Ali Çalışkan

Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with B-Spline Curves

The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped.

The exchange variations between bezier directrix curves of two developable ruled surfaces

Abstract Developable ruled surfaces and Bezier curves axe widely used in Computer Aided Geometric Deisgn (CAGD). A ruled surface is a surface generated by sweeping a line through space, or more specifically, sweeping a line along a directrix curve. A developable ruled surface is a surface where the surface normal at all points along a given ruling is constant. If the generators and directrix curve of a developable ruled surface are known, operations with these surfaces and designs of them are much simplified. In this paper, we present obtaining the Bezier directrix curve of a developable ruled surface from the Bezier directrix curve of the other developable ruled surface and the exchange variations of the arc lengths of these directrix curves. Also, we expressed the curvature exchanges between these Bezier directrix curves of two developable ruled surfaces. Also, based on this variation, we have discussed some ideas about the variations of developable ruled surfaces.

Dual Minimal Curves

In this study, a dual minimal curves of a dual unit sphere, and the minimal ruled surfaces corresponding it are defined, and represented that dual unit tangent, binormal and surface normal vectors, related to these, are dual isotropic lines. E.Study theorem is also given, for dual minimal curves, belonging to minimal curves and we give general solution of differential equation of this curves.