plots a polytope in H-representation or V-representation
h = viewPolytope returns the handles to the patch objects, which
represent the facets of the polytope.
viewPolytope(Pt, 'optionname', option) applies the following options:
option - a structure containing fields with options as below
(additional values are preferred compared to options given
here)
color - sets default color {'r' or [1 1 1]}
shade - level of transparency (0 - transparent, 1 - opaque)
colormap - sets a different colormap (default: 'hsv')
edgecolor - color of edges (default is black)
linewidth - width of the border of polytope (default is 1)
linestyle - style of the border of each polytope (could be either '-',
':', ';' or 'none') (default is '-')
flatness - for degenerate objects; look for: help convertVrepToHrep.
(default is 0)
zerotol - zerotol is used to identify values that are close to zero
by zero. (default is 1e-7)
infinityBoxSize - look for: help convertHrepToVrep (default is 1e3)
See also: obtainVrep, paintFacet0001 function h = viewPolytope(poly, varargin) 0002 % plots a polytope in H-representation or V-representation 0003 % 0004 % h = viewPolytope returns the handles to the patch objects, which 0005 % represent the facets of the polytope. 0006 % 0007 % viewPolytope(Pt, 'optionname', option) applies the following options: 0008 % option - a structure containing fields with options as below 0009 % (additional values are preferred compared to options given 0010 % here) 0011 % color - sets default color {'r' or [1 1 1]} 0012 % shade - level of transparency (0 - transparent, 1 - opaque) 0013 % colormap - sets a different colormap (default: 'hsv') 0014 % edgecolor - color of edges (default is black) 0015 % linewidth - width of the border of polytope (default is 1) 0016 % linestyle - style of the border of each polytope (could be either '-', 0017 % ':', ';' or 'none') (default is '-') 0018 % flatness - for degenerate objects; look for: help convertVrepToHrep. 0019 % (default is 0) 0020 % zerotol - zerotol is used to identify values that are close to zero 0021 % by zero. (default is 1e-7) 0022 % infinityBoxSize - look for: help convertHrepToVrep (default is 1e3) 0023 % 0024 % See also: obtainVrep, paintFacet 0025 0026 % The elk-library: convex geometry applied to crystallization modeling. 0027 % Copyright (C) 2012 Alexander Reinhold 0028 % 0029 % This program is free software: you can redistribute it and/or modify it 0030 % under the terms of the GNU General Public License as published by the 0031 % Free Software Foundation, either version 3 of the License, or (at your 0032 % option) any later version. 0033 % 0034 % This program is distributed in the hope that it will be useful, but 0035 % WITHOUT ANY WARRANTY; without even the implied warranty of 0036 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0037 % General Public License for more details. 0038 % 0039 % You should have received a copy of the GNU General Public License along 0040 % with this program. If not, see <http://www.gnu.org/licenses/>. 0041 0042 %% map options 0043 % [opt.option, opt.shade, opt.color,... 0044 % opt.linestyle, opt.linewidth, opt.edgecolor,... 0045 % opt.flatness, opt.infinityBoxSize, opt.zerotol] = ... 