function varargout = teapotdemo(varargin) %TEAPOTDEMO A demo that uses the famous Newell teapot % to demonstrate MATLAB graphics features. The teapot % is defined by 32 bicubic bezier patches. The % patches can be tesselated to surfaces at a wide % range of resolutions. The resulting surfaces can % be rendered with a variety of properties and % effects. % Copyright 1984-2002 The MathWorks, Inc. % $Revision: 1.2 $ $Date: 2002/04/15 03:35:34 $ if nargin == 0 % LAUNCH GUI fig = figure(openfig(mfilename,'reuse')); % Generate a structure of handles to pass to callbacks, and store it. handles = guihandles(fig); guidata(fig, handles); if nargout > 0 varargout{1} = fig; end daspect([1 1 1]); xlim([-4 4]); ylim([-3 3]); axis vis3d off; view(3); light('Position',[ 0.25 -0.433 -0.866],'Style','infinite'); light('Position',[-0.433 0.25 0.866],'Style','infinite'); colormap autumn; % create teapot s=struct('resolution',12,'colorby','z','lidoffset',0,'bottom',1); p = teapot(12,'z',0,1); set(p,'UserData',s); % make it look nice set(p,'EdgeColor',[0 0 0],'LineStyle','none','FaceColor','interp'); lighting gouraud; set(gcf,'UserData',p); elseif ischar(varargin{1}) % INVOKE NAMED SUBFUNCTION OR CALLBACK try if (nargout) [varargout{1:nargout}] = feval(varargin{:}); % FEVAL switchyard else feval(varargin{:}); % FEVAL switchyard end catch disp(lasterr); end end function runcmd(cmd) eval(cmd); cw=findobj('Tag','minicmdwin'); set(cw,'String',cmd); function rebuildteapot() cr = sprintf('\n'); p=get(gcf,'UserData'); s=get(p,'UserData'); cmdStr=['p = get(gcf,''UserData'');',cr, ... 'teapot(', ... num2str(s.resolution), ... ',''', ... s.colorby,... ''',', ... num2str(s.lidoffset), ... ',', ... num2str(s.bottom), ... ',p);']; runcmd(cmdStr); % -------------------------------------------------------------------- function varargout = lightingmenu_Callback(h, eventdata, handles, varargin) n=get(h,'value'); cmddata={'flat' 'gouraud' 'phong'}; runcmd(['lighting ' cmddata{n} ';']); % -------------------------------------------------------------------- function varargout = colormapmenu_Callback(h, eventdata, handles, varargin) n=get(h,'value'); cmddata={'autumn' 'copper' 'hsv' 'winter'}; runcmd(['colormap ' cmddata{n} ';']); % -------------------------------------------------------------------- function varargout = materialmenu_Callback(h, eventdata, handles, varargin) n=get(h,'value'); cmddata={'default' 'shiny' 'dull' 'metal'}; runcmd(['material ' cmddata{n} ';']); % -------------------------------------------------------------------- function varargout = renderstylemenu_Callback(h, eventdata, handles, varargin) n=get(h,'value'); fmtData = { { '.', 'none', 'none' }; { 'none', '-', 'none' }; { 'none', 'none', 'interp' } }; runcmd2 = sprintf('p = get(gcf,''UserData'');\nset(p,''Marker'',''%s'')\nset(p,''LineStyle'',''%s'')\nset(p,''FaceColor'',''%s'')\n',... fmtData{n}{:}); runcmd(runcmd2); % -------------------------------------------------------------------- function varargout = colorbymenu_Callback(h, eventdata, handles, varargin) n=get(h,'value'); p=get(gcf,'UserData'); s=get(p,'UserData'); cmddata={'none' 'x' 'y' 'z' 'u' 'v' 'index'}; s.colorby=cmddata{n}; set(p,'UserData',s); if n==1 set(p,'FaceColor','none'); else set(p,'FaceColor','interp'); end rebuildteapot; % -------------------------------------------------------------------- function varargout = transparentbutton_Callback(h, eventdata, handles, varargin) if get(h,'value') == 1 runcmd('alpha(0.5);'); else runcmd('alpha(1);'); end % -------------------------------------------------------------------- function varargout = infobutton_Callback(h, eventdata, handles, varargin) helpwin(mfilename); % -------------------------------------------------------------------- function varargout = closebutton_Callback(h, eventdata, handles, varargin) close(gcf) % -------------------------------------------------------------------- function varargout = edgebutton_Callback(h, eventdata, handles, varargin) if get(h,'value') == 0 runcmd('p = get(gcf,''UserData''); set(p,''LineStyle'',''none'');'); else runcmd('p = get(gcf,''UserData''); set(p,''LineStyle'',''-'');'); end % -------------------------------------------------------------------- function varargout = bottombutton_Callback(h, eventdata, handles, varargin) p=get(gcf,'UserData'); s=get(p,'UserData'); if get(h,'value') == 1 s.bottom=1; else s.bottom=0; end set(p,'UserData',s); rebuildteapot; % -------------------------------------------------------------------- function varargout = resolutionslider_Callback(h, eventdata, handles, varargin) res = get(h,'value'); p=get(gcf,'UserData'); s=get(p,'UserData'); s.resolution=round(res); set(p,'UserData',s); rebuildteapot; % -------------------------------------------------------------------- function varargout = lidoffsetslider_Callback(h, eventdata, handles, varargin) res = get(h,'value'); p=get(gcf,'UserData'); s=get(p,'UserData'); s.lidoffset=round(res); set(p,'UserData',s); rebuildteapot; % -------------------------------------------------------------------- % End of GUIDE generated code % % This is the function that actually creates the teapot function pout=teapot(n,colorBy,lidoffset,bottom,pin) %TEAPOT(N,COLORBY) Generates a surface representation of the infamous Newell teapot. % Each bezier patch is tesselated at NxN resolution. COLORBY controls how the % surface's colors are generated: % x the X coordinates are used % y the Y coordinates are used % z the Z coordinates are used % y the U parameter values are used % v the V parameter values are used % index the INDEX of the patch is used % none no colors