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classdef HelperDrawRotation
% This class is for internal use only. It may be removed in the future
%HELPERDRAWROTATION - Class used for drawing figures in Rotation,
% Orientation and Quaternions example.
% Copyright 2017-2018 The MathWorks, Inc.
properties (Constant, Hidden)
LabelPos = 0.9;
SubaxisScale = 0.9;
ArcPos = 0.75;
end
methods (Static)
function drawTeapotRotations
% Teapot Rotation example
f = figure;
dr = getDR;
ax = subplot(1,3,1);
dr.drawTeapot(ax);
xlim(ax, [-1.5 1.5]);
ylim(ax, [-1.5 1.5]);
zlim(ax, [0 2]);
title(ax, 'Teapot');
view(ax, [5 10]);
doGrids(ax);
ax = subplot(1,3,2);
dr.drawRotatedTeapot(ax, [0 0 1], 45);
title(ax, ['Teapot Rotated 45' char(176) ' around Z-axis']);
xlim(ax, [-1.5 1.5]);
ylim(ax, [-1.5 1.5]);
zlim(ax, [0 2]);
view(ax, [5 10]);
doGrids(ax);
ax = subplot(1,3,3);
dr.drawRotatedTeapot(ax, [1 0 1], 15);
title(ax, ...
['Teapot Rotated 15' char(176) 'around axis (1,0,1)']);
xlim(ax, [-1.5 1.5]);
ylim(ax, [-1.5 1.5]);
zlim(ax, [-0.1 2]);
view(ax, [5 10]);
doGrids(ax);
f.Position(3:4) = [1200 300];
end
function draw2DPointRotation(ax)
% 2D Point rotation example
dr = getDR;
dr.drawGlobalAxes(ax,{'x','y','z'});
pt = [0.7 0.5 0];
deg = 30;
q = quaternion([deg 0 0], 'eulerd','ZYX','point');
ptnew = rotatepoint(q, pt);
dr.addPoint(ax, pt);
dr.addPoint(ax, ptnew);
dr.drawArc(ax, pt, ptnew, deg);
% Annotate
oldstr = sprintf('(%g, %g, %g)', pt);
newstr = sprintf('(%.2g, %.2g, %.2g)', ptnew);
text(ax, pt(1), pt(2), pt(3), oldstr);
text(ax, ptnew(1), ptnew(2), ptnew(3), newstr, ...
'HorizontalAlignment', 'right');
view(ax, [0 0 1]);
title(ax, 'Point Rotation');
doGrids(ax);
end
function draw2DFrameRotation(ax)
% 2D Frame rotation example
dr = getDR;
dr.drawGlobalAxes(ax, {'x_{original}', ...
'y_{original}', ''});
pt = [0.7 0.5 0];
deg = 30;
q = quaternion([deg 0 0], 'eulerd','ZYX','point');
ptnew = rotateframe(q, pt);
dr.addPoint(ax, pt);
dr.drawRotatedAxesByEuler(ax, [deg 0 0], ...
{'x_{rotated}', 'y_{rotated}', ''}, 1);
% Annotate point
oldstr = sprintf('(%g, %g, %g)', pt);
newstr = sprintf('(%.2g, %.2g, %.2g)', ptnew);
text(ax, pt(1), pt(2), pt(3), ...
['Coordinate in orignal frame ' newline , ...
oldstr, newline, newline, ...
'Coordinate in rotated frame ', newline newstr ], ...
'HorizontalAlignment', 'right');
view(ax, [0 0 1]);
title(ax, 'Frame Rotation');
doGrids(ax);
end
function draw3DOrientation(ax, rotax, rotangd)
% 3D Orientation example
dr = getDR;
dr.drawGlobalAxes(ax,{'x_{parent}','y_{parent}','z_{parent}'});
rotang = deg2rad(rotangd);
rotax = rotax./norm(rotax);
q = quaternion([cos(rotang./2) sin(rotang./2).*rotax]);
dr.drawRotatedAxesByQuaternion(ax, q, ...
{'x_{child}', 'y_{child}', 'z_{child}'});
dr.drawAxAngRot(ax, rotax, rotangd, 0.75);
view(gca, [110 13]);
% title(gca, ['Frame Rotation of 30' char(176) , ...
% ' Around the Vector [1/3 2/3 2/3]']);
doGrids(ax);
end
function drawEulerRotation(ax, euld)
% Draw Frame rotation using Euler angles
dr = getDR;
dr.drawGlobalAxes(ax, {'x_{parent}', ...
