Stochastic visualization of intersection curves of implicit surfaces

We propose a stochastic method to visualize intersection curves of complex implicit surfaces. Our method performs a stochastic ‘uniform search’ on an implicit surface to visualize its intersection curves, which scatter over the whole surface disconnectedly. The method also offers the capability to perform an efficient ‘intensive search’ that enables quick investigation of only a part of interest on an implicit surface. The method generates high-density points on intersection curves. This realizes precise visualization of the curves with point-based graphics. The visualization precision realized by our method is higher than that of the conventional intersection-finding/visualizing methods, e.g., the marching methods. Our method is also applicable to precise visualization of contours based on general curvilinear coordinates. This can help our visual understanding of rough/fine structures of complex implicit surfaces. To demonstrate effectiveness of the method, we apply it to complex implicit surfaces that approximate data sets of 105105 or 106106 3D points.