Abstract
Parts of pipeline need a long piece, a short segment, and various inflate-deflate models. They require as well the thickness and curvature of the pipes. The objective of this paper is to obtain some formulas for modeling the long pipe, the short tube, and various inflate-deflate pipe patches. Relating to the purposes, we use their cross-section, longitudinal section, and center curves of the pipe parts. The methods are, the using of the polar coordinates and of the real functions, to define the cross and longitudinal section of the pipe patches, respectively. Then, we calculate three orthonormal vectors that are determined by the tangent vectors of the pipe center curves and two unit vectors that are perpendicular to the tangent vectors. After that, we evaluate the formulas to model the long pipes and the short pipes, both inflate-deflate and thickness shapes. The results show that, using its center curves of the pipe, it is handy to design the long and short pipes, multiple thicknesses, various volume fluctuations of the pipes, and useful to model the inflate-deflate pipe parts.
Highlights
There were presented some methods to define the pipeline models
The objective of this paper is to obtain some formulas for modeling the long pipe, the short tube, and various inflate-deflate pipe patches
We calculate three orthonormal vectors that are determined by the tangent vectors of the pipe center curves and two unit vectors that are perpendicular to the tangent vectors
Summary
There were presented some methods to define the pipeline models. Lü& Pottmann (1996) introduced an algorithm for computing the pipe surfaces of rational spine curve (center curve of pipe) that can admit a rational parameterization. Maekawa, et al (1998) investigated the pipe surface intersection both local and global self-intersection. We can evaluate the substantial form of transitional tube parts whose cross sections have a polygonal shape and made of materials that cannot be creased or prolonged (Obradovic et al, 2012) This geometrical theory is based on the classical line geometry, and it can be straightforwardly implemented to the conception of a computer algorithm that generates the middle surfaces between two polygons. Because of its curve curvatures formula, it is useful to design the short pipes of constant radius, but, they lack in constructing and connecting the tubes of long pieces. Departing from these limitations, we will present a new formula that offers to design the long pipes with its surfaces of inflate-deflate form.
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