Issue 1

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https://diglib.eg.org/handle/10.2312/66

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    Efficient Parallel Gouraud Shading and Linear Interpolation over Triangles
    (Blackwell Science Ltd and the Eurographics Association, 1995) Narayanaswami, Chandrasekhar
    A parallel raster algorithm to draw Gouraud shaded triangles is presented. At the heart of the algorithm is a new constrained parallel edge-traversal technique. This parallel traversal represents an increased level of parallelism compared to the existing solutions. Next, traditional algorithms take different amounts of time to advance from one horizontal span to another for the left edge and the right edge of the triangle when the slope of one of the edges is more than one and that of the other edge is less than one. This causes one processor to wait for another processor. The parallel constrained edge traversal technique removes this problem by directly jumping from one span to the next. It also ensures that adjacent triangles that share an edge do not share any pixels. Moreover, no cracks occur between adjacent polygons. Unlike some existing algorithms whose complexity depends on the size of the bounding box of the triangle, the complexity of our algorithm is solely dependenton the perimeter and area of the triangle.Due to the above features, the algorithm presented here exposes a greater degree of parallelism at considerably lesser cost and achieves better processor utilization, compared to existing algorithms for this problem1, 2, 3, 4, 5, 6. The algorithm is well suited for hardware implementation.
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    Isometric Piecewise Polynomial Curves
    (Blackwell Science Ltd and the Eurographics Association, 1995) Fiume, Eugene
    The main preoccupations of research in computer-aided geometric design have been on shape-specification techniques for polynomial curves and surfaces, and on the continuity between segments or patches. When modelling with such techniques, curves and surfaces can be compressed or expanded arbitrarily. There has been relatively little work on interacting with direct spatial properties of curves and surfaces, such as their arc length or surface area. As a first step, we derive families of parametric piecewise polynomial curves that satisfy various positional and tangential constraints together with arc-length constraints. We call these curves isometric curves. A space curve is defined as a sequence of polynomial curve segments, each of which is defined by the familiar Hermite or Bezier constraints for cubic polynomials- as well, each segment is constrained to have a specified arc length. We demonstrate that this class of curves is attractive and stable. We also describe the numerical techniques used that are sufficient for achieving real time interaction with these curves on low-end workstations.
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    Symbolic and Numeric Computation in Curve Interrogation
    (Blackwell Science Ltd and the Eurographics Association, 1995) Elber, Gershon
    The control of shape of curves is of great importance in computer aided geometric design. Determination of planar curves convexity, the detection of infection points, coincident regions, and self intersection points, the enclosed area of a closed curve, and the locations of extreme curvature are importantfeatures of curves that can affect the design, in modelling environments.In this paper, we investigate the ability to robustly answer the above queries and related questions using an approach which exploits both symbolic computation and numeric analysis.
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    Image Warping Using Few Anchor Points and Radial Functions
    (Blackwell Science Ltd and the Eurographics Association, 1995) Arad, Nur; Reisfeld, Daniel
    Transformations based on radial basis junctions have proven to be a powerful tool in image warping. In the present work we decompose these transformations into linear and radial terms, and show examples where such a decomposition is advantageous. Locally supported basis functions are introduced. Several applications are demonstrated, and a comparison with other warping techniques is carried out. Finally, some fine points of image warping are discussed.
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    An Algorithm for Perspective Viewing of Objects Represented by Octrees
    (Blackwell Science Ltd and the Eurographics Association, 1995) Aref, Walid G.; Samet, Hanan
    A new algorithm is presented for viewing three-dimensional objects, represented by an octree, from an arbitrary location. The algorithm generates aperspective view of the objects while eliminating hidden surfaces. The viewer can be located anywhere inside or outside the objects. The algorithm presented in this short notefixes an artifact that is generated by a previously published algorithm due to Meagher when the viewer is located in certain regions in space. The new algorithm traverses the octree in a back-to-front order and recursively chooses correct orders for visiting the sons of non-leaf nodes.
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    Line Clipping Using Semi-Homogeneous Coordinates
    (Blackwell Science Ltd and the Eurographics Association, 1995) Nielsen, Hans Peter
    The dual intersection test is described. It is a new method for deciding whether a line intersects a window. The concept of semi-homogeneous coordinates is introduced. It allows us to define line segments in projective space, and to derive a generalized Cohen-Sutherland end-point test for such segments. When this is combined with the dual intersection test, we obtain new clipping algorithms for 2D and 3D projective space.