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function vrml(h,filename)
%VRML Save graphics to VRML 2.0 file.
% VRML(H,FILENAME) saves a VRML 2.0 file containing the object
% with handle H and its descendants.
% If the FILENAME does not include an extension, ".wrl" is
% appended. If a file with the name FILENAME exists, it is
% overwritten.
% VRML(H) saves H and its descendants to the file "matlab.wrl".
%
% VRML files can be viewed using a VRML 2.0 plug-in in a browser.
% There are several plug-ins available. A web search for "vrml client"
% will bring up several options.
%
% IMPORTANT NOTICE:
% If you have a VRML 1.0 plugin it will read a VRML 2.0 file
% without a problem but it will NOT display anything. Please make
% sure you have a VRML 2.0 plugin
%
% Note that there are rendering differences between MATLAB and the
% plug-ins. Some of these differences are due to VRML 2.0 spec
% features that are not implemented by the plug-ins. Others are due
% to features not implemented by vrml.m. In some cases some features
% provided by MATLAB are not part of the VRML 2.0 spec. For details on
% features supported by different plug-ins, please refer to the vendors'
% release notes.
%
% Some of the most notable features NOT supported by CosmoPlayer:
% Color interpolation.
% Text.
%
% The following MATLAB features are not supported by vrml.m
% Texturemapping.
% Axes tickmarks.
% 'Box' property. (It is always set to on).
% X,Y,Z Dir property of axes.
% Markers.
% Transparent NaN's.
% Truecolor CData
%
% These MATLAB features are not in the VRML2.0 spec.
% linestyles in VRML 2.0.
% orthographic projections.
% Phong and Gouraud lighting.
% 'Stitching' of edgelines on patch and surface objects.
% R. Paxson, 4-10-97.
% Copyright 1984-2008 The MathWorks, Inc.
% $Revision: 1.14.4.10 $
global VRML_OUTPUT_FILE;
switch nargin
case 0
error(id('minrhs'),'Not enough input arguments');
case 1
filename = 'matlab.wrl';
case 2
if ischar(filename)
[pathstr,name,ext] = fileparts(filename);
if isempty(ext)
ext = '.wrl';
end
filename = fullfile(pathstr,[name,ext]);
else
error(id('InvalidFileName'), 'Filename argument is not a string');
end
end
if ~any(ishghandle(h))
error(id('InvalidObjectHandle'), 'First argument must be a valid object handle');
end
VRML_OUTPUT_FILE = fopen(filename,'w');
try
WriteFileHeaderAndInfo;
ProcessObject(h);
fclose(VRML_OUTPUT_FILE);
clear global VRML_OUTPUT_FILE
catch err
fclose(VRML_OUTPUT_FILE);
clear global VRML_OUTPUT_FILE
delete(filename);
rethrow(err)
end
function WriteFileHeaderAndInfo()
sendStr(0,'#VRML V2.0 utf8\n');
sendStr(0,'WorldInfo {title "Matlab-VRML"}\n');
sendStr(0,'NavigationInfo {\n');
sendStr(1,'headlight FALSE\n');
sendStr(1,'type "EXAMINE"\n');
sendStr(0,'}\n');
function ProcessObject(obj_handle)
obj = get(obj_handle);
switch obj.Type
case 'figure', HandleFigure( obj);
case 'axes', HandleAxes( obj_handle);
case 'light', HandleLight( obj);
case 'patch', HandlePatch( obj_handle);
case 'surface', HandleSurface(obj_handle);
case 'line', HandleLine( obj);
case 'image', HandleImage( obj);
case 'text', HandleText( obj);
end
function HandleFigure(obj)
if(strcmp(obj.Visible,'on'))
sendStr(0,'Background {\n');
sendStr(1,sprintf('skyColor [%f %f %f]\n',obj.Color));
sendStr(0,'}\n');