'y_{parent}', 'z_{parent}'});
dr.drawRotatedAxesByEuler(ax, euld, ...
{'x_{child}', 'y_{child}', 'z_{child}'}, 0.9);
title(ax, ['Frame Rotation using Euler Angles of ', newline,...
num2str(euld(1)) char(176) 'Around Z-axis, ', ...
num2str(euld(2)) char(176) 'Around Y-axis, ', ...
num2str(euld(3)) char(176) 'Around Z-axis']);
view(ax, [125 10]);
doGrids(ax);
end
end
methods (Static, Hidden) % Helpers
function ax = drawRotatedAxesByEuler(ax, euld, axlabel, scl)
% Draw rotated set of axes by each Euler angle
eul = deg2rad(euld);
qz = quaternion([eul(1), 0, 0], 'euler', 'ZYX', 'frame');
qy = quaternion([0, eul(2), 0], 'euler', 'ZYX', 'frame');
qx = quaternion([0, 0, eul(3)], 'euler', 'ZYX', 'frame');
x = [1 0 0];
y = [0 1 0];
z = [0 0 1];
% 1st rotation about Z
xr1 = rotatepoint(qz,x);
yr1 = rotatepoint(qz,y);
zr1 = z;
% 2nd rotation about Y
xr2 = rotatepoint(qy,xr1);
yr2 = yr1;
zr2 = rotatepoint(qy,zr1);
% 3nd rotation about X
yr3 = rotatepoint(qx,yr2);
xr3 = xr2;
zr3 = rotatepoint(qx,zr2);
dr = getDR;
%Draw axes. Only label last one.
ap = dr.ArcPos;
dr.drawAxis(ax, scl*xr1, ':', '', 'g', scl*xr1);
dr.drawAxis(ax, scl*yr1, ':', '', 'r', scl*yr1);
dr.drawAxis(ax, scl*zr1, ':', '', 'b', scl*zr1);
dr.drawArc(ax, ap*y, ap*yr1, euld(1));
dr.drawArc(ax, ap*x, ap*xr1, euld(1));
dr.drawAxis(ax, scl*xr2, ':', '', 'g', scl*xr2);
dr.drawAxis(ax, scl*yr2, ':', '', 'r', scl*yr2);
dr.drawAxis(ax, scl*zr2, ':', '', 'b', scl*zr2);
dr.drawArc(ax, ap*zr1, ap*zr2, euld(2));
dr.drawArc(ax, ap*xr1, ap*xr2, euld(2));
dr.drawAxis(ax, scl*xr3, '-', axlabel{1}, 'g', scl*xr3);
dr.drawAxis(ax, scl*yr3, '-', axlabel{2}, 'r', scl*yr3);
dr.drawAxis(ax, scl*zr3, '-', axlabel{3}, 'b', scl*zr3);
dr.drawArc(ax, ap*yr2, ap*yr3, euld(3));
dr.drawArc(ax, ap*zr2, ap*zr3, euld(3));
view(ax, [1 1 1]);
end
function ax = drawRotatedAxesByQuaternion(ax, q, axlabel)
% Draw axes rotated by a quaternion (frame rotation)
x = [1 0 0];
y = [0 1 0];
z = [0 0 1];
xr = rotatepoint(q,x);
yr = rotatepoint(q,y);
zr = rotatepoint(q,z);
dr = getDR;
%Draw axes. Only label last one.
scl = dr.SubaxisScale;
dr.drawAxis(ax, xr, '-', axlabel{1}, 'g', scl*xr);
dr.drawAxis(ax, yr, '-', axlabel{2}, 'r', scl*yr);
dr.drawAxis(ax, zr, '-', axlabel{3}, 'b', scl*zr);
end
function ax = drawGlobalAxes(ax, axlabel)
% Draw X Y Z axes
x = [1 0 0];
y = [0 1 0];
z = [0 0 1];
dr = getDR;
dr.drawAxis(ax, x, ':', axlabel{1}, 'g', x*dr.LabelPos);
dr.drawAxis(ax, y, ':', axlabel{2}, 'r', y*dr.LabelPos);
dr.drawAxis(ax, z, ':', axlabel{3}, 'b', z*dr.LabelPos);
view([1 1 1]);
end
function verts = drawTeapot(~)
% Draw a teapot
[verts, faces, cindex] = teapotGeometry;
verts = verts*0.4;
patch('Faces',faces,'Vertices',verts,'FaceVertexCData', ...
