A scan line algorithm for rendering curved tubular objects

Parametric surfaces and implicit surfaces are generally used for representing curved surfaces in CAD/CG Systems. This paper discusses a curved tubular object which is a surface swept by a sphere/circle moving along a curve. For the trajectory curve, a 3D Bezier curve is employed, and its radius can be varied along the curve. In general, its surface cannot be defined by a closed form, while a high degree of polynomial must be solved for ray/surface intersection. This paper proposes an effective rendering method which uses a scan line algorithm for detecting curved tubular objects on the projection plane. The calculation of the distance from a point to a curve plays an important role in our algorithm. Bezier Clipping Method is employed for this calculation.