for i=1:length(obj.Children)
ProcessObject(obj.Children(i));
end
end
function HandleAxes(obj_handle)
obj = get(obj_handle);
global VRML_USE_MATERIAL_PROPS;
sendStr(0,'Transform {\n');
sendStr(1,sprintf('scale %f %f %f\n',obj.PlotBoxAspectRatio./obj.DataAspectRatio));
sendStr(1,'children [\n');
sendStr(2,'Transform {\n');
sendStr(3,sprintf('translation %f %f %f\n',[-sum(obj.XLim)/2 -sum(obj.YLim)/2 -sum(obj.ZLim)/2]));
sendStr(3,'children [\n');
sendStr(2,'Viewpoint {\n');
sendStr(3,sprintf('position %f %f %f\n',obj.CameraPosition));
sendStr(3,sprintf('fieldOfView %f\n',obj.CameraViewAngle*pi/180));
sendStr(3,sprintf('orientation %f %f %f %f\n',computeOrientation(get(obj_handle,'Xform'))));
sendStr(3,'description "Original"\n');
sendStr(2,'}\n');
outputOtherViewpoints(obj);
if(strcmp(obj.Visible,'on'))
outputAxesCube(obj);
outputAxesTicks(obj);
outputAxesTickLabels(obj);
end
VRML_USE_MATERIAL_PROPS = 0;
if ~isempty(findobj(obj_handle,'Type','light','Visible','on'))
VRML_USE_MATERIAL_PROPS = 1;
end
for i=1:length(obj.Children)
ProcessObject(obj.Children(i));
end
sendStr(3,']\n');
sendStr(2,'}\n');
sendStr(1,']\n');
sendStr(0,'}\n');
clear global VRML_USE_MATERIAL_PROPS
function HandleLight(obj)
if(strcmp(obj.Visible,'on'))
switch obj.Style
case 'infinite'
sendStr(2,'DirectionalLight {\n');
sendStr(3,sprintf('direction %f %f %f\n',obj.Position));
case 'local'
sendStr(2,'PointLight {\n');
sendStr(3,sprintf('location %f %f %f\n',obj.Position));
otherwise
error(id('InvalidLightMode'),'Unknown light mode in HandleLight');
end
% Define the intensity of the ambient light as 0.3, determined
% empirically.
sendStr(3,'ambientIntensity 0.3\n');
sendStr(3,sprintf('color %f %f %f\n',obj.Color));
sendStr(2,'}\n');
end
function HandleText(obj)
% check to see what kind of object we received
% a real HG object or maybe just a label of the axis.
field = fieldnames(obj);
if strcmp(field{1},'String');
% we have a ticklabel;
sendStr(2,'Transform {\n');
sendStr(3,sprintf('translation %f %f %f\n',obj.Position));
sendStr(3,'children [\n');
BeginShape('Text');
sendStr(5,sprintf('string ["%s"]\n',obj.String));
sendStr(5,'fontStyle FontStyle {\n');
sendStr(6,'size 0.07\n');
sendStr(6,'justify "MIDDLE"\n');
sendStr(5,'}\n');
EndShape;
sendStr(3,']\n');
sendStr(2,'}\n');
else
% we have a text object;
sendStr(2,'Transform {\n');
sendStr(3,sprintf('translation %f %f %f\n',obj.Position));
sendStr(3,'children [\n');
BeginShape('Text');
sendStr(5,sprintf('string ["%s"]\n',obj.String));
sendStr(5,'fontStyle FontStyle {size 0.07}\n');
EndShape;
sendStr(3,']\n');
sendStr(2,'}\n');
end
function HandlePatch(obj_handle)
handler.coord = 'patchCoord';
handler.coordIndex = 'patchCoordIndex';
handler.color = 'patchColor';
handler.colorIndex = 'patchColorIndex';
HandlePatch_SurfaceObjs(obj_handle, handler);
function HandleSurface(obj_handle)
handler.coord = 'surfCoord';
handler.coordIndex = 'surfCoordIndex';
handler.color = 'surfColor';
handler.colorIndex = 'surfColorIndex';
HandlePatch_SurfaceObjs(obj_handle, handler);
function HandlePatch_SurfaceObjs(obj_handle,info)
obj = get(obj_handle);
handle_str = sprintf('%s%g',deblank(obj.Type),obj_handle);
handle_str = abs(handle_str);
h = find(handle_str == '.');
handle_str(h) = []; %#ok
handle_str = char(handle_str);
