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A sphere with three handles  

A sphere with three handles  

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We propose new approaches to the investigation of tubular and canal surfaces, regarded as swept surfaces, we give a parametric representa-tion of the inverse of a canal surface and we suggest several applications of tubular surfaces in scientific vizualization.

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Citations

... Then, the ESP is the path connecting P P P and Q Q Q, which has the minimum length and has to be through a given tubular space. The mathematical definition of tubular space is given as follows [35]: ...
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We propose a novel algorithm to determine the Euclidean shortest path (ESP) from a given point (source) to another point (destination) inside a tubular space. The method is based on the observation data of a virtual particle (VP) assumed to move along this path. In the first step, the geometric properties of the shortest path inside the considered space are presented and proven. Utilizing these properties, the desired ESP can be segmented into three partitions depending on the visibility of the VP. Our algorithm will check which partition the VP belongs to and calculate the correct direction of its movement, and thus the shortest path will be traced. The proposed method is then compared to Dijkstra’s algorithm, considering different types of tubular spaces. In all cases, the solution provided by the proposed algorithm is smoother, shorter, and has a higher accuracy with a faster calculation speed than that obtained by Dijkstra’s method. Keywords: Euclidean shortest path; tubular space; reactive algorithm; visibility; oriented drilling process; Dijkstra’s algorithm
... The authors [4] have studied some characterizatons of the tubular surfaces generated by non-null curves in Minkowski 3−space. Blaga [11] has presented a new approach to the tubular surfaces and provided CAD applications. Arslan et.al. ...
... Best known examples of them: Karacan and Yaylı [11] examined geodesics and some properties of tubular surfaces in Minkowski 3−space, Tuncer [10] studied about the linear Weingarten conditions for tubular surfaces by using their Gaussian and mean curvatures in Galilean and pseudo-Galilean 3−spaces and the authors examined the properties of the tube surfaces according to Bishop and Darboux frames in [4,5]. Blaga [2] handled the tubular surfaces as swept surfaces and put forward the new approaches to the investigation of tubular and canal surfaces. Moreover, he gave some applications of tubular surfaces in scientific visualization. ...
... By using the eq. 2 for the surface X (s, θ) and since r > 0, we obtain the condition in (i). ...
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In this paper, we study tubular surfaces whose centers are semi-spherical indicatrices of a spatial curve using the alternative moving frame \( \left\{ N,C,W\right\} \). The first objective is to examine the basic properties of these surfaces. Then, we investigate the condition of the parameter curves on these surfaces to be asymptotic and geodesic curves. Finally, we present the graphs of some related examples using the Mathematica.
... Blaga [2] used tubular surfaces as swept surfaces and put forward new approaches for the investigation of tubular and canal surfaces in addition to showing applications of tubular surfaces in scientific visualization. ...
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... For example; Takashi Maekawa et al. [15] concerned with the question of when a pipe surface is nonsingular. More precisely, given a regular space curve α(s) they investigated the maximum R > 0, so that the pipe surface is nonsingular, whenever r < R. Blaga [3] handled the tubular surfaces as swept surfaces and he was put forward new approaches to the investigation of tubular and canal surfaces. Then, he gave several applications of tubular surfaces in scientific vizualization. ...
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In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces and some theorems and results are given. Moreover, the fundamental forms, the mean curvature and the Gaussian of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface, the center curve of which is eight curves, is drawn according to the Frenet frame and the modified orthogonal frame.