ISSN 2079-3537      


Scientific Visualization, 2019, volume 11, number 1, pages 91 - 106, DOI: 10.26583/sv.11.1.08

Building and Visualization of Sleek 3D Surfaces without Misplaced Extremes

Authors: K.V. Ryabinin1, K.A. Matkin2

Perm State University, Perm, Russia

1 ORCID: 0000-0002-8353-7641,

2 ORCID: 0000-0002-0444-9476,



The paper is devoted to the visualization of functional dependencies expressed as y= f(x,z) by building sleek 3D surfaces based on discrete sets of points. The criteria of sleek surface quality are formulated taking into account the needs of scientific visualization and visual analytics. The most important criterion is the absence of misplaced extremes and oscillations on the result surface, because such artifacts can deliver false information about the process being represented by the visualized data. The methods of building smooth surfaces in the most popular scientific visualization software are examined against the formulated criteria and it is discovered that the misplaced extremes are an issue in modern visualization tools. To tackle this problem the new approach of building sleek surfaces is proposed. This approach is based on the previously developed algorithm of building smooth 2D curves that was generalized to the three-dimensional case.

The developed surface building algorithm consists of the following main steps. Assuming to have the input data as a regular grid of 3D points, which correspond to the table-defined function y= f(x,z), we first propose to build the set of smooth 2D curves along X and Z axes. Afterwards, we propose to build bicubically blended Coons patches for all quads bounded by each 4 neighbor points from the original data set. Then we discretize each Coons patch by emitting new points to reach needed surface resolution. Next, we triangulate the created set of points and calculate vertex normals using smoothing groups algorithm. Last, we smooth the field of normals using Gaussian blur function.

The proposed algorithm meets the formulated criteria and ensures high visual quality of result surfaces. It was integrated into multiplatform charting library NChart3D and scientific visualization system SciVi, where it proved its correctness and stability by solving real-world scientific visualization tasks.


Keywords: smooth interpolation, Bezier curve, Coons patch, Gaussian filter, misplaced extremes, smooth surface, charts rendering, visual analytics.