The Application of Quadratic Bezier Curve on Rotational and Symmetrical Lampshade

Abstract

The procedure of constructing lampshade is through parameter merger and selection of Bezier surfaces shapeshifters; thus it produces perfect and varied sitting-lamp shades. Constructing sitting-lamp shades requires the study of the physical (lighting) and geometry aspects. In terms of geometry, the existed sittinglamp shade creation models is generally monotonous and constructed from objects pieces. In line with these problems, this research is divided into four stages: First, preparing the data to build a sitting-lamp shade. Second, technical studying to construct the symmetricity of the sitting-lamp shade shape. Third, constructing the parts of the sitting-lamp shade, namely the base, the main part, the roof. Fourth, constructing the complete sitting-lamp shade. The results of this research to obtain the procedures of constructing the sitting-lamp shade namely: First, dividing the major axis into three non-homogeneous sub segments. Second, constructing parts of the sitting-lamp shade namely the base, the main part, and the roof by combining the sitting-lamp shade components from the geometrical objects deformation. Third, filling each sub segment of non-homogeneous parts with parts of the lampshade and creating the boundary curves producing a varied innovative symmetrical models of sitting-lamp shade.

Desain Kotak Hantaran Pernikahan dari Hasil Deformasi Prisma dan Kurva Bezier

“…dengan 𝑘 1 , 𝑘 2 , 𝑘 3 ∈ ℝ (Octafiatiningsih & Sujarwo, 2016). ii) Menginterpolasi segmen garis yang bersesuaian dengan persamaan (5).…”

Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

“…Furthermore, Bezier curve is easier to specify the shape of control polyline than Hermitian curve. For more details about Hermitian and Bezier curves, we refer to [6,9,10]. Now, let us investigate the rotational surfaces according to the axes of rotation in 3 .…”

“…have been studied by geometers and engineers widely in Euclidean space, Minkowski space, Galilean space, pseudo-Galilean space and etc [1,2,3,4,5,7,8]. For example, E. Octafiatiningsih and I. Sujarwo have used Quadratic Bezier curve on rotational and symmetrical lampshade in [9]. So, by using this work we have constructed the present paper which is divided into three steps as follows:…”

“…The most important of these curves are the Hermitian curves, Ferguson curves, Bezier curves and etc. The De Casteljau algorithm has shown that, Bezier curves are written as linear combinations of Bernstein polynomials (for detail about these curves, see [6,9,10]). Also, the geometry of surfaces such as, rotational surfaces, ruled surfaces, rational Bezier surfaces, rational B-spline surfaces, non-uniform rational B-spline surfaces, discrete surfaces and etc.…”

Surface Applications of T-Bezier curves

“…There are lots of curves used in surface design and the Bezier curve is one of the most important of these curves which is named by French engineer Pierre Bézier , who used the Bezier curve in the 1960s for designing curves for bodywork of Renault cars. De Casteljau's algorithm is a recursive method and has an important role to evaluate polynomials in Bernstein form or (for application and analysis about this curve, (see [2], [3], [4], [5], [8], [9]). Bezier curves are studied in different areas.…”