DEFINED_OBJ_COORD = 0;
if(strcmp(obj.Visible,'on'))
% Handle FaceColor mode
if ~strcmp(obj.FaceColor,'none')
BeginShape('IndexedFaceSet');
sendStr(3,'solid FALSE\n');
coord(obj,info.coord,handle_str,'define');
DEFINED_OBJ_COORD = 1;
coordIndex(obj,info.coordIndex);
facecolor(obj,info.color,obj.FaceColor);
if ~ischar(obj.FaceColor)
sendStr(3,'colorPerVertex FALSE\n');
else
switch obj.FaceColor
case 'flat'
sendStr(3,'colorPerVertex FALSE\n');
colorIndex(obj,info.colorIndex,'flat');
case 'interp'
sendStr(3,'colorPerVertex TRUE\n');
colorIndex(obj,info.colorIndex,'interp');
case 'texturemap'
otherwise
error(id('InvalidFaceColor'),'Unknown FaceColor type in Handle Patch');
end
end
EndShape;
end
% Handle EdgeColor mode
if ~strcmp(obj.EdgeColor,'none')
BeginShape('IndexedLineSet');
if DEFINED_OBJ_COORD == 1
coord(obj,info.coord,handle_str,'use');
else
coord(obj,info.coord);
end
coordIndex(obj,info.coordIndex);
color(obj,info.color,obj.EdgeColor);
if ~ischar(obj.EdgeColor)
sendStr(3,'colorPerVertex FALSE\n');
else
switch obj.EdgeColor
case 'flat'
sendStr(3,'colorPerVertex FALSE\n');
colorIndex(obj,info.colorIndex,'flat');
case 'interp'
sendStr(3,'colorPerVertex TRUE\n');
colorIndex(obj,info.colorIndex,'interp');
otherwise
error(id('InvalidEdgeColor'),'Unknown EdgeColor type in Handle Surface');
end
end
EndShape;
end
end
function HandleLine(obj)
if(strcmp(obj.Visible,'on'))
BeginShape('IndexedLineSet');
coord(obj,'lineCoord');
coordIndex(obj,'lineCoordIndex');
color(obj,'lineColor',obj.Color);
sendStr(4,'colorPerVertex FALSE\n');
EndShape;
end
% TODO: experimental version of the Image object
% the browser motion keys are much faster if the
% object is in the scale 0 -> 1 so we might want to do this
% it is most notable with images.
function HandleImage(obj)
if(strcmp(obj.Visible,'on'))
sendStr(2,'Shape {\n');
sendStr(3,'appearance Appearance {\n');
texture(obj);
sendStr(2,'}\n');
sendStr(3,'geometry IndexedFaceSet {\n');
sendStr(4,'coord Coordinate { \n');
sendStr(5,'point [\n');
x = [obj.XData(1) obj.XData(end)];
y = [obj.YData(1) obj.YData(end)];
ins = [x(1) y(1);x(2) y(1);x(2) y(2);x(1) y(2)];
sendStr(6,sprintf('%d %d 0,',ins'));
sendStr(5,'] }\n');
sendStr(4,'coordIndex [0, 1, 2, 3, -1]\n');
sendStr(4,'texCoord TextureCoordinate {\n');
sendStr(5,'point [0 0,1 0,1 1,0 1]\n');
sendStr(4,'}\n');
sendStr(3,'}\n');
sendStr(2,'}\n');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%% VRML Node Generation %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: would like to abstract appearance node out of here.
function BeginShape(type)
global VRML_USE_MATERIAL_PROPS;
sendStr(2,'Shape {\n');
if(VRML_USE_MATERIAL_PROPS)
sendStr(3,'appearance Appearance {material Material{}}\n');
end
sendStr(3,sprintf('geometry %s {\n',type));
function EndShape
sendStr(3,'}\n'); % closes geometry node
sendStr(2,'}\n'); % closes Shape node
% fcn: function pointer used to provide color data
% type: flat, interp, texture, ColorSpec.
function color(hgObj,fcn,type)
sendStr(4,'color Color {\n');
sendStr(5,'color [\n');
if ~ischar(type)
sendStr(6,sprintf('%d %d %d',type));
else
feval(fcn,hgObj);
end
sendStr(5,'\n');
sendStr(5,']\n');
sendStr(4,'}\n');
% fcn: function pointer used to provide color data
% type: flat, interp, texture, ColorSpec.
