Pipes Construction Using Quartic Bézier Curves

A Pipe consists of cross-sectional and longitudinal directions that determine its volume. The objective of this paper is to obtain some formulas for modeling the cross-section and the radius length variation along the center curve of the pipe. The methods are as follows. By using real quartic Bézier functions, we define the cross-section and lengthwise-section radii of the pipe, respectively. Then, we calculate three orthonormal vectors that are the tangent vectors of the center curve and two-unit vectors that are perpendicular to the tangent vectors. After that, we evaluate the formulas to model the pipes. The research results indicate that this proposed method is useful for designing pipe cross-sections and for modifying their volume.