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.
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Ohmori, K., Kunii, T.L. (2013). Mathematical Foundations for Designing a 3-Dimensional Sketch Book. In: Gavrilova, M.L., Tan, C.J.K., Kuijper, A. (eds) Transactions on Computational Science XVIII. Lecture Notes in Computer Science, vol 7848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38803-3_3
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DOI: https://doi.org/10.1007/978-3-642-38803-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38802-6
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