Visualization Of Curve And Surface Data Using Rational Cubic Ball Functions
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Date
2018-02
Authors
Wan Jaafar, Wan Nurhadani
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
This study considered the problem of shape preserving interpolation through
regular data using rational cubic Ball which is an alternative scheme for rational
Bézier functions. A rational Ball function with shape parameters is easy to
implement because of its less degree terms at the end polynomial compared to
rational Bézier functions. In order to understand the behavior of shape parameters
(weights), we need to discuss shape control analysis which can be used to modify the
shape of a curve, locally and globally. This issue has been discovered and brought to
the study of conversion between Ball and Bézier curve. A conversion formula was
obtained after a Bézier curve converted to the generalized form of Ball curve. It
proved that this formulae not only valuable for geometric properties studies but also
improves on the computational speed of the Ball curves. A rational cubic Ball
function is extended to a rational bi-cubic Ball function for rectangular patches. It
can also be extended to a rational bi-cubic Ball partially blended function. The
proposed curve and surface schemes preserved and improved inherent shape features
of positivity, monotonicity, convexity and constrained of regular data everywhere in
the domain as compared to the existing ordinary curve, PCHIP (Piecewise Cubic
Hermite Interpolating Polynomial) and surface interpolants, which absolutely do not
preserve the shape of the underlying data. This study added up new knowledge to
shape preserving curve and surface schemes with shape parameters. The schemes
with free parameters help user/designer to modify the curve and surface as they
desires.
Description
Keywords
Visualization of curve and surface data , using rational cubic ball functions