A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Scan line methods for displaying parametrically defined surfaces
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An improved illumination model for shaded display
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A reflectance model for computer graphics
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Automatic analysis of real algebraic curves
ACM SIGSAM Bulletin
Ray tracing objects defined by sweeping planar cubic splines
ACM Transactions on Graphics (TOG)
Ray tracing generalized cylinders
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Ray tracing parametric surface patches utilizing numerical techniques and ray coherence
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Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
Scan line display of algebraic surfaces
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Ray tracing of Steiner patches
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Visualization of equations in an interactive environment
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Point based rendering of non-manifold surfaces with contours
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Technical Section: Progressive refinement rendering of implicit surfaces
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Point rendering of non-manifold surfaces with features
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Technical Section: Real-time ray casting of algebraic B-spline surfaces
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Wavelet-based multiresolution isosurface rendering
VG'10 Proceedings of the 8th IEEE/EG international conference on Volume Graphics
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Many interesting surfaces can be written as polynomial functions of the spatial coordinates, often of low degree. We present a method based on a ray casting algorithm, extended to work in more than three dimensions, to produce pictures of these surfaces. The method uses a symbolic algebra system to automatically derive the equation of intersection between the ray and the surface and then solves this equation using an exact polynomial root finding algorithm. Included are illustrations of the cusp catastrophe surface, and two unusually shaped quartic surfaces, Kummer's quadruple and Steiner's surface.