Topological Integrity for Dynamic Spline Models During Visualization of Big Data

In computer graphics and scientific visualization, B-splines are common geometric representations. A typical display method is to render a piecewise linear (PL) approximation that lies within a prescribed tolerance of the curve. In dynamic applications it is necessary to perturb specified points on the displayed curve. The distance between the perturbed PL structure and the perturbed curve it represents can change significantly, possibly changing the underlying topology and introducing unwanted artifacts to the display. We give a strategy to perturb the curve smoothly and keep track of the error introduced by perturbations. This allows us to refine the PL curve when appropriate and avoid spurious topological changes. This work is motivated by applications to visualization of Big Data from simulations on high performance computing architectures.