object is determined based on the coordinate values of the shape specific points after coordinate transformation.

Abstract: There is provided an apparatus including a plurality of processors 20, which generates a plurality of candidate status variable values as a candidate of status variable value at which the status of object image is fixed and which selects a status variable value having the highest consistency with the condition from among them, and an influence controller 10 obtains the status variable value from each processor to broadcast the obtained status variable value to all processors at the same time. Since each processor selects a status variable value having the highest consistency with the condition from among the plurality of candidates, an appropriate image can be obtained. Moreover, the processor can generate the status variable value at the next point in consideration of the status variable values of all processors sent from the influence controller so as to obtain an image in which a plurality of objects is influenced each other.

Abstract: A method for generating image compression quantization matrices is disclosed. A method includes a step of locating a frequency coefficient (120) within a transform array (107). A method also includes a step determining a frequency content (122) for the frequency coefficient (120). Method also includes the step of determining the orientation content for the frequency coefficient (120). The method also includes the step of selecting a quantization matrix (110) correlating to the frequency content (122) and the orientation content. The method also includes the step of quantizing the transform array (107) with the quantization matrix (110).

Abstract: A method, apparatus and article of manufacture are provided for handling both scalar and vector components during graphics processing. To accomplish this, vertex data is received in the form of vectors after which vector operations are performed on the vector vertex data. Next, scalar operations may be executed on an output of the vector operations, thereby rendering vertex data in the form of scalars. Such scalar vertex data may then be converted to vector vertex data for performing vector operations thereon.

Abstract: Disclosed are an arithmetic unit and an arithmetic processing method. In the arithmetic unit, in linear interpolation of a parameter of a pixel to be used to plot an object in a three-dimensional video, an operation result value can be fixed in response to a particular gradient value of the parameter and power consumption arising from charging and discharging through a clock wiring line can be reduced. The arithmetic unit includes an arithmetic operation element for linearly interpolating a parameter of a pixel in a triangle based on coordinate values of a vertex of the triangle and gradient values of the parameters in X and Y directions, a clock supply element for supplying a clock signal to the arithmetic operation element, a detection element for detecting a particular gradient value of the parameter in the X direction or/and the Y direction, and a control element for controlling the clock supply element in response to a gradient value of the parameter detection signal received from the detection element.

Abstract: A method and apparatus for implementing stack extensions in a modifier stack that is associated with a plurality of components that are sequentially applied to a geometry object when the modifier stack is evaluated. According to one aspect of the invention, an extension channel object is attached to the geometry object. The extension channel object is associated with a notification mechanism that notifies the extension channel object if a particular event occurs while the modifier stack is being evaluating. In response to receiving a notification that one of the plurality of components has caused a particular event to occur while the modifier stack is being evaluated, the extension channel object influences how the geometry object is modified by the component within the modifier stack.

Abstract: An improved method of digital halftoning using “screens” or dither arrays is provided, including stochastic dither arrays (e.g., stochastic screening). The weakness of ordinary stochastic dithering is its isolated or dispersed dots and the related problems of dot gain and consistent dot formation when used with certain types of printers. However, the inconsistent formation of isolated dots causes unpredictable variations in uniformity and tone. The present invention solves this problem by grouping dots into small clusters, which may be rendered more consistently. Unlike conventional clustered-dot halftoning, however, this method arranges the dot clusters in a stochastic fashion to avoid objectionable periodic artifacts. A novel weighting function is used to generate the dot clusters, in which one function of a first extent is subtracted from another function of a second extent, thereby creating clusters of dots that center at locations where the weighting function chooses to place dots.

Abstract: A polygon that is made visible in an image. A selection is made between a first and second algorithm for computing a visual effect of the polygon. The first algorithm computes an update value for the polygon and pixel values for spatially successive pixels in the polygon by successively updating the pixel values using the update value. The second algorithm computes the pixel values for each pixel in the polygon individually, without said updating, the first algorithm being selected if the size of the polygon exceeds a threshold, the second algorithm being selected if the polygon size does not exceed the threshold.

Abstract: In a system for displaying medical images, medical images are generated from views internally within a body by means of x-rays, CAT scan, or MRI. The images are spaced in time or are views of spaced slices through tissue or through an organ within a body. The spacing between the images is such that the display of the images as a motion picture would result in the motion being depicted as jerky in the motion picture. A video processor generates dense motion vector fields between adjacent frames of the original set of images and, from the dense motion vector fields, generates interpolated images between the images of the original set. The interpolated images are assembled into a motion picture set of images, which are displayed by a video display device.