cindex,'FaceColor','interp');
end
function drawRotatedTeapot(ax, rotax, angd)
% Draw a teapot rotated by angd (degrees) around rotax
dr = getDR;
ang = deg2rad(angd);
q = quaternion([cos(ang/2) sin(ang/2)*rotax]);
[verts, faces, cindex] = teapotGeometry;
verts = verts*0.4;
vertR = rotatepoint(q,verts);
patch('Faces',faces,'Vertices',vertR,'FaceVertexCData',...
cindex,'FaceColor','interp');
dr.drawAxAngRot(ax, rotax, angd, 1.3 * max(vertR(:)));
end
function addPoint(ax, pt)
hold(ax, 'on');
plot3(pt(1), pt(2), pt(3), 'r*');
hold(ax, 'off');
end
function drawAxis(ax, endpts, style, txt, color, txtloc)
%Draw a single axis. If txt is '', then no text is added.
%If txt is not empty, txtloc can be used if it is passed,
%otherwise endpts is used.
wd = 2;
% Translate to "lines" colormap
cm =lines;
switch color
case 'g'
color = cm(1,:);
case 'r'
color = cm(2,:);
case 'b'
color = cm(3,:);
end
line(ax, [0 endpts(1)], [ 0 endpts(2)], [0 endpts(3)], ...
'LineWidth', wd, 'Color', color, 'LineStyle', style);
if ~isempty(txt)
if nargin < 6
tloc = 0.75 * endpts;
else
tloc = txtloc;
end
text(ax, tloc(1), tloc(2), tloc(3), txt, 'FontSize', 20);
end
end
function drawAxAngRot(ax, rotax, rotangd, scale)
% Draw axis and angle of rotation
hold(ax, 'on');
pts = 20;
dr = getDR;
dr.drawAxis(ax, rotax*scale, '-', '', 'k');
% It's much easier to draw the rotation arc around the x axis
% and then swing it up to the axis of rotation.
x = [1 0 0];
bisector = x + rotax./norm(rotax); % Parallelogram Law
offset = 0.1* scale;
start = [scale 0 -offset];
angspace = linspace(0,pi,pts).';
qarc = quaternion([cos(angspace./2) sin(angspace./2).*[1 0 0]]);
arcX = rotatepoint(qarc, start);
% Now rotate arcX up to the right spot.
qbis = quaternion([cos(pi/2) sin(pi/2)*bisector]);
arc = rotatepoint(qbis, arcX);
plot3(ax, arc(:,1), arc(:,2), arc(:,3), 'k-');
arrowstart = arc(end-1,:);
arrowend = arc(end,:);
dr.drawArc(gca, arrowstart, arrowend, rotangd);
hold(ax, 'off');
end
function drawArc(ax,start,stop, angdeg)
%Draw an arc from start to stop in axes ax.
% angdeg is the angle label for the rotation
hold(ax, 'on');
pts = 20;
dr = getDR;
ang = acos(dot(start,stop)./( norm(start) .* norm(stop) ));
rotax = cross(start,stop);
rotax = rotax./norm(rotax);
angspace = linspace(0,ang, pts).';
q = quaternion( [cos(angspace./2) sin(angspace./2).*rotax]);
o = rotatepoint(q,start);
plot3(ax, o(:,1), o(:,2), o(:,3), 'k-');
arrowstart = o(end-1,:);
arrowend = o(end,:);
dr.arrow(arrowstart, arrowend);
half = pts/2;
text(ax, o(half,1), o(half,2), o(half,3), ...
sprintf('%4.1d%c', int32(angdeg), char(176)), ...
'FontSize', 10);
hold(ax, 'off');
end
function arrow(start, stop)
% Draw an arrow with the tip at stop.
% The direction of the arrow is the vector from
% start to stop.
ang = 60;
h = 0.05;
vec = stop - start;
vec = h.*vec./norm(vec(:));
newstart = stop - vec;
halfbase = [h./tand(ang) 0 0];
top = stop;
bottom1 = newstart + halfbase;
bottom2 = newstart - halfbase;
pts = [top; bottom1; bottom2];
patch(pts(:,1), pts(:,2), pts(:,3), 'k');
end
end
end
function dr = getDR
dr = HelperDrawRotation;
end
function doGrids(ax)
grid(ax, 'on');
grid(ax, 'minor');
end
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