Relationship of Interpolation and Approximation Curve Conversion Based on Monomial Form

In Computer Aided Geometric Design (CAGD), the utilization of using curves for geometric design and modeling is undertaken by most research works. Due to the high degree of shape preservation of the approximation curve and ease of configuration of the interpolation curve, they are commonly used in CAD and CAM application. However, there are very few works that pay attention to the integration and transformation of those types of curve in graphical modeling tools. In 2010, Aphirukmatakun et al [1] proposed the transformation scheme based on Monomial Form technique to transform the CAGD curve into Newton-Lagrange curve and vice versa. However, Newton-Lagrange has a limitation in dealing with loops curve and zigzag. In this paper, we propose an interpolation and approximation curve conversion scheme to provide more flexible and efficient conversion between them. To this end, we combine Chebyshev polynomial representation and monomial matrix conversion to develop a set of conversion algorithms. The paper presents how the curves are converted and it is considered to be feasible and sound to implement in CAGD application.