Mathematical foundations for designing a 3-dimensional sketch book

Abstract

This paper describes mathematical foundations for designing a 3-dimensional sketch book and the development of an experimental system. The system helps a non-professional user draw a mountain from a rough image to a fine image using filtration. The user draws important critical points (summits, ravine bottoms and saddles), which are used to obtain a 0-dimensional approximation. The system generates a Reeb graph to provide height information of the saddles with a partial order in height. Then, the contours are provided from the Reeb graph. The user draws ridges and ravines by pushing and pulling contours. The system generates a 1-dimensional approximation from these curves. Finally, NURBS surfaces are generated to give a 2-dimensional approximation and a 3-dimensional rendering image is obtained. The above procedure is repeated until a satisfactory result is obtained by giving the most important points and curves at the first stage and adds less important points and curves, later. © 2013 Springer-Verlag Berlin Heidelberg.