Rendering the intersections of implicit surfaces

The article presents algorithms for rendering the intersection curves of implicit surfaces. The algorithms use octree-based recursive space subdivision techniques, within a viewing cube specified by the user. The subdivision process employs interval techniques to increase the algorithms' robustness. Applications for these algorithms include rendering the intersection curves of two surfaces, aiding the visualization of individual surfaces, plotting contour lines and rendering contour maps of functions defined on implicit surfaces, and trimming one implicit surface against another. Examples of functions whose contour lines can be plotted by the techniques described are various planar contours, and the Gaussian and mean curvatures of implicit surfaces.