The Application of Quadratic Bezier Curve on Rotational and Symmetrical Lampshade

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.


INTRODUCTION
The fabrication process of lampshade requires several treatments.First, building a model of the object to be constructed.Second, converting raw materials into semi-finished object.Third, forming semi-finished object to a subtler form.And the last, smoothing the surface of objects.The problem is that it turns out the existed design and fabrication techniques, often causes industry losses.First, using mall design technique that widely used by the craftsmen, the obtained results are often fails to meet the export contract orders, it is because the size of the object become incompatible with the buyer's order.Second, trial and error technique fabrication requires more expensive cost, since it produces many risks and errors on fabrications.It also requires extra time and effort for the production process.In addition, the lack of awareness of the manufactured object needs, many raw materials are wasted.
Constructing sitting-lamp shades requires the study of the physical (lighting) and geometry aspects.In terms of geometry, the existed sitting-lamp shade creation models is generally monotonous and constructed from objects pieces.It can be seen that the industrial sitting-lamp shade products are still simple and the used design techniques are still conventional.The technique takes a very long time so the customer orders are often not completed on time.
Besides, the resulted products are generally constants, no improvements in terms of arts and innovations needed by customers.The diversity is in the form of the level of symmetricity, harmony, and model variations as well as from the types and sizes of the offered products.
This article is a scientific effort to obtain innovative and varied sitting-lamp shade models.This article attempts to construct a sitting-lamp shade, so that the procedure of its construction can be determined.

Quadratic Hermitian Curve
The Hermitian curve is in the form of (0) = initial point of the curve in the form of ( 0 ,  0 ,  0 ) (1) = end point of the curve in the form of ( 1 ,  1 ,  1 )  ′ (1) = control point of curvature of the curve with 0 ≤  ≤ 1 [1] Second Order Bezier Curve The second order Bezier curve is represented in parametric form:

Displacement
If (  ,   ,   ) is the initial position, (  ,   ,   ) is the position after point is displaced,  is the identity matrix, and (  ,   ,   ) is a constant value that indicates the amount of displacement in each coordinate axes, then the displacement can be expressed as [3] (  ,   ,   ) = (  +   ,   +   ,   +   ) (6) The Application of Quadratic Bezier Curve on Rotational and Symmetrical Lampshade

RESULTS AND DISCUSSION
This article describes the procedures of constructing the sitting-lamp shade.The first procedure is to construct the used components of siting-lamp shade.The next step is to construct parts of the sitting-lamp shade namely the base, and the main part of the roof.The latter procedure is to construct the full sitting-hood.A. Constructing sitting-lamp shade components 1. Tube deformation Suppose given a tube of radius , the minimum radius of the tube is 10 cm, while the maximum limit of the tube radius is 20 cm, the minimum height tube is 10 cm while the maximum height of the tube is 30 cm, and the base is centered in ( 0 ,  0 ,  0 ).Thus, the sizes of the tube is 10 ≤  ≤ 30 and 10 ≤  ≤ 20.The selection of the value of  and  in the interval aims to differences in size of shape components of sittinglamp shade.Based on these data designed various forms of constituent components of the sitting-lamp shade using surface curve modification techniques and surface arch dilatation technique.

Figure 1 .
Figure 1.Special case of Linear Interpolation of two line segments

Figure 2 .
Figure 2. A linear interpolation on curves