voicebox工具包

function [vlist,edgeq,flist,info]=upolyhedron(w,md) % UPOLYHEDRON calculate uniform polyhedron characteristics % % Inputs: W Specifies the desired polyhedron in one of three forms: % (a) name e.g. W='cube'; precede by 'dual' for dual or % 'laevo' or 'dextro' [default] for chiral polyhedra % (b) index in the list given below e.g. W=6 is the cube; negative for dual % n.{1,2,3,4,5} gives n-sided prism, antiprism, grammic prism, grammic antiprism or grammic crossed antiprism % (c) Wythoff symbol (see below) e.g. W=[3 0 2 4] is the cube % |p q r, p|q r, p q|r or p q r| respectively with 0 for | % using -1 instead of 0 gives the dual of the polyhedron % using -2 (or -3 for dual) gives a reflected version of a snub polyhedron % MD specifies a mode string % 'g' plot image % 'w' plot wireframe % 'f' plot coloured faces % 'v' number vertices % 't' plot vertex figure (a slice centred on a vertex) % % ? homogeneous output coordinates % ? create net % ? segment faces to remove internal portions of the surfaces % ? size: [max] diameter=1, [longest] edge=1, include anisotropic normalization % to minimize variance of vertex radius or edge vector length % ? orientation: vertex at the top, largest stable base at bottom % % Outputs: % VLIST(:,7) gives the [x y z d n e t] for each vertex % x,y,z = position, d=distance from origin, n=valency, e=edge index, t=type (-ve for reflected) % EDGEQ(:,9) has one row for each direction of each edge: % 1 v1 first vertex (normally start) % 2 v2 second vertex % 3 f1 first face (normally on left) % 4 f2 second face % 5 ev1 next edge around vertex 1 (normally anticlockwise) % 6 ef1 next edge around f1 (normally anticlockwise) % 7 er reverse edge % 8 z twisted edge: clockwise neighbours around v1 and v2 are on the same face % 9 sf swap face order: ??? % 10 sv swap vertex order: v2 preceeds v1 around f1 % FLIST(:,7) gives the [x y z d n e t] for each face % x,y,z = unit normal, d=distance from origin, n=valency, e=edge index, t=type (-ve for reflected) % INFO structure containing the following fields: % hemi true if faces are hemispherical (i.e. pass through the origin) % onesided true is one-sided (like a moebius strip) % snub true if a snub polyhedron % This software is based closely on a Mathmatica program described in [1] which, in turn, was based on a % C program described in [2]. % % Wythoff Symbol % p,q,r define a spherical triangle whose angles at the corners are pi/p, pi/q and pi/r; % this triangle tiles the sphere if repeatedly reflected in its sides. The % polyhedron vertices are at the reflections of a seed vertex as follows % where the Vertex configuration gives the polygon orders of the faces around each vertex: % |p q r : Vertex at a point such that when rotated around any of p,q,r by twice the angle at that % corner is displaced by the same distance for each corner. This is a snub polyhedron and % only even numbers of reflections are used to generate vertices. Configuration {3 p 3 q 3 r} % p|q r : Vertex at p. Configuration = {q r q r ... q r} with 2n terms where n is the numerator of p % p q|r : Vertex on pq and on the bisector of angle r. Configuration {p 2r q 2r} % p q r| : Vertex at incentre: meeting point of all the angle bisectors. Configuration {2p 2q 2r} % |3/2 5/3 3 5/2 This special case is the great dirhombicosidodecahedron. It is a bit weird because % many of the edges are shared by four faces instead of the usual two. % If two of p,q,r = 2 then the third is arbitrary (prisms and antiprisms), otherwise only the numerators % 1:5 can occur, and 4 and 5 cannot occur together. If all are integers then the poyhedron is convex. % % References: % [1] R. E. Maeder. Uniform polyhedra. The Mathematica Journal, 3 (4): 48–57, 1993. % [2] Z. Har’El. Uniform solution for uniform polyhedra. Geometriae Dedicata, 47: 57–110, 1993. % [3] H. S. M. Coxeter, M. S. Longuet-Higgins, and J. C. P. Miller. Uniform polyhedra. % Philosophical Transactions of the Royal Society A, 246 (916): 401–450, May 1954. % [4] P. W. Messer. Closed-form expressions for uniform polyhedra and their duals. % Discrete and Computational Geometry, 27 (3): 353–375, Jan. 2002. %%%% BUGS and SUGGESTIONS %%%%%% % (1) we should ensure the "first" edges of the vertices and faces are consistent % (2) need to sort faces and vertices into a type order % (3) should ensure that for a non-chiral polyhedron, the vertex polarity alternates % (4) w=75 does not work % (5) dual of henispherical poyhedron % (6) flist not calculated correctly for duals % (7) add additional stuff into info.* % (8) vertex figures seem to include additional (duplicated) lines % (9) sort out when reflected vertices are really rotationally congruent % (10) could optionally colour by face type % (11) order alphabetically by noun % (12) allow abbreviated names + prisms with preceding decimal number % (13) calculate correct names % (14) include names for duals % (15) make "names" etc persistent % Example slide show: % for i=1:74, disp(num2str(i)); upolyhedron(i); pause(2); end % for i=5:10, disp(num2str(i)); for j=1:5, upolyhedron(i+j/10); pause(2); end, end % Copyright (C) Mike Brookes 1997 % Version: $Id: upolyhedron.m 713 2011-10-16 14:45:43Z dmb $ % % VOICEBOX is a MATLAB toolbox for speech processing. % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This program is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation; either version 2 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You can obtain a copy of the GNU General Public License from % http://www.gnu.org/copyleft/gpl.html or by writing to % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % [line nn] referes to the kaleido Mathematica program on which this is based % see http://www.mathconsult.ch/showroom/unipoly/unipoly.html#Images % Variables used % adjacent adjacency matrix % chi characteristic % cosa cos of the angle subtended by a half edge % d density % e number of edges % even number of even faces to remove % f number of faces % fi(n) number of faces of type i % g order of group % gamma(n) included spherical triangle angle between centre of face, % vertex and edge for face type i % hemiQ =1 for hemispherical faces (includes polyhedron centre) % incidence faces incident at vertex %