Title: Parametric Interval Bezier Curve Interpolation  
Author(s): O. Ismail  
Pages: 15  Paper ID:1729031818IJVIPNSIJENS  Published: June, 2017 
Abstract: Bezier curves are a method of designing polynomial curve segments when you want to control their shape in an easy way. Bezier curves make sense for any degree. In Computer Aided Geometric Design (CAGD), the Bezier curve and surface have been widely used for geometric modeling. This paper presents a simple matrix form for parametric interval Bezier curve interpolation. The four fixed Kharitonov's polynomials (four fixed Bezier curves) P_n^j (u) for (j=1,2,3,4) associated with the original interval Bezier curve P_n^I (u) are obtained. The fixed control points α_(i,n)^j for (i=0,1 ,⋯,n) and (j=1,2,3,4) of the four fixed Kharitonov's polynomials (four fixed Bezier curves) that cause the four fixed Kharitonov's polynomials (four fixed Bezier curves) to pass through α_(i,n)^j for (i=0,1 ,⋯,n) and (j=1,2,3,4) are computed. The desired interval control points {[q_i^,q_i^+ ]}_(i=0)^n of the desired parametric interval Bezier curve Q_n^I (u) that cause the parametric interval Bezier curve to pass through the regions determined by {[q_i^,q_i^+ ]}_(i=0)^n are obtained from the fixed control points of the four fixed Kharitonov's polynomials (four fixed Bezier curves) α_(i,n)^j for (i=0,1 ,⋯,n) and (j=1,2,3,4). An illustrative example is included in order to demonstrate the effectiveness of the proposed method.


Keywords: CAGD, computer graphics, interpolation, interval Bezier curves.  
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