We investigate the relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface. We show that focal surfacesF1andF2of the surfaceMcan be obtained by means of some special surfaces at a constant distance from the edge of regression on the surfaceM.
There are many ways to approximate cosine curve. In this study we have
examined the way how the cosine curve can be written as any order Bezier
curve. As a result using the Maclaurin series we have examined cosine curve
as the 4th and the 6th order Bezier curve based on the control points with
matrix form in E2. We give the control points of the 4th and the 6th order
Bezier curve based on the coefficients. Also we give the coefficients based
on the the control points of the 4th and the 6th order Bezier curve too.
In this paper, it's introduced the curves lying on parallel-like surface M^{f} of a surface M in Euclidean space. Taking into account the definition of the parallel-like surface it's obtained parametric expression of these curves and examined the Darboux frame for these curves which we call image curves. And finally, the curves lying on the surfaces M and M^{f} are compared by considering their geodesic and normal curvatures, the geodesic torsion.
In this study, it has been researched the exponential curve as a $3^{rd},$ $5^{th}$ and $7^{th}$ order B\'{e}zier curve in $\mathbf{E}^{2}$. Also, the numerical matrix representations of these curves have been calculated using the Maclaurin series in the plane via the control points.
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