function facecolor(hgObj,fcn,type)
sendStr(4,'color Color {\n');
sendStr(5,'color [\n');
if ~ischar(type) && isfield(hgObj,'Faces')
sendStr(6,repmat(sprintf('%d %d %d\n',type),1,length(hgObj.Faces)));
else
feval(fcn,hgObj);
sendStr(5,'\n');
end
sendStr(5,']\n');
sendStr(4,'}\n');
% Outputs a VRML coord node.
function coord(hgObj,fcn,name,usage)
if nargin > 2
if strcmp(usage,'define')
sendStr(4,sprintf('coord DEF %s Coordinate{\n',name ));
sendStr(5,'point [\n');
feval(fcn,hgObj);
sendStr(5,']');
sendStr(4,'}\n');
elseif strcmp(usage,'use')
sendStr(4,sprintf('coord USE %s\n',name));
end
else
sendStr(4,'coord Coordinate{\n');
sendStr(5,'point [\n');
feval(fcn,hgObj);
sendStr(5,']');
sendStr(4,'}\n');
end
function coordIndex(hgObj,fcn)
sendStr(4,'coordIndex [\n');
feval(fcn,hgObj);
sendStr(4,']\n');
% need to make a node of colorIndex to have name and usage
% make sense. That could use DEF and USE as well.
function colorIndex(hgObj,fcn,type)
sendStr(4,'colorIndex [\n');
feval(fcn,hgObj,type);
sendStr(4,']\n');
function texture(hgObj)
sendStr(4,'texture PixelTexture { \n');
sendStr(5,'repeatS FALSE\n');
sendStr(5,'repeatT FALSE\n');
sendStr(5,sprintf('image %d %d 3\n',size(hgObj.CData,2), size(hgObj.CData,1)));
if ndims(hgObj.CData) == 2
cmap = round(get(get(hgObj.Parent,'Parent'),'Colormap') * 255);
cdata = (hgObj.CData - 1); cdata = cdata*(length(cmap)-1)/max(max(cdata));
cdata = round(cdata' + 1);
sendStr(6,sprintf('0x%.2x%.2x%.2x ',cmap(cdata,:)'));
else
error(id('RGBTexturesNotSupported'),'RGB Textures not supported yet');
end
sendStr(0,'\n');
sendStr(3,'}\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% Per node output utils %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function surfColor(obj)
if ndims(obj.CData) == 2
outputColormap(get(get(obj.Parent,'Parent'),'Colormap'));
else
error(id('RGBTexturesNotSupported'),'Not dealing with rgb data yet'); % TODO
end
function patchColor(obj)
if ndims(obj.FaceVertexCData) < 3
outputColormap(get(get(obj.Parent,'Parent'),'Colormap'));
else
error(id('RGBTexturesNotSupported'),'Not dealing with rgb data yet'); %TODO
end
function surfCoordIndex(obj)
[rows cols] = size(obj.ZData);
for i=0:rows-2
for j=0:cols-2
curr = i + j*rows;
%sendStr(5,sprintf('%d,%d,%d,%d,-1\n',[curr curr+rows curr+rows+1 curr+1]));
sendStr(5,sprintf('%d,%d,%d,%d,-1\n',[curr+rows curr curr+1 curr+rows+1]));
end
end
% pax I will need to come and optimize this
% for not this is ok but need to handle nan and those
% kind of things.
function patchCoordIndex(obj)
nvert = size(obj.Faces,2);
str = '%d,';
nstr = abs(str)'*ones(1,nvert);
nstr = [char(nstr(:)') '-1\n'];
sendStr(5,sprintf(nstr,obj.Faces'-1));
function patchColorIndex(obj,type)
len = length(get(get(obj.Parent,'Parent'),'Colormap'));
cdat = colorMapping(obj.FaceVertexCData, get(obj.Parent,'Clim'), len, obj.CDataMapping);
switch type
case 'flat'
sendStr(5,sprintf('%d,\n',cdat));
case 'interp'
error(id('InterpolatedColorsNotSupported'),...
