An updated cross-indexed guide to the ray-tracing literature
ACM SIGGRAPH Computer Graphics
Extrusion and revolution mapping
ACM Transactions on Graphics (TOG)
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In ray tracing a surface of revolution, the problem of finding the point of intersection of an arbitrary ray with the surface of revolution can be reduced to that of finding a point of intersection between two curves in a plane — the so called cut plane. In the cut plane, by using a local coordinate system (x′=x2,z′=z) instead of (x, z) where z is along the direction parallel to the axis of the surface of revolution, and then further translating the origin of the coordinate system along the x′ axis (depending upon the ray), the curve(s) of intersection of the surface of revolution with the cut plane are expressed exactly by the square radial curve defining the surface of revolution itself. We need to find the point(s) of intersection between this square radial curve and a transformed quadratic form of the ray in the cut plane. We represent the square radial curve of the surface of rotation by a variation of the usual strip_tree such that the direction of the sides of the rectangles corresponding to different nodes are parallel to the axes of the local coordinate system, instead of being in arbitrary directions. The terminal nodes in the Strip_tree contain the segments of the square radial curve divided approximately equally lengthwise. The method works efficiently for all cases with a smooth radial curve or a piecewise smooth radial curve.