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Author (up) Miura, K.T.; Shirahata, R.; Agari, S.ichi doi  openurl
  Title Non-stationarization of the typical curves and its extension to surfaces Type Journal Article
  Year 2010 Publication Computer-Aided Design and Applications Abbreviated Journal  
  Volume 7 Issue 3 Pages 297-308  
  Abstract It is known that if the degree of the typical plane Be}zier curve is increased infinitely, the curve will converge to the logarithmic (equiangular) spiral. The logarithmic spiral is one of log-aesthetic curves and they are formulated by : the slope of the logarithmic curvature graph. In this paper we define the non-stationary typical Be}zier curve by making the transition matrix of the typical Be}zier curve non-stationary and dependent on each side of the control polyline and defining the transition matrix in the Frenet frame. We propose a method that generates a curve such that if its degree is increased infinitely it will converge to a log-aesthetic curve with arbitrary and : the slope of the logarithmic torsion graph in case of the space curve, by controlling the relationship between the rotation angle and the scaling factor. Furthermore we extend the non-stationarization for free-form surfaces and propose the non-stationary typical surface with the unit scaling factor. © 2010 CAD Solutions, LLC.  
  Corporate Author Thesis  
  Publisher Place of Publication P. O. Box 48693, Tampa, FL 33647-0123, United States Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1686-4360 ISBN Medium  
  Area Expedition Conference  
  Notes Control polyline;Free-form surface;Frenet frame;Log-aesthetic curve;Logarithmic curvature;Logarithmic spiral;Nonstationary;Rotation angles;Scaling factors;Space curve;Transition matrices;Typical curves; Approved no  
  Call Number refbase @ user @ Miura2010 Serial 11763  
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