A univariate rational quadratic trigonometric interpolating spline to visualize shaped data

This study was concerned with shape preserving interpolation of 2D data. A piecewise C1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of data. Each scheme was tested for plentiful shaped data sets to substantiate the assertion made in their construction. Moreover, these schemes were compared with conventional shape preserving rational quadratic splines to demonstrate the usefulness of their construction

Constrained modification of the cubic trigonometric Bézier curve with two shape parameters

A new type of cubic trigonometric Bézier curve has been introduced in [1]. This trigonometric curve has two global shape parameters λ and µ. We give a lower boundary to the shape parameters where the curve has lost the variation diminishing property. In this paper the relationship of the two shape parameters and their geometric effect on the curve is discussed. These shape parameters are independent and we prove that their geometric effect on the curve is linear. Because of the independence constrained modification is not unequivocal and it raises a number of problems which are also studied. These issues are generalized for surfaces with four shape parameters. We show that the geometric effect of the shape parameters on the surface is parabolic. Keywords: trigonometric curve, spline curve, constrained modificatio

The Construction of Cubic Bezier Curve

The construction of Bezier curves is one of the curves that are commonly discussed in Computer-Aided Geometric Design (CAGD). This study focuses on cubic Bezier curve. The objectives in this study are to review the properties of cubic Bezier curve and construct the cubic Bezier curves. In this study, the expanding equations from the basis function of the curve is used to construct the cubic Bezier curve. Future researchers can expand the degree of the Bezier curves, which is more useful in Computer-Aided Design (CAD), CAGD and engineering. The next studies in Bezier curve are recommended as a contribution for further research

Visualization Of Curve And Surface Data Using Rational Cubic Ball Functions

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

Modelling of Surfaces of Engineering Products on the Basis of Array of Points

The method of designing elements of the surfaces\u27 frames based on array of points is suggested in the work. Elements of frames are contours that are received via interpolation of sets of points, which are selected from the initial array of points. The algorithms have been developed for design plane and spatial contours that represent the curves with specified geometrical properties with prescribed accuracy. Formed contours are used as elements of «Profile» and «Guide Curves» at forming the model of surface by means of function of «Lofted Surface» in CAD system. Using the method of designing elements of frames of the surfaces is actual for modeling of surfaces of technical items that function-interact with the environment. The developed method was proven while modelling functional surfaces that bound an impeller blade channel of a turbine compressor