Truchet curves and surfaces
نویسنده
چکیده
Spanning tree contours, a special class of Truchet contour based upon a random spanning tree of a Truchet tiling’s underlying graph, are presented. This spanning tree method is extended to three dimensions to define a Truchet surface with properties similar to its twodimensional counterpart. Both contour and surface are smooth, have known minimum curvature and known maximum distance to interior points, and high ratios of perimeter to area and area to volume, respectively. Expressions for calculating contour length, contour area, surface area and surface volume directly from the spanning tree are given. r 2007 Elsevier Ltd. All rights reserved.
منابع مشابه
Hyperbolic Truchet Tilings
About 300 years ago Sébastien Truchet systematically studied patterns that could be formed from square tiles that were divided by a diagonal into a white triangle and a black triangle. Other pattern creators have been inspired by him to make Truchet-like tilings composed of circular arcs and other motifs. These tilings are all based on Euclidean tessellations, usually the tiling by squares. In ...
متن کاملEnumerations of Hyperbolic Truchet Tiles
Sébastien Truchet was a pioneer in applying combinatorics to the study of regular patterns. He enumerated the patterns that could be formed from square tiles that were divided by a diagonal into a black and a white triangle Following Truchet, others have created Truchet-like tilings composed of circular arcs and other motifs. These patterns are all based on Euclidean tessellations, usually the ...
متن کاملTENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE
In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...
متن کاملYet Another Application of the Theory of ODE in the Theory of Vector Fields
In this paper we are supposed to define the θ−vector field on the n−surface S and then investigate about the existence and uniqueness of its integral curves by the Theory of Ordinary Differential Equations. Then thesubject is followed through some examples.
متن کاملNumerical parameterization of curves and surfaces
A method for parameterizing nearly arbitrary implicit plane/space curves and surfaces is introduced. The parameterizations are of class Cn−1 if the given curves/surfaces are of class Cn. The computation of points and derivatives is performed numerically. These parameterizations can be used for controlled determination of points on curves and surfaces and for the application of developed techniq...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computers & Graphics
دوره 32 شماره
صفحات -
تاریخ انتشار 2008