Abstract: A method and apparatus for parallel processing of geometric aspects of video graphics data include processing that begins by determining whether an object-element is within a clipped volume. The processing continues by determining whether the object-element is to be clipped when it is within the clipped volume. The processing then continues by performing in parallel, a clipping function and an attribute derivation function upon the object-element when the object-element is to be clipped. The attribute derivation function may include performing a light function, texture map function, etc.

Abstract: A normalization circuit suitable for use in a graphics adapter is disclosed. The circuit is configured to receive vertex data and includes a set of multiplexer circuits, a set of functional units, and a control circuit. The outputs of the set of multiplexer circuits provide inputs to the set of function units and the control circuit is configured to control the select inputs of the set of multiplexer units to calculate a unit normal vector and a unit eye vector from the received vertex data. The set of functiontional units may include a pair of floating point multipliers and a floating point adder. The inputs of the first floating point multiplier may be connected to outputs of first and second mulitplexers such that the first multiplier is enabled to generate square values for x, y, and z components of the vertex data. The inputs of the floating point adder may be connected to outputs of third and fourth multiplexers, wherein the floating point adders is enabled to generate a sum of squares values.

Abstract: A system and method are provided for a dedicated hardware-implemented viewport operation in a graphics pipeline. Included is a transform/lighting module for transforming and lighting vertex data. Also provided is viewport hardware coupled to the transform/lighting module for performing a viewport operation on the vertex data. A rasterizer is coupled to the viewport hardware for rendering the vertex data.

Abstract: A method for modifying, in particular optimizing, the design of a component with regard to one or more criteria using a virtual model of the component, having the following steps:

Abstract: By making it possible to freely change calculations of as well as variables that are input into the same calculation circuits, dedicated circuits corresponding to rendering functions become unnecessary, and in order to realize multi-functional rendering with circuitry of a small scale, a graphic image rendering apparatus includes a rendering information generation portion that generates rendering parameters corresponding to X and Y coordinates of pixels constituting a graphic image, a pixel calculation portion that, for each pixel, makes a selection as appropriate from the rendering parameters and a constant and performs a calculation, and a memory interface portion that writes a calculation result of the pixel calculation portion into a frame memory.

Abstract: A reconfigurable system for performing a set of arithmetic operations. The reconfigurable system may have a frame buffer, an accumulation buffer and a pixel computation unit. The pixel computation unit includes a control unit and one or more copies of a reconfigurable circuit. The reconfigurable circuit may include a subtractor, a multiplier, an adder, and a set of multiplexors. The control logic drives selects lines of the set of multiplexors in the one or more circuit copies through one or more computational cycles in order to implement a programmable operation (such as scale and/or bias, accumulate, dynamic blend and matrix multiply). The pixel computation unit may receive pixels values from one or more sources including the frame buffer and the texture buffer, and operate on the pixels using the one or more circuit copies to generate a stream of output pixels.

Abstract: A method renders a graphical object for display on a destination raster of pixels having a destination resolution by rendering the graphical object at a resolution higher than the destination resolution to generate one or more pieces, the pieces in the aggregate representing the graphical object at the higher resolution, and each of the pieces having a position with respect to the destination raster, whereby each piece overlaps one or more pixels; for each of the pieces, calculating a contribution made by the piece to each of one or more pixels according to a selected algorithm, the algorithm being selected by a process applying a plurality of factors; and aggregating all the contributions made to each pixel to determine a value for the pixel.

Abstract: A system and method for converting bitmapped data, for example, weather data or thermal imaging data, to polygons is disclosed. The conversion of the data into polygons creates smaller data files. The invention is adaptive in that it allows for a variable degree of fidelity of the polygons. Matrix data is obtained. A color value is obtained. The color value is a variable used in the creation of the polygons. A list of cells to check is determined based on the color value. The list of cells to check is examined in order to determine a boundary list. The boundary list is then examined to determine vertices. The determination of the vertices is based on a prescribed maximum distance. When drawn, the ordered list of vertices create polygons which depict the cell data. The data files which include the vertices for the polygons are much smaller than the corresponding cell data files.