are generated % figure out the default values for all of the args if nargin<1 n=12; end if nargin<2 colorBy='none'; end if nargin<3 lidoffset=0; end if nargin<4 bottom=1; end % Get the teapot coords from the local functions below. verts = teapotVertices; quads = teapotControlPoints; % Vertices 204-269 define the lid. The lidoffset arg can % be used to move them along the Z axis. if lidoffset > 0 verts(204:269,3) = verts(204:269,3) + lidoffset; end % The last 4 quads are the optional bottom. Strip them % off if the bottom flag is false. if bottom==0 quads=quads(:,:,1:28); end pv = []; pf = []; pc = []; % loop over the patches, creating (n-1)*(n-1) quads on the surface for i=1:size(quads,3) % extract the control points for this bezier patch points=verts(quads(:,:,i),:); % rip the vertices into X, Y, and Z components x=points(:,1); y=points(:,2); z=points(:,3); % use evalCubicBezierPatch to generate quadrilaterals [f v c] = evalCubicBezierPatch(n,x,y,z,i,colorBy); % append these quads to the list numv = size(pv,1); pv = [pv; v]; pf = [pf; f+numv]; pc = [pc; c]; end % Create a patch containing all of the quads if nargin<5 pout = patch('faces', pf, 'vertices', pv); p = pout; else set(pin,'faces',pf,'vertices',pv); p = pin; end % Add vertex colors if desired if strcmp(colorBy,'none') set(p, 'facecolor', [.5 .5 .5]); else set(p,'FaceVertexCData',pc); end % These are the control points for the bezier patches. function verts = teapotVertices() verts = [ 1.4 0. 2.4 ; 1.4 -0.784 2.4 ; 0.784 -1.4 2.4 ; 0. -1.4 2.4 ; 1.3375 0. 2.53125 ; 1.3375 -0.749 2.53125 ; 0.749 -1.3375 2.53125 ; 0. -1.3375 2.53125 ; 1.4375 0. 2.53125 ; 1.4375 -0.805 2.53125 ; 0.805 -1.4375 2.53125 ; 0. -1.4375 2.53125 ; 1.5 0. 2.4 ; 1.5 -0.84 2.4 ; 0.84 -1.5 2.4 ; 0. -1.5 2.4 ; -0.784 -1.4 2.4 ; -1.4 -0.784 2.4 ; -1.4 0. 2.4 ; -0.749 -1.3375 2.53125 ; -1.3375 -0.749 2.53125 ; -1.3375 0.0 2.53125 ; -0.805 -1.4375 2.53125 ; -1.4375 -0.805 2.53125 ; -1.4375 0.0 2.53125 ; -0.84 -1.5 2.4 ; -1.5 -0.84 2.4 ; -1.5 0. 2.4 ; -1.4 0.784 2.4 ; -0.784 1.4 2.4 ; 0. 1.4 2.4 ; -1.3375 0.749 2.53125 ; -0.749 1.3375 2.53125 ; 0. 1.3375 2.53125 ; -1.4375 0.805 2.53125 ; -0.805 1.4375 2.53125 ; 0. 1.4375 2.53125 ; -1.5 0.84 2.4 ; -0.84 1.5 2.4 ; 0. 1.5 2.4 ; 0.784 1.4 2.4 ; 1.4 0.784 2.4 ; 0.749 1.3375 2.53125 ; 1.3375 0.749 2.53125 ; 0.805 1.4375 2.53125 ; 1.4375 0.805 2.53125 ; 0.84 1.5 2.4 ; 1.5 0.84 2.4 ; 1.75 0. 1.875 ; 1.75 -0.98 1.875 ; 0.98 -1.75 1.875 ; 0. -1.75 1.875 ; 2. 0. 1.35 ; 2. -1.12 1.35 ; 1.12 -2. 1.35 ; 0. -2. 1.35 ; 2. 0. 0.9 ; 2. -1.12 0.9 ; 1.12 -2. 0.9 ; 0. -2. 0.9 ; -0.98 -1.75 1.875 ; -1.75 -0.98 1.875 ; -1.75 0. 1.875 ; -1.12 -2. 1.35 ; -2. -1.12 1.35 ; -2. 0. 1.35 ; -1.12 -2. 0.9 ; -2. -1.12 0.9 ; -2. 0. 0.9 ; -1.75 0.98 1.875 ; -0.98 1.75 1.875 ; 0. 1.75 1.875 ; -2. 1.12 1.35 ; -1.12 2. 1.35 ; 0. 2. 1.35 ; -2. 1.12 0.9 ; -1.12 2. 0.9 ; 0.0 2. 0.9 ; 0.98 1.75 1.875 ; 1.75 0.98 1.875 ; 1.12 2. 1.35 ; 2. 1.12 1.35 ; 1.12 2. 0.9 ; 2. 1.12 0.9 ; 2. 0. 0.45 ; 2. -1.12 0.45 ; 1.12 -2. 0.45 ; 0. -2. 0.45 ; 1.5 0. 0.225 ; 1.5 -0.84 0.225 ; 0.84 -1.5 0.225 ; 0. -1.5 0.225 ; 1.5 0. 0.15 ; 1.5 -0.84 0.15 ; 0.84 -1.5 0.15 ; 0.0 -1.5 0.15 ; -1.12 -2. 0.45 ; -2. -1.12 0.45 ; -2. 0. 0.45 ; -0.84 -1.5 0.225 ; -1.5 -0.84 0.225 ; -1.5 0. 0.225 ; -0.84 -1.5 0.15 ; -1.5 -0.84 0.15 ; -1.5 0. 0.15 ; -2. 1.12 0.45 ; -1.12 2. 0.45 ; 0. 2. 0.45 ; -1.5 0.84 0.225 ; -0.84 1.5 0.225 ; 0. 1.5 0.225 ; -1.5 0.84 0.15 ; -0.84 1.5 0.15 ; 0. 1.5 0.15 ; 1.12 2. 0.45 ; 2. 1.12 0.45 ; 0.84 1.5 0.225 ; 1.5 0.84 0.225 ; 0.84 1.5 0.15 ; 1.5 0.84 0.15 ; -1.6 0. 2.025 ; -1.6 -0.3 2.025 ; -1.5 -0.3 2.25 ; -1.5 0 2.25 ; -2.3 0. 2.025 ; -2.3 -0.3 2.025 ; -2.5 -0.3 2.25 ; -2.5 0. 2.25 ; -2.7 0. 2.025 ; -2.7 -0.3 2.025 ; -3. -0.3 2.25 ; -3. 0. 2.25 ; -2.7 0. 1.8 ; -2.7 -0.3 1.8 ; -3. -0.3 1.8 ; -3. 0. 1.8 ; -1.5 0.3 2.25 ; -1.6 0.3 2.025 ; -2.5 0.3 2.25 ; -2.3 0.3 2.025 ; -3. 0.3 2.25 ; -2.7 0.3 2.025 ; -3. 0.3 1.8 ; -2.7 0.3 1.8 ; -2.7 0. 1.575 ; -2.7 -0.3 1.575 ; -3. -0.3 1.35 ; -3. 0. 1.35 ; -2.5 0. 1.125 ; -2.5 -0.3 1.125 ; -2.65 -0.3 0.9375 ; -2.65 0. 0.9375 ; -2. -0.3 0.9 ; -1.9 -0.3 0.6 ; -1.9 0. 0.6 ; -3. 0.3 1.35 ; -2.7 0.3 1.575 ; -2.65 0.3 0.9375 ; -2.5 0.3 1.125 ; -1.9 0.3 0.6 ; -2. 0.3 0.9 ; 1.7 0. 1.425 ; 1.7 -0.66 1.425 ; 1.7 -0.66 0.6 ; 1.7 0. 0.6 ; 2.6 0. 1.425 ; 2.6 -0.66 1.425 ; 3.1 -0.66 0.825 ; 3.1 0. 0.825 ; 2.3 0. 2.1 ; 2.3 -0.25 2.1 ; 2.4 -0.25 2.025 ; 2.4 0. 2.025 ; 2.7 0. 2.4 ; 2.7 -0.25 2.4 ; 3.3 -0.25 2.4 ; 3.3 0. 2.4 ; 1.7 0.66 0.6 ; 1.7 0.66 1.425 ; 3.1 0.66 0.825 ; 2.6 0.66 1.425 ; 2.4 0.25 2.025 ; 2.3 0.25 2.1 ; 3.3 0.25 2.4 ; 2.7 0.25 2.4 ; 2.8 0. 2.475 ; 2.8 -0.25 2.475 ; 3.525 -0.25 2.49375 ; 3.525 0. 2.49375 ; 2.9 0. 2.475 ; 2.9 -0.15 2.475 ; 3.45 -0.15 2.5125 ; 3.45 0. 2.5125 ; 2.8 0. 2.4 ; 2.8 -0.15 2.4 ; 3.2 -0.15 2.4 ; 3.2 0. 2.4 ; 3.525 0.25 2.49375 ; 2.8 0.25 2.475 ; 3.45 0.15 2.5125 ; 2.9 0.15 2.475 ; 3.2 0.15 2.4 ; 2.8 0.15 2.4 ; 0. 0. 3.15 ; 0. -0.002 3.15 ; 0.002 0. 3.15 ; 0.8 0. 3.15 ; 0.8 -0.45 3.15 ; 0.45 -0.8 3.15 ; 0. -0.8 3.15 ; 0. 0. 2.85 ; 0.2 0. 2.7 ; 0.2 -0.112 2.7 ; 0.112 -0.2 2.7 ; 0. -0.2 2.7 ; -0.002 0. 3.15 ; -0.45 -0.8 3.15 ; -0.8 -0.45 3.15 ; -0.8 0. 3.15 ; -0.112 -0.2 2.7 ; -0.2 -0.112 2.7 ; -0.2 0. 2.7 ; 0 0.002 3.15 ; -0.8 0.45 3.15 ; -0.45 0.8 3.15 ; 0. 0.8 3.15 ; -0.2 0.112 2.7 ; -0.112 0.2 2.7 ; 0. 0.2 2.7 ; 0.45 0.8 3.15 ; 0.8 0.45 3.15 ; 0.112 0.2 2.7 ; 0.2 0.112 2.7 ; 0.4 0. 2.55 ; 0.4 -0.224 2.55 ; 0.224 -0.4 2.55 ; 0. -0.4 2.55 ; 1.3 0. 2.55 ; 1.3 -0.728 2.55 ; 0.728 -1.3 2.55 ; 0. -1.3 2.55 ; 1.3 0. 2.4 ; 1.3 -0.728 2.4 ; 0.728 -1.3 2.4 ; 0. -1.3 2.4 ; -0.224 -0.4 2.55 ; -0.4 -0.224 2.55 ; -0.4 0. 