Analogous to the cubic Bézier curve, a quartic trigonometric Bézier curve with a shape parameter is presented in this paper. Each curve segment is generated by four consecutive control points. The shape of the curve can be adjusted by altering the values of shape parameters while the control polygon is kept unchanged. These curves are closer to the control polygon than the cubic Bézier curves, ...

M athematics and the visual arts mutually reinforce one another [10]. On the one hand, many mathematical objects appear in artistic or decorative works [5, 6]. In particular, mathematical curves and art have a long-standing connection through the application of geometric principles [13, 20]. Simple curves such as the catenary are ubiquitous, for example in the work of the Catalan architect Anto...

A few years ago S-H Kim investigated some problems at the boundary of number theory, optimization, and geometry. One question regarded an optimal packing of certain útriangular ovalø planar curves and another looked at some related transformations of R2 to R2 . These were investigated primarily using tools from calculus but it turns out that computational algebra methods may instead be employed...

We have measured the positions of H2O masers in Sgr B2, a massive star forming region in the Galactic center, relative to an extragalactic radio source with the Very Long Baseline Array. The positions measured at 12 epochs over a time span of one year yield the trigonometric parallax of Sgr B2 and hence a distance to the Galactic center, R0, of R0 = 7.9 +0.8 −0.7 kpc. The proper motion of Sgr B...

In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape α(t) and β(t) are constructed in a space span{1,sin2t,(1−sint)2α(t),(1−cost)2β(t)}, which includes lots previous work as special cases. Sufficient conditions concerning to guarantee construction given, three specific examples related application...

A total solution for computer facial animation is proposed. First, a well-de ned 3D head model is deformed according to several photographs with di erent views, where the 3D head model exhibits good animation features. After pose recovery, B ezier curves are used to depict the subtle contours on a face. Moreover, elastic deformation can be applied to adjust the locations of global features. We ...

In this paper, we give a simple method for drawing a closed rational curve speciied in terms of control points as two B ezier segments. The main result is the following: For every aane frame (r; s) (where r < s), for every rational curve F(t) speciied over r; s] by some control polygon (0 ; : : : ; m) (where the i are weighted control points or control vectors), the control points (0 ; : : : ; ...

in this paper, we study b-focal curves of biharmonic b -general helices according to bishop frame in the heisenberg group heis   finally, we characterize the b-focal curves of biharmonic b- general helices in terms of bishop frame in the heisenberg group heis