Minimum-area Ellipse with Three Non-collinear Points and Its Application in Parametric Interpolation

摘要

The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view, and present a new method of determining knots. This method replaces the chord length, which is closer to the arc length of the mini-mum-area ellipse with arc length, and avoids the occurrence of‘oscillation’ and‘loops’. We compare the new method with the uni-form method, chord length method and the centripetal method. The comparison is performed on the quality of cubic spline curves using these methods. In most cases, the result of our method is better than others.