ARROW3   EXAMPLES   (R13)

Two-Dimensional Quiver Plots

Example 1.  (cf. Joukowski Airfoil Transformation)

t=10*pi/180; u=0.1; v=0.1; r=1.1; tol=8e-2;
s=u+i*v; k=2*r*sin(t); w=exp(i*t);
[x,y]=meshgrid(-2.5:0.1:3.5,-3:0.1:3);
z=x+i*y; z(abs(z-s)<r-tol)=NaN;
f=w*z+exp(-i*t)*r^2./(z-s)+i*k*log(z);
a=0:0.1:2*pi; zc=r*(cos(a)+i*sin(a))+s;
c1=-1.5; c2=2.5; c3=c2-c1;
c=contour(x,y,imag(f),c1:c3/16:c2);
set(gca,'color',0.5*[1 1 1])
hold on, daspect([1 1 1])
fill(real(zc),imag(zc),'y'), colorbar
map=get(gcf,'colormap');
domain=0:1/(size(map,1)-1):1; m=1;
while m<length(c), n=m+c(2,m);
  if c(2,m)>9, p=c(:,m+1:n)';
    if p(end,1)>p(1,1), p=flipud(p); end
    ndx=10:10:length(p);
    p2=p(ndx,:); p1=p(ndx-3,:);
    cc=interp1(domain,map,(c(1,m)-c1)/c3);
    set(gca,'ColorOrder',cc)
    arrow3(p1,p2,'0o',0.8)
  end, m=n+1;
end, hold off

Example 1.  Joukowski Airfoil Transformation
Example 1.

 
Example 2.  (cf. Quiver)

[x,y]=meshgrid(-1:1/21:1);
z=x.*exp(-x.^2-y.^2);
[c,h]=contour(x,y,z);
set(h,'EdgeColor',0.45*[1 1 1])
ndx=1:3:length(x);
x=x(ndx,ndx); y=y(ndx,ndx); z=z(ndx,ndx);
[u,v]=gradient(z,1/7);
p1=[x(:),y(:)]; u=u(:); v=v(:);
m=abs(u+i*v); % gradient magnitude
daspect([1 1 1]), set(gca,'color',0.3*[1 1 1])
hold on, colormap hot, scale=0.4;
arrow3(p1,p1+scale*[u,v],'|',min(1.25*m,0.85))
hold off, h=colorbar;
set(h,'YTickLabel',num2str(str2num(get(h,...
  'YTickLabel'))/scale))

Example 2.  Surface Gradients
Example 2.

 
Example 3.  (cf. Two-Dimensional Quiver Plots)

[x,y,z]=peaks(-2:0.05:2);
contour(x,y,z,10); h=gca;
ndx=1:4:length(x);
x=x(ndx,ndx); y=y(ndx,ndx); z=z(ndx,ndx);
[u,v]=gradient(z,0.2);
p1=[x(:),y(:)]; u=u(:); v=v(:);
m=abs(u+i*v); % gradient magnitude
hold on, daspect([1 1 1]), scale=0.025;
arrow3(p1,p1+scale*[u,v],'|',0.9*m/max(m))
hold off, title('Dual Colormap')
h1=colorbar; h2=copyobj(h1,gcf);
set(h,'color',0.4*[1 1 1],...
  'position',get(h,'position')+[0.05 0 0 0])
% ---------------------------------------------- Right Colorbar
p=get(h1,'position');
set(h1,'position',[0.87,p(2),0.05,p(4)],...
  'YTickLabel',num2str(str2num(get(h1,...
  'YTickLabel'))/scale))                         % freeze labels
map=colormap; cdata=reshape(map,size(map,1),1,3);
set(get(h1,'children'),'cdata',cdata)            % freeze colors
set(get(h1,'title'),'string','Gradient')
% ---------------------------------------------- Left Colorbar
caxis auto, colorbar, colormap autumn
set(h2,'YAxisLocation','left',...
  'position',[0.08,p(2),0.05,p(4)])
set(get(h2,'title'),'string','Contour')

Example 3.  Dual Colormap
Example 3.


Three-Dimensional Quiver Plots

Example 4.  (cf. Quiver3)

[x,y]=meshgrid(-2:0.25:2,-1:0.25:1);
z=x.*exp(-x.^2-y.^2);
surf(x,y,z,'EdgeColor','none')
axis([-2.5 2.5 -1.5 1.5 -1 1]), daspect([1 1 1])
set(gca,'CameraViewAngle',7)
[u,v,w]=surfnorm(x,y,z);
p1=[x(:),y(:),z(:)]; N=[u(:),v(:),w(:)];
hold on
arrow3(p1,p1+0.5*N,'1.5_b')
hold off, colormap spring
light('position',[-1 -1 -1],'style','local')
light('position',[0 1 1]), lighting gouraud

Example 4.  Surface Normals
Example 4.

 
Example 5.  (cf. Three-Dimensional Quiