Shape Preserving Parametric Spline Curve With Given Tangent Polygon

In this paper,we analyze and investigate 3 type of curves which are generally used in CAGD (Computer Aided Geometric Design) :rational Bezier curves,NURBS (Non-Uniform Rational B-Spline) and C-curves.Algorithms for constructing closed and shape preserving curves with given tangent polygon are presented and implemented with programme.The first chapter,prolegomenon,we simply introduce the provenience and development of the Computer Aided Geometric Design and present the background of the research and the main contents of the paper.Finally,we introduce the necessary Mathematics knowledge.The second chapter,we construct degree 2 rational Bezier spline curve with given tangent polygon.The tangential points of the curve are produced directly from the vertices of the given tagent polygon.And we can control the curve form through adjusting the shape invariant.The curve is shape preserving and G~1 continuity.We also construct G~2 continuous and shape preserving degree 3 rational Bezier curve.An assisted control point is produced from the vertices of the given tagent polygon besides the tangential point.We can control the curve form through adjusting its shape factor σ and Τ.The third chapter,we construct degree 2 and 3 NURBS curves with given tangent polygon, and the algorithm for constructing (m+l)th degree NURBS curve with C~m continuity is given too.The Deboor points are produced directly from the vertices of the given tagent polygon.The knot vectors are obtained from the vertices of control polygon using Resenfeld method. The spline curves are similar with uniform B/Bezier and NURBS...