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Mathematical Progress in Expressive Image Synthesis III

Part of the Mathematics for Industry Book Series (volume 24)

Editors: Dobashi, Yoshinori; Ochiai, Hiroyuki

DOI: 10.1007/978-981-10-1076-7

ISBN: 978-981-10-1075-0

Publisher: Springer Singapore - Springer Journals

May 22, 2016

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Chapter 11Drawing Curves

Oshima, Toshio

Pages: 95 –106

[We propose a method to determine piecewise cubic Bézier curves passing through given points. Our main purpose is to draw accurate graphs of mathematical functions with smaller data. A program drawing such graphs using our method is realized in a computer algebra and outputs the graphs in a...
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Chapter 12Aesthetic Design with Log-Aesthetic CurvesLog-aesthetic curve and SurfacesLog-aesthetic curve and surface

Miura, Kenjiro T.; Gobithaasan, R. U.

Pages: 107 –119

[Bézier, B-Spline and NURBS are de facto flexible curves developed for various design intent. However, these curves possess complex curvature function complicating the process of aesthetic shape design. In order to shorten the process, we introduce the fundmental equations of aesthetic curves and...
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Chapter 13Attractive Plane Curves in Differential Geometry

Inoguchi, Jun-ichi

Pages: 121 –135

[The purpose of chapter is to discuss plane curves from differential geometric point of view and applications of plane curves to computer aided designs. Plane curves are determined uniquely by curvatures up to Euclidean motions. Thus geometry of plane curves are formulated by the Euclidean motion...
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Chapter 14dNLS Flow on Discrete Space Curves

Hirose, Sampei; Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

Pages: 137 –149

[The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schrödinger equation (NLS). In this paper, we present its discrete...

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Mathematical Progress in Expressive Image Synthesis III

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