Abstract: The invention in one embodiment is an apparatus. The apparatus includes a lookup table having a set of entries, each entry capable of maintaining a value. The apparatus also includes a DDA (Differential Digital Analyzer) table having a set of entries, each entry capable of maintaining a value and each entry of the DDA table corresponding to an entry of the lookup table. The apparatus further includes a first multiplexing unit having a set of inputs, each input corresponding to and coupled to an entry of the DDA table. The first multiplexing unit also having a control input, the control input causing the first multiplexing unit to route one of the inputs of the set of inputs to an output. Additionally, the apparatus includes a comparison block having logic suitable for comparing each entry of the lookup table to a comparison value.

Abstract: A method for controlling a data display of the present invention, controlling a display of data including at least one attribute, includes: an attribute conversion step of converting at least one attribute of the data into a display attribute by using at least one mapping function; a display step of displaying the data based on the display attribute; and a parameter changing step of changing a parameter of the mapping function.

Abstract: The present invention is a method and apparatus to generate an anti-flickered pixel from a source pixel having a source pixel value in a display memory. The apparatus comprises a plurality of storage elements, a filter, a comparator, and an output selector. The plurality of storage elements store a sequence of pixels in the display memory which includes the source pixel. The filter is coupled to the plurality of storage elements to filter the sequence of pixels. The filter generates a filtered pixel corresponding to the source pixel. The comparator is coupled to the plurality of storage elements to compare the source pixel value with a threshold value. The comparator generates a comparison result. The output selector is coupled to the filter and the storage elements to select one of the source and filtered pixels according to the comparison result. The selected one of the source and filtered pixels is the anti-flickered pixel.

Abstract: A configurable vertex blending circuit that allows both morphing and skinning operations to be supported in dedicated hardware is presented. Such a configurable vertex blending circuit includes a matrix array that is used for storing the matrices associated with the various portions of the vertex blending operations. Vertex data that is received is stored in an input vertex buffer that includes multiple position buffers such that the multiple positions associated with morphing operations can be stored. Similarly, the single position typically associated with skinning operations can be stored in one of the position buffers. The input vertex buffer further stores blending weights associated with the various component operations that are included in the overall vertex blending operation. An arithmetic unit, which is configured and controlled by a transform controller, performs the calculations required for each of a plurality of component operations included in the overall vertex blending operation.

Abstract: A computer method, apparatus and storage medium is provided for creating quantitative aesthetic graphics from data. The invention utilizes a graph algebra to construct graphs and visually or otherwise represents the graphs as a quantitative aesthetic graphic representation. To create the quantitative aesthetic graphics from data, the data is indexed to form a data set. Thereafter, the data is converted into a variable data structure composed of an index set, a range and a function. The variable data structure is converted into a variable set by using at least one of a blend step, a cross step and a nest step. The variable set is mapped into a set of points and the set of points is mapped into an aesthetic representation.

Abstract: The invention concerns an apparatus for image data computation and for synchronous data output. The invention further concerns an arrangement for producing and reproducing two partial light images which together can be perceived as a light image having a three-dimensional effect. Finally the invention concerns a method of synchronous reproduction of time image sequences by at least two image reproduction devices. The apparatus according to the invention has a master-client structure. A graphics master unit (88) and at least two graphics clients (94) are connected together by way of a first message channel (82) and by way thereof exchange first messages, by means of which computation and projection of the partial images is synchronized.

Abstract: A computer method, apparatus and storage medium is provided for creating quantitative aesthetic graphics from data. The invention utilizes a graph algebra to construct graphs and visually or otherwise represents the graphs as a quantitative aesthetic graphic representation. To create the quantitative aesthetic graphics from data, the data is indexed to form a data set. Thereafter, the data is converted into a variable data structure composed of an index set, a range and a function. The variable data structure is converted into a variable set by using at least one of a blend step, a cross step and a nest step. The variable set is mapped into a set of points and the set of points is mapped into an aesthetic representation.

Abstract: In an image processing apparatus, when the image quality is adjusted, an image before performing an adjustment operation, a default adjustment image and an image to be adjusted are simultaneously displayed, and images of the same video source are simultaneously displayed by a multiscreen display according to a multiscreen synthesis function in order that the image quality adjustment operation can be easily performed.

Abstract: A set diagram display control apparatus performs a set diagram display process. When the elements or number count of each of a plurality of sets is input to a set relation list, the element counts of all set relations are calculated in accordance with the elements or element counts of those sets. A display range of a set diagram is determined in accordance with the input or calculated element counts. The areas of circular diagrams which compose the set diagram are displaced in correspondence to their elements counts in the displayed range. And the displayed positions and radii of the circular diagrams are determined depending on the element count of the set diagram, in order to display the set diagram as composed of the circular diagrams.