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Scientific Visualization
| Issue Year: | 2017 |
| Quarter: | 1 |
| Volume: | 9 |
| Number: | 1 |
| Pages: | 50 - 72 |
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| Article Name: |
VISUALIZATION OF SMOOTH CURVES WITHOUT MISPLACED EXTREMES BASED ON DISCRETE POINT SET |
| Authors: |
K.V. Ryabinin (Russian Federation) |
| Address: |
K.V. Ryabinin
kostya.ryabinin@gmail.com
Perm State University, Perm, Russian Federation |
| Abstract: |
The paper is devoted to the visualization of discrete point set as a smooth curve that should have no misplaced extremes (extremes not belonging to the input point set), awry self-intersections (self-intersections of the interpolation curve while the polygonal line connecting the input points has no self-intersections) and oscillations (essential divergence of the interpolation curve from the polygonal line connecting the input points). Such requirements are critical in some visual analytics tasks, for example while analysing the representative measurement results (in econometrics, physics, etc.), because they help to interpret the input data properly and uniquely.
Popular visualization software products that are able to render smooth curves based on discrete point sets and popular smooth interpolation algorithms are examined. It is found out that only a few of them meet the mentioned requirements. Therefore the development of a new smooth interpolation approach ensuring absence of misplaced extremes, awry self-intersections and oscillations is a challenging task.
The original solution of this task for 2D-case is described. The proposed solution is based on the piecewise parametric curve constructed of cubic Bezier curves. The endpoints of each Bezier curve belong to the input data set while the intermediate control points are calculated to make the result curve meet the declared requirements.
The proposed interpolation method can be easily configured for solving scientific visualization problems with the special requirements of visual features. In common case the visual quality of the result curve is competitive with the known methods and software means. The implementation of the described interpolation algorithm is integrated in the data visualization library NChart3D and in the scientific visualization system SciVi. |
| Language: |
Russian |
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