2.55 ; -0.728 -1.3 2.55 ; -1.3 -0.728 2.55 ; -1.3 0. 2.55 ; -0.728 -1.3 2.4 ; -1.3 -0.728 2.4 ; -1.3 0. 2.4 ; -0.4 0.224 2.55 ; -0.224 0.4 2.55 ; 0. 0.4 2.55 ; -1.3 0.728 2.55 ; -0.728 1.3 2.55 ; 0. 1.3 2.55 ; -1.3 0.728 2.4 ; -0.728 1.3 2.4 ; 0. 1.3 2.4 ; 0.224 0.4 2.55 ; 0.4 0.224 2.55 ; 0.728 1.3 2.55 ; 1.3 0.728 2.55 ; 0.728 1.3 2.4 ; 1.3 0.728 2.4 ; 0. 0. 0. ; 1.5 0. 0.15 ; 1.5 0.84 0.15 ; 0.84 1.5 0.15 ; 0. 1.5 0.15 ; 1.5 0. 0.075 ; 1.5 0.84 0.075 ; 0.83 1.5 0.075 ; 0. 1.5 0.075 ; 1.425 0. 0. ; 1.425 0.798 0. ; 0.798 1.425 0. ; 0. 1.425 0. ; -0.84 1.5 0.15 ; -1.5 0.84 0.15 ; -1.5 0. 0.15 ; -0.84 1.5 0.075 ; -1.5 0.84 0.075 ; -1.5 0. 0.075 ; -0.798 1.425 0. ; -1.425 0.798 0. ; -1.425 0. 0. ; -1.5 -0.84 0.15 ; -0.84 -1.5 0.15 ; 0. -1.5 0.15 ; -1.5 -0.84 0.075 ; -0.84 -1.5 0.075 ; 0. -1.5 0.075 ; -1.425 -0.798 0. ; -0.798 -1.425 0. ; 0. -1.425 0. ; 0.84 -1.5 0.15 ; 1.5 -0.84 0.15 ; 0.84 -1.5 0.075 ; 1.5 -0.84 0.075 ; 0.798 -1.425 0. ; 1.425 -0.798 0. ]; % These select which control points are used for each of the 32 bezier patches . function quads = teapotControlPoints() quads = cat(3, [ % rim 1 2 3 4 ; 5 6 7 8 ; 9 10 11 12 ; 13 14 15 16 ] , [ 4 17 18 19 ; 8 20 21 22 ; 12 23 24 25 ; 16 26 27 28 ] , [ 19 29 30 31 ; 22 32 33 34 ; 25 35 36 37 ; 28 38 39 40 ] , [ 31 41 42 1 ; 34 43 44 5 ; 37 45 46 9 ; 40 47 48 13 ] , [ % body 13 14 15 16 ; 49 50 51 52 ; 53 54 55 56 ; 57 58 59 60 ] , [ 16 26 27 28 ; 52 61 62 63 ; 56 64 65 66 ; 60 67 68 69 ] , [ 28 38 39 40 ; 63 70 71 72 ; 66 73 74 75 ; 69 76 77 78 ] , [ 40 47 48 13 ; 72 79 80 49 ; 75 81 82 53 ; 78 83 84 57 ] , [ 57 58 59 60 ; 85 86 87 88 ; 89 90 91 92 ; 93 94 95 96 ] , [ 60 67 68 69 ; 88 97 98 99 ; 92 100 101 102 ; 96 103 104 105 ] , [ 69 76 77 78 ; 99 106 107 108 ; 102 109 110 111 ; 105 112 113 114 ] , [ 78 83 84 57 ; 108 115 116 85 ; 111 117 118 89 ; 114 119 120 93 ] , [ % handle 121 122 123 124 ; 125 126 127 128 ; 129 130 131 132 ; 133 134 135 136 ] , [ 124 137 138 121 ; 128 139 140 125 ; 132 141 142 129 ; 136 143 144 133 ] , [ 133 134 135 136 ; 145 146 147 148 ; 149 150 151 152 ; 69 153 154 155 ] , [ 136 143 144 133 ; 148 156 157 145 ; 152 158 159 149 ; 155 160 161 69 ] , [ % spout 162 163 164 165 ; 166 167 168 169 ; 170 171 172 173 ; 174 175 176 177 ] , [ 165 178 179 162 ; 169 180 181 166 ; 173 182 183 170 ; 177 184 185 174 ] , [ 174 175 176 177 ; 186 187 188 189 ; 190 191 192 193 ; 194 195 196 197 ] , [ 177 184 185 174 ; 189 198 199 186 ; 193 200 201 190 ; 197 202 203 194 ] , [ % lid 204 204 204 204 ; 207 208 209 210 ; 211 211 211 211 ; 212 213 214 215 ] , [ 204 204 204 204 ; 210 217 218 219 ; 211 211 211 211 ; 215 220 221 222 ] , [ 204 204 204 204 ; 219 224 225 226 ; 211 211 211 211 ; 222 227 228 229 ] , [ 204 204 204 204 ; 226 230 231 207 ; 211 211 211 211 ; 229 232 233 212 ] , [ 212 213 214 215 ; 234 235 236 237 ; 238 239 240 