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Starting to add funnels, using code from Ani.
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@@ -7,3 +7,5 @@ figures | |
| print.out | ||
| trajlib/ | ||
| abort.txt | ||
| funnels/funnelStuff.mat | ||
| funnels/inside_verification0.mat | ||
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| Original file line number | Diff line number | Diff line change |
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| function h=plotFunnel3(obj,options) | ||
| % Plots the one-level set of V in 3d | ||
| % | ||
| % @param options options structure | ||
| % | ||
| % @option plotdims coordinates along which to plot given as a 1x3 array | ||
| % @dull [1, 2, 3] | ||
| % @option x0 dull coordinates (e.g. to be used in the slice) | ||
| % @option inclusion = { 'slice' | 'projection' } | ||
| % 'slice' -- include the points in the plane of the given | ||
| % dimensions for which V(x) < 1. | ||
| % 'projection' -- plot the projection of {x | V(x) < 1} into the | ||
| % given plane. | ||
| % @option tol tolerance for computing the level set | ||
| % | ||
| % @retval h column vector of handles for any graphics objects created | ||
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| % todo: support wrapping coordinates | ||
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| if (nargin<2) options=struct(); end | ||
| if ~isfield(options,'plotdims') options.plotdims = [1;2;3]; end | ||
| if ~isfield(options,'x0') options.x0 = zeros(obj.getFrame.dim,1); end | ||
| if (~isfield(options,'inclusion')) options.inclusion = 'slice'; end | ||
| if (~isfield(options,'color')) options.color=.7*[1 1 1]; end | ||
| if (~isfield(options,'tol')) options.tol = .01; end | ||
| if (~isfield(options,'inflate_radius')) options.inflate_radius = 0.0; end | ||
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| if length(options.plotdims) ~= 3 | ||
| error('Handles 3d plots only.') | ||
| end | ||
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| % Setup colormaps | ||
| cmap = colormap('bone'); | ||
| cmapdark = cmap(1:end-10,:); | ||
| cmaplight = cmap(10:end,:); | ||
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| hold on; | ||
| view(3); | ||
| % view(0,90); | ||
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| if isTI(obj) | ||
| % TODO: Here we split between projection and slice. | ||
| if strcmp(options.inclusion,'slice') | ||
| x=getLevelSet(obj,0,options); | ||
| elseif strcmp(options.inclusion,'projection') | ||
| x=getProjection(obj,0,options.x0,options.plotdims,options); | ||
| else | ||
| error(['Unknown inclusion method: ' options.inclusion]); | ||
| end | ||
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| if options.inflate_radius ~= 0.0 | ||
| % Add in inflate_radius | ||
| x_origin_centered = x - repmat(mean(x,2),1,size(x,2)); | ||
| norms = sqrt(sum(x_origin_centered(1,:).^2 + x_origin_centered(2,:).^2 + x_origin_centered(3,:).^2,2)); | ||
| x_origin_centered = x_origin_centered + options.inflate_radius*(x_origin_centered./[norms;norms;norms]); | ||
| x = x_origin_centered + repmat(mean(x,2),1,size(x,2)); | ||
| end | ||
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| % Compute convex hull of points | ||
| K = convhulln(x'); | ||
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| % Plot with trisurf | ||
| h = trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.3,'EdgeAlpha',0.9); | ||
| colormap(cmapdark); | ||
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| % Label axes | ||
| xlabel(obj.getFrame.coordinates{options.plotdims(1)}); | ||
| ylabel(obj.getFrame.coordinates{options.plotdims(2)}); | ||
| zlabel(obj.getFrame.coordinates{options.plotdims(3)}); | ||
| else | ||
| if ~isfield(options,'ts') error('you must specify the time samples for this system using options.ts'); end | ||
| ts = options.ts; | ||
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| if isnumeric(options.x0) options.x0 = ConstantTrajectory(options.x0); end | ||
| x0 = options.x0; | ||
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| h=[]; | ||
| for i=length(ts)-1:-1:1 | ||
| if strcmp(options.inclusion,'slice') | ||
| options.x0 = x0.eval(ts(i)); | ||
| xfun0 = getLevelSet(obj,ts(i),options); | ||
| options.x0 = x0.eval(ts(i+1)-eps); | ||
| xfun1 = getLevelSet(obj,ts(i+1)-eps,options); | ||
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| if options.inflate_radius ~= 0.0 | ||
| % Add in inflate_radius | ||
| x_origin_centered = xfun0 - repmat(mean(x,2),1,size(x,2)); | ||
| norms = sqrt(sum(x_origin_centered(1,:).^2 + x_origin_centered(2,:).^2 + x_origin_centered(3,:).^2,2)); | ||
| x_origin_centered = x_origin_centered + options.inflate_radius*(x_origin_centered./[norms;norms;norms]); | ||
| xfun0 = x_origin_centered + repmat(mean(x,2),1,size(x,2)); | ||
| end | ||
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| if options.inflate_radius ~= 0.0 | ||
| % Add in inflate_radius | ||
| x_origin_centered = xfun1 - repmat(mean(x,2),1,size(x,2)); | ||
| norms = sqrt(sum(x_origin_centered(1,:).^2 + x_origin_centered(2,:).^2 + x_origin_centered(3,:).^2,2)); | ||
| x_origin_centered = x_origin_centered + options.inflate_radius*(x_origin_centered./[norms;norms;norms]); | ||
| xfun1 = x_origin_centered + repmat(mean(x,2),1,size(x,2)); | ||
| end | ||
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| % opts = options; | ||
| % opts.plotdims = options.plotdims(2:3); | ||
| % xring = getLevelSet(obj,ts(i+1),opts); | ||
| elseif strcmp(options.inclusion,'projection') | ||
| xfun0 = getProjection(obj,ts(i),x0.eval(ts(i)),options.plotdims,options); | ||
| xfun1 = getProjection(obj,ts(i+1)-eps,x0.eval(ts(i+1)-eps),options.plotdims,options); | ||
| % xring = getProjection(obj,ts(i+1),x0.eval(ts(i+1)),options.plotdims(2:3),options); | ||
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| % Add in inflate_radius | ||
| x_origin_centered = xfun0 - repmat(mean(xfun0,2),1,size(xfun0,2)); | ||
| norms = sqrt(sum(x_origin_centered(1,:).^2 + x_origin_centered(2,:).^2 + x_origin_centered(3,:).^2,1)); | ||
| x_origin_centered = x_origin_centered + options.inflate_radius*(x_origin_centered./[norms;norms;norms]); | ||
| xfun0 = x_origin_centered + repmat(mean(xfun0,2),1,size(xfun0,2)); | ||
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| % Add in inflate_radius | ||
| x_origin_centered = xfun1 - repmat(mean(xfun1,2),1,size(xfun1,2)); | ||
| norms = sqrt(sum(x_origin_centered(1,:).^2 + x_origin_centered(2,:).^2 + x_origin_centered(3,:).^2,1)); | ||
| x_origin_centered = x_origin_centered + options.inflate_radius*(x_origin_centered./[norms;norms;norms]); | ||
| xfun1 = x_origin_centered + repmat(mean(xfun1,2),1,size(xfun1,2)); | ||
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| else | ||
| error(['Unknown inclusion method: ' options.inclusion]); | ||
| end | ||
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| if (i == (length(ts)-1)) | ||
| x = xfun1; | ||
| K = convhulln(x'); | ||
| % hi = trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.6,'EdgeAlpha',0); % 0.6 | ||
| hi = trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.6,'EdgeAlpha',0,'FaceLighting','gouraud','AmbientStrength',0.9); % 0.6 | ||
| h = [h;hi]; | ||
| colormap(cmap); | ||
| material dull | ||
| % set(hi,'colormap',cmapdark'); | ||
| end | ||
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| x = [xfun0,xfun1(:,end:-1:1)]; | ||
| K = convhulln(x'); | ||
| % h = [h;trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.2,'EdgeAlpha',0,'FaceLighting','flat')]; | ||
| h = [h;trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.2,'EdgeAlpha',0,'FaceLighting','gouraud','AmbientStrength',0.9)]; | ||
| colormap(cmap); | ||
| material dull | ||
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| % x01 = x0.eval(ts(i+1)); x01 = x01(options.plotdims(1)); | ||
| % plot3(repmat(x01,1,length(xring)), xring(1,:), xring(2,:),'k','LineWidth',2); | ||
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| x = xfun0; | ||
| K = convhulln(x'); | ||
| % h = [h;trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.3,'EdgeAlpha',0,'FaceLighting','flat')]; % 0.3 | ||
| h = [h;trisurf(K,x(1,:),x(2,:),x(3,:),'FaceColor','interp','EdgeColor','interp','FaceAlpha',0.1,'EdgeAlpha',0,'FaceLighting','gouraud','AmbientStrength',0.9)]; | ||
| % colormap(cmapdark); | ||
| colormap(cmap); | ||
| material dull | ||
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| end | ||
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| % Flip colormap since we flip axes (usually) | ||
| cmap = colormap; | ||
| colormap(flipud(cmap)); | ||
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| material dull; | ||
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| % Add some lighting | ||
| % keyboard; | ||
| % light('Position',[-1;-3;-5]); % ,'Style','local') | ||
| % light('Position',[-1;3;-5]); | ||
| % camlight | ||
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| % Plot rings at the beginning and end | ||
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| % if strcmp(options.inclusion,'slice') | ||
| % opts = options; | ||
| % opts.x0 = x0.eval(ts(1)); | ||
| % opts.plotdims = options.plotdims(2:3); | ||
| % xring = getLevelSet(obj,ts(1),opts); | ||
| % else | ||
| % xring = getProjection(obj,ts(1),x0.eval(ts(1)),options.plotdims(2:3),options); | ||
| % end | ||
| % | ||
| % x01 = x0.eval(ts(1)); x01 = x01(options.plotdims(1)); | ||
| % plot3(repmat(x01,1,length(xring)), xring(1,:), xring(2,:),'k','LineWidth',2); | ||
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| % if strcmp(options.inclusion,'slice') | ||
| % opts = options; | ||
| % opts.x0 = x0.eval(ts(end)); | ||
| % opts.plotdims = options.plotdims(2:3); | ||
| % xring = getLevelSet(obj,ts(end),opts); | ||
| % else | ||
| % xring = getProjection(obj,ts(end),x0.eval(ts(end)),options.plotdims(2:3),options); | ||
| % end | ||
| % | ||
| % x01 = x0.eval(ts(end)); x01 = x01(options.plotdims(1)); | ||
| % plot3(repmat(x01,1,length(xring)), xring(1,:), xring(2,:),'k','LineWidth',2); | ||
| end | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,9 @@ | ||
| function plotShiftedFunnel(V,x0,options) | ||
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| frameShifted = CoordinateFrame('shiftedFrame',length(x0)); | ||
| frameShifted.addTransform(AffineTransform(frameShifted,V.getFrame,eye(length(x0)),-x0)); | ||
| Vshifted = V.inFrame(frameShifted); | ||
| plotFunnel3(Vshifted,options); | ||
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| end | ||
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