0046 % mapOption(varargin,... 0047 % 'option', struct([]),... 0048 % 'shade', 0.8,... 0049 % 'color', [1 1 1]*0.5,... 0050 % 'linestyle', '-',... 0051 % 'linewidth', 1.5,... 0052 % 'edgecolor', [0 0 0],... 0053 % 'flatness', 0, ... 0054 % 'infinityBoxSize', 1e2, ... 0055 % 'zerotol', elkZerotol ... 0056 % ); 0057 opt = mapOptionStruct(varargin,... 0058 'shade', 0.8,... 0059 'color', [1 1 1]*0.5,... 0060 'linestyle', '-',... 0061 'linewidth', 1.5,... 0062 'edgecolor', [0 0 0],... 0063 'flatness', 0, ... 0064 'infinityBoxSize', 1e2, ... 0065 'zerotol', elkZerotol ... 0066 ); 0067 0068 % opt = mergeStruct(opt.option, opt); 0069 % opt = rmfield(opt, 'option'); 0070 0071 %% check input dimension 0072 infoPoly = identifyPolytope(poly); 0073 if infoPoly.dim > 3 || infoPoly.dim < 2 0074 error('elk:polytope:wrongType', ... 0075 'viewPolytope can only plot 2D and 3D polytopes'); 0076 end 0077 0078 %% convert input to plottable polytope 0079 [vrep, hrep] = makePlottablePolytope(poly, opt.zerotol, opt.flatness, ... 0080 opt.infinityBoxSize); 0081 % empty polytope 0082 if isempty(vrep.V) 0083 h = []; 0084 return 0085 end 0086 0087 %% Plot 0088 switch infoPoly.dim 0089 case 2 0090 % all at once - a single patch 0091 if size(vrep.V, 1) > 2 0092 K = convhull(vrep.V(:, 1), vrep.V(:, 2)); 0093 elseif size(vrep.V, 1) == 2 0094 K = 1:2; 0095 elseif size(vrep.V, 1) == 1 0096 K = 1; 0097 end 0098 h = patch(vrep.V(K, 1), vrep.V(K, 2), vrep.V(K, 2)*0+1); 0099 case 3 0100 % cycle through facet normals - each facet a patch 0101 h = zeros(size(hrep.A, 1), 1); 0102 for iFacet = 1:size(hrep.A, 1) 0103 % filter vertices 0104 thisFacetVrep.V = ... 0105 vrep.V(isZero(... 0106 hrep.A(iFacet, :) * vrep.V' - hrep.h(iFacet), ... 0107 opt.zerotol), :); 0108 0109 % calculate facet in 2d 0110 thisFacetVrep2d = rotateVrep3d(... 0111 thisFacetVrep, 'vector', hrep.A(iFacet, :), [0 0 0]); 0112 thisFacetVrep2d = moveVrep(... 0113 thisFacetVrep2d, hrep.h(iFacet)*[0 0 -1]); 0114 thisFacetVrep2d.V(:, 3) = []; 0115 0116 % resort vertices for facet 0117 if size(thisFacetVrep2d.V, 1) > 2 0118 K = convhull(thisFacetVrep2d.V(:, 1), ... 0119 thisFacetVrep2d.V(:, 2)); 0120 elseif size(thisFacetVrep2d.V, 1) == 2 0121 K = 1:2; 0122 elseif size(thisFacetVrep2d.V, 1) == 1 0123 K = 1; 0124 else 0125 continue 0126 error('elk:polytope:NumericalProblem', ... 0127 'something is wrong with the dimension of the provided polytope'); 0128 end 0129 thisFacetVrep.V = thisFacetVrep.V(K, :); 0130 0131 % plot vertices 0132 h(iFacet) = patch(thisFacetVrep.V(:, 1), ... 0133 thisFacetVrep.V(:, 2), ... 0134 thisFacetVrep.V(:, 3), ... 0135 ones(1,3)); 0136 view([42, 23]); 0137 end 0138 end 0139 0140 % filter empty patches - should this happen?? 0141 h(h==0) = []; 0142 0143 %% apply options 0144 set(h, 'facealpha', opt.shade, ... 0145 'facecolor', opt.color, ... 0146 'linewidth', opt.linewidth, ... 0147 'linestyle', opt.linestyle, ... 0148 'edgecolor', opt.edgecolor); 0149 0150 if opt.shade == 0 0151 set(h, 'facecolor', 'none') 0152 end 0153 0154 0155 set(gca, 'PlotBoxAspectRatio', [1 1 1], ... 0156 'DataAspectRatio', [1 1 1],... 0157 'XGrid', 'off', 'YGrid', 'off', 'ZGrid', 'off'); 0158 0159 if nargout < 1 0160 clear h 0161 end 0162 0163