241 ; 242 243 244 245 ] , [ 215 220 221 222 ; 237 246 247 248 ; 241 249 250 251 ; 245 252 253 254 ] , [ 222 227 228 229 ; 248 255 256 257 ; 251 258 259 260 ; 254 261 262 263 ] , [ 229 232 233 212 ; 257 264 265 234 ; 260 266 267 238 ; 263 268 269 242 ] , [ % bottom 270 270 270 270 ; 279 280 281 282 ; 275 276 277 278 ; 271 272 273 274 ] , [ 270 270 270 270 ; 282 289 290 291 ; 278 286 287 288 ; 274 283 284 285 ] , [ 270 270 270 270 ; 291 298 299 300 ; 288 295 296 297 ; 285 292 293 294 ] , [ 270 270 270 270 ; 300 305 306 279 ; 297 303 304 275 ; 294 301 302 271 ] ); %this is the function that teapot uses to convert the bezier patches into surfaces function varargout = evalCubicBezierPatch(n,xc,yc,zc,index,colorBy) %EVALCUBICBEZIERPATCH(N,XC,YC,ZC,INDEX,COLORBY) Creates a surface from % a cubic bezier patch. N is the number of interpolation steps which % are to be used along each axis of the UV parameter space. XC, YC, and ZC % are the X, Y, and Z coordinates of the 16 control points. % % The eqn for a point on the surface is: % % P(u,v) = [u^3 3u^2(1-u) 3u(1-u)^2 (1-u)^3]*P*[v^3 3v^2(1-v) 3v(1-v)^2 (1-v)^3]' % % where: % 0<=u<=1 % 0<=v<=1 % P is a 4x4 containing the 16 control points % % COLORBY controls how the surface's colors are generated: % x the X coordinates are used % y the Y coordinates are used % z the Z coordinates are used % y the U parameter values are used % v the V parameter values are used % index the value of INDEX is used % % generate N values for U u = (0:n-1)'/(n-1); % and build the params for curves of constant U A = [(u.^3) (3 * u.^2 .* (1-u)) (3 * u .* (1-u).^2) ((1-u).^3)]; % generate N values for V v = (0:n-1)'/(n-1); % and build the params for curves of constant V B = [(v.^3) (3 * v.^2 .* (1-v)) (3 * v .* (1-v).^2) ((1-v).^3)]; % build the tensor product of the U's & V's mat=kron(A,B); % multiply by the control points xd = mat*xc; yd = mat*yc; zd = mat*zc; % reshape the 1x...'s into square matrices x=reshape(xd,n,n); y=reshape(yd,n,n); z=reshape(zd,n,n); % how should we color the patch? if strcmp(colorBy,'x') colors=x; elseif strcmp(colorBy,'y') colors=y; elseif strcmp(colorBy,'z') colors=z; elseif strcmp(colorBy,'u') colors=repmat([0:1/(n-1):1],n,1); elseif strcmp(colorBy,'v') colors=repmat([0:1/(n-1):1]',1,n); elseif strcmp(colorBy,'index') colors=repmat(index,n,n); elseif strcmp(colorBy,'none') colors=[]; end % if no output args, use surface to draw the geometry if nargout==0 % create surface s = surface(reshape(xd,n,n),reshape(yd,n,n),reshape(zd,n,n),colors); % make it look nice set(s,'EdgeColor','none','FaceColor','interp') % otherwise, return the geometry in the correct form for patch elseif nargout==3 [f v c] = surf2patch(reshape(xd,n,n),reshape(yd,n,n),reshape(zd,n,n),colors); varargout{1} = f; varargout{2} = v; varargout{3} = c; end