Next Article in Journal
Elementary Error Model Applied to Terrestrial Laser Scanning Measurements: Study Case Arch Dam Kops
Previous Article in Journal
A Generic Approach to Covariance Function Estimation Using ARMA-Models
Previous Article in Special Issue
Family of Enneper Minimal Surfaces
Open AccessArticle

An Efficient Method for Forming Parabolic Curves and Surfaces

Department of Computer Aided Design, Saint Petersburg Electrotechnical University “LETI”, Professora Popova 5, 197376 Saint Petersburg, Russia
Mathematics 2020, 8(4), 592; https://doi.org/10.3390/math8040592
Received: 26 February 2020 / Revised: 9 April 2020 / Accepted: 10 April 2020 / Published: 15 April 2020
(This article belongs to the Special Issue Geometric and Topological Methods for Imaging, Graphics and Networks)
A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given. View Full-Text
Keywords: computer graphics; parabolic curves; local coordinate system; new forming method; matrix calculation computer graphics; parabolic curves; local coordinate system; new forming method; matrix calculation
Show Figures

Figure 1

MDPI and ACS Style

Lyachek, Y. An Efficient Method for Forming Parabolic Curves and Surfaces. Mathematics 2020, 8, 592.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop