A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Rapid raster ellipsoid shading
ACM SIGGRAPH Computer Graphics
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A system is described for producing 16 mm animated films of moving humanoid figurines and other figures composed of concatenated articulated interpenetrating ellipsoids. For such figures, the hidden line algorithm used consists in solving the quartic equations which result from simultaneous pairs of ellipses viz. (a) the projection of the outline of one being drawn, and (b) that of one potentially obscuring it. This is done in terms of Cohen's parameter, resulting in an ordered list of compacted hidden arcs of each outline. The visible outlines are then generated to the required fidelity separately. Where two ellipsoids interpenetrate, the outline of each is drawn up to the points where it disappears into the other. These points can be found by the simultaneous solution of the ellipse equations of (a) the projection of the outline being drawn, and (b) the projection of the ellipse of intersection of the obscuring ellipsoid with the plane of the outline of the drawn ellipsoid. The viewing window is assumed to be an ellipse also. Parts of objects projecting outside this ellipse are not drawn. The number of quartics to be solved is reduced significantly by testing each pair of ellipsoids for non-intersection of projected outlines by comparing the projected separation of centres with the sum of their maximum semiaxis lengths, and taking advantage of the total obscuration of one ellipsoid by another when discovered.