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Computer Graphics and Applications, IEEE

Issue 2 • Date March 1990

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Displaying Results 1 - 8 of 8
  • Visualizing chaos: Lyapunov surfaces and volumes

    Page(s): 15 - 19
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (607 KB)  

    The use of a graphic technique to visualize chaos for a dual-parameter one-dimensional map is described. It involves plotting the Lyapunov exponent with both height and color in a three-dimensional map, as a function of the two parameters. Color is determined using a geographic lookup table. A graphics supercomputer can rotate the map in real time. The technique demonstrates graphically interesting behavior in chaotic systems.<> View full abstract»

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  • Volumetric rendering of computed tomography data: principles and techniques

    Page(s): 24 - 32
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (876 KB)  

    The methods and algorithms used for volumetric rendering of medical computed tomography data are described in detail. Volumetric rendering allows for the use of a mixture paradigm for representation of the volume to be rendered and uses mathematical techniques to reduce or eliminate aliasing. A step-by-step description of the process used to generate two types of images (unshaded and shaded surfaces) is included. The technique generates three-dimensional images of computed tomography data with unprecedented image quality. Images generated with this technique are in routine clinical use.<> View full abstract»

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  • A hybrid ray tracer for rendering polygon and volume data

    Page(s): 33 - 40
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (775 KB)  

    Volume rendering, a technique for visualizing sampled functions of three spatial dimensions by computing 2-D projections of a colored semitransparent volume, is extended to handle polygonally defined objects. A hybrid ray-tracing algorithm, whereby rays are simultaneously cast through a set of polygons and a volume data array, is used. Samples of each are drawn at equally spaced intervals along the rays, and the resulting colors and opacities are composited together in depth-sorted order. To avoid aliasing of polygonal edges at modest computational expense, a form of selective supersampling is used. To avoid errors in visibility at polygon-volume intersections, special treatment is given to volume samples lying immediately in front of and behind polygons. The cost, image quality, and versatility of the algorithm are evaluated using data from 3-D medical imaging applications.<> View full abstract»

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  • Investigation of medical 3D-rendering algorithms

    Page(s): 41 - 53
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3046 KB)  

    An investigation of the quality of surface-shading algorithms using computer-simulated test objects is reported. Test results are presented for four algorithms: z-buffer gradient, gray-level gradient, adaptive gray-level gradient, and marching cubes with two extensions. It was found that gray-level gradient shading and marching cubes did not differ greatly, except for thin objects, where adaptive gray-level gradient shading was better. Transparent visualization using transparent gray-level gradient shading is examined. It is shown that although there is no way to assure the fidelity of transparent shading, it is useful when no other surface at all can be determined. Use of a combination of shading methods appears to yield the best visualization of the respective objects.<> View full abstract»

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  • Conformal image warping

    Page(s): 54 - 61
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1537 KB)  

    Numerical and computer-graphic methods for conformal image mapping between two simply connected regions are described. The immediate motivation for this application is that the visual field is represented in the brain by mappings which are, at least approximately, conformal. Thus, to simulate the imaging properties of the human visual system (and perhaps other sensory systems), conformal image mapping is a necessary technique. For generating the conformal map, a method for analytic mappings and an implementation of the Symm algorithm for numerical conformal mapping are shown. The first method evaluates the inverse mapping function at each pixel of the range, with antialiasing by multiresolution texture prefiltering and bilinear interpolation. The second method is based on constructing a piecewise affine approximation of the mapping in the form of a joint triangulation, or triangulation map, in which only the nodes of the triangulation are conformally mapped. The texture is then mapped by a local affine transformation on each pixel of the range triangulation with the same antialiasing used in the first method. The algorithms are illustrated with examples of conformal mappings constructed analytically from elementary mappings, such as the linear fractional map, the complex algorithm, etc. Applications of numerically generated maps between highly irregular regions and an example of the visual field mapping that motivates this work are also shown.<> View full abstract»

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  • A general algorithm for oblique image reconstruction

    Page(s): 62 - 65
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (630 KB)  

    It is shown how to generate oblique slices from a set of parallel slices. An algorithm that can produce planes or contours through the volume without any loss of the volume resolution of the original data set is presented. The algorithm uses the Fourier-shift theorem and is efficient for calculating large numbers of slices. Although the algorithm is general, it is particularly well suited for three-dimensional magnetic resonance images, as demonstrated with examples.<> View full abstract»

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  • Computer modeling of surfaces with arbitrary shapes

    Page(s): 67 - 77
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (874 KB)  

    A detailed description is given of a local mathematical procedure for constructing a geometrically C/sup 1/ surface by interpolating a grid of cubic Bezier curves that meet in a quite general fashion (for example, they need not meet rectangularly). The constructed surface is a composite mosaic of independently parameterized tensor-product Bezier patches of different degrees (maximum of 6*6). Adjacent patches can be made either C/sup 1/ or C/sup 0/ continuous, as desired. The overall surface can have almost any shape that arises in practice, including the closed surfaces used in solid modeling. Because of its locality, the procedure can be applied at different times in different locations of a surface-to-be; for example, it can be used to combine preexisting smaller surfaces.<> View full abstract»

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  • The truth about texture mapping

    Page(s): 78 - 83
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    The author describes how the unique configuration of the planet Uranus influenced him to take a close look at how the layout of a texture map in memory affects the performance of the rendering algorithm. A planet rendering program that calculates, for each occupied pixel on the screen, the latitude and longitude visible at that pixel, is described. It uses this latitude and longitude to index into a texture map to get a surface color. The actual texture color comes from bilinearly interpolating the texture colors at the four texture map pixels that surround that latitude and longitude. This, along with the shading calculations, gives the net color of the pixel. The use of virtual memory, handling page faults, tiling, and address generation are considered.<> View full abstract»

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IEEE Computer Graphics and Applications bridges the theory and practice of computer graphics.

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L. Miguel Encarnação
University of Iowa