'Interpolated colors in patch object not supported yet by vrml.m');
otherwise
error(id('InvalidColorType'),'Unknown color type in patchColorIndex');
end
% this guy will have to listen to CDataScaling and Mapping and so forth pax
function surfColorIndex(obj,type)
switch type
case 'flat'
[rows cols] = size(obj.CData);
cmap_len = length(get(get(obj.Parent,'Parent'),'Colormap'));
cdat = colorMapping(obj.CData, get(obj.Parent,'Clim'), cmap_len, obj.CDataMapping);
for i=1:rows-1
for j=1:cols-1
sendStr(5,sprintf('%d,\n',cdat(i,j)));
end
end
case 'interp'
[rows cols] = size(obj.CData);
cmap_len = length(get(get(obj.Parent,'Parent'),'Colormap'));
cdat = colorMapping(obj.CData, get(obj.Parent,'Clim'), cmap_len, obj.CDataMapping);
for i=1:rows-1
for j=1:cols-1
curr = i + (j-1)*rows;
sendStr(5,sprintf('%d,%d,%d,%d,-1\n',cdat([curr curr+rows curr+rows+1 curr+1])));
end
end
otherwise
error(id('InvalidColorIndexType'),'Unknown colorIndex type in surfColorIndex');
end
function lineCoord(obj)
if(isempty(obj.ZData))
for i=1:length(obj.XData)
sendStr(6,sprintf('%f %f %f,\n',[obj.XData(i) obj.YData(i) 0]));
end
else
for i=1:length(obj.XData)
sendStr(6,sprintf('%f %f %f,\n',[obj.XData(i) obj.YData(i) obj.ZData(i)]));
end
end
function lineCoordIndex(obj)
sendStr(5,'');
for i=1:length(obj.XData)
sendStr(1,sprintf('%d, ',i-1));
end
sendStr(1,'-1\n');
function surfCoord(obj)
if(all(size(obj.ZData)==size(obj.XData)) && all(size(obj.ZData)==size(obj.YData)))
d = [obj.XData(:)'; obj.YData(:)'; obj.ZData(:)'];
else
[x y] = meshgrid(obj.XData,obj.YData);
d = [x(:)'; y(:)'; obj.ZData(:)'];
end
sendStr(6,sprintf('%f %f %f,\n',d));
function patchCoord(obj)
if size(obj.Vertices,2) == 2
sendStr(6,sprintf('%f %f 0.0,\n',obj.Vertices'));
else
sendStr(6,sprintf('%f %f %f,\n',obj.Vertices'));
end
% could use scalar expansion here.
function axesTickCoord(obj)
% XTICK
tx = .05;
x = obj.XTick';
y = obj.YLim(1)*ones(length(x),1);
z = obj.ZLim(1)*ones(length(x),1);
xticks = [x y z ;x y+tx z];
sendStr(6,sprintf('%f %f %f,\n',xticks'));
% YTICK
ty = .05;
y = obj.YTick';
x = obj.XLim(1)*ones(length(y),1);
z = obj.ZLim(1)*ones(length(y),1);
yticks = [x y z ;x+ty y z];
sendStr(6,sprintf('%f %f %f,\n',yticks'));
% ZTICK
tz = .05;
z = obj.ZTick';
x = obj.XLim(1)*ones(length(z),1);
y = obj.YLim(2)*ones(length(z),1);
zticks = [x y z;x y+tz z];
sendStr(6,sprintf('%f %f %f,\n',zticks'));
% come clean this function up TODO
function axesTickCoordIndex(obj)
n = length(obj.XTick);
from = 0:n-1;
to = from + n;
index = [from;to];
sendStr(6,sprintf('%d %d -1\n',index));
currindex = 2*n;
n = length(obj.YTick);
from = currindex:currindex+n-1;
to = from + n;
index = [from; to];
sendStr(6,sprintf('%d %d -1\n',index));
currindex = currindex + 2*n;
n = length(obj.ZTick);
from = currindex:currindex+n-1;
to = from + n;
index = [from; to];
sendStr(6,sprintf('%d %d -1\n',index));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% Support Functions %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function outputAxesCube(obj)
BeginShape('IndexedLineSet');
sendStr(4,'coord Coordinate {\n');
sendStr(5,'point [\n');
cubepts = [0 0 0;0 0 1;0 1 0;0 1 1;1 0 0;1 0 1;1 1 0;1 1 1];
cubepts(:,1) = cubepts(:,1).*diff(obj.XLim) + obj.XLim(1);
cubepts(:,2) = cubepts(:,2).*diff(obj.YLim) + obj.YLim(1);
cubepts(:,3) = cubepts(:,3).*diff(obj.ZLim) + obj.ZLim(1);
sendStr(6,sprintf('%f %f %f,\n',cubepts'));
sendStr(5,']\n');
sendStr(4,'}\n');
sendStr(4,'coordIndex [\n');
sendStr(5,'0,1,3,2,-1\n');
sendStr(5,'4,6,7,5,-1\n');
sendStr(5,'0,2,6,4,-1\n');
sendStr(5,'1,5,7,3,-1\n');
sendStr(5,'6,2,3,7,-1\n');
sendStr(5,'0,4,5,1,-1\n');
sendStr(4,']\n');
sendStr(4,sprintf('color Color {color [%f %f %f]}\n',obj.XColor));
sendStr(4,'colorPerVertex FALSE\n');
sendStr(3,'}\n');
sendStr(2,'}\n');
function outputAxesTickLabels(obj)
off = .1;
for i=1:length(obj.XTick)
tobj.String = num2str(obj.XTick(i));
tobj.Position = [obj.XTick(i) obj.YLim(1)-off*diff(obj.YLim) obj.ZLim(1)];
HandleText(tobj);
end
for i=1:length(obj.YTick)
tobj.String = num2str(obj.YTick(i));
tobj.Position = [obj.XLim(1)-off*diff(obj.XLim) obj.YTick(i) obj.ZLim(1)];
HandleText(tobj);
end
for i=1:length(obj.ZTick)
tobj.String = num2str(obj.ZTick(i));
tobj.Position = [obj.XLim(1)-off*diff(obj.XLim) obj.YLim(2) obj.ZTick(i)];
HandleText(tobj);
end
function outputAxesTicks(obj)
BeginShape('IndexedLineSet');
coord(obj,'axesTickCoord');
coordIndex(obj,'axesTickCoordIndex');
EndShape;
% later this function will make a def and use decision pax
function outputColormap(cmap)
sendStr(6,sprintf('%f %f %f,\n',cmap'));
function rdata = colorMapping(data, clim, colormap_length, mapping_type)
switch mapping_type
case 'direct'
rdata = floor(data);
lower = find(rdata < 1);
rdata(lower) = 1; %#ok
higher = find(rdata > colormap_length);
rdata(higher) = colormap_length; %#ok
case 'scaled'
h = find(data < clim(1)); data(h) = clim(1); %#ok
h = find(data > clim(2)); data(h) = clim(2); %#ok
rdata = floor(((data - clim(1))/(clim(2) - clim(1)))*(colormap_length - 1));
otherwise
error(id('InvalidMappingType'),'Unknown mapping type in function colorMapping');
end
% Send a string to the VRLM file
function sendStr(indent,str)
global VRML_OUTPUT_FILE;
tabs = ' ';
fprintf(VRML_OUTPUT_FILE,tabs(1:indent));
fprintf(VRML_OUTPUT_FILE,str);
% Output other Viewpoints other than the original HG one
function outputOtherViewpoints(obj)
dist = norm(obj.CameraTarget - obj.CameraPosition);
sendStr(2,'Viewpoint {\n');
pos = [obj.CameraTarget([1 2]) dist];
sendStr(3,sprintf('position %f %f %f\n',pos));
sendStr(3,sprintf('fieldOfView %f\n',obj.CameraViewAngle*pi/180));
sendStr(3,'description "View along Z"\n');
sendStr(2,'}\n');
% Computes a quaternion from a View Transform Matrix
function o = computeOrientation(T)
T = T(1:3,1:3);
T(3,:) = -T(3,:);
w = .5*sqrt(trace(T)+1);
s = 4*w;
x = (T(3,2) - T(2,3))/s;
y = (T(1,3) - T(3,1))/s;
z = (T(2,1) - T(1,2))/s;
q = [w x y z];
o(1) = acos(q(1)); % angle/2 in radians
s = sin(o(1));
if s == 0
% no rotation case
o = [0 0 0 0];
else
o(1) = o(1)*360/pi; % angle in degrees
o(2) = q(2)/s;
o(3) = q(3)/s;
o(4) = q(4)/s;
o(1) = o(1)*pi/180;
o(2:end) = -o(2:end);
no = [o(2) o(3) o(4) o(1)];
o = no;
end
% return message id for vrml
function msgID = id(errID)
msgID = ['MATLAB:vrml:' errID];