Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines

Localized Editing of Catmull-Rom Splines

Catmull-Rom (C-R) splines offer many useful modeling properties, such as affine invariance, global smoothness, and local control. They are therefore of great interest to Computer Aided Design (CAD) users. C-R splines are easily evaluated and are a good choice for interactive applications because they interpolate their control points and therefore provide an intuitive way to represent and edit c...

Representation of Facial Features by Catmull-Rom Splines

This paper describes a technique for the representation of the 2D frontal view of faces, based on Catmull-Rom splines. It takes advantage of the a priori knowledge about the face structure and of the proprieties of Catmull-Rom splines, like interpolation, smoothness and local control, in order to define a set of key points that correspond among different faces. Moreover, it can compactly descri...

Lang, Origami and Geometric Constructions Origami and Geometric Constructions 1 Lang, Origami and Geometric Constructions Introduction

By Robert J. Lang Copyright ©1996–2015. All rights reserved. Introduction ................................................................................................................................... 3 Preliminaries and Definitions ...................................................................................................... 3 Binary Divisions ........................................

Lang, Origami and Geometric Constructions Origami and Geometric Constructions Introduction

Splines and geometric modeling

Piecewise polynomials of some xed degree and continuously di erentiable upto some order are known as splines or nite elements. Splines are used in applications ranging from image processing, computer aided design, to the solution of partial di erential equations via nite element analysis. The spline tting problem of constructing a mesh of nite elements that interpolate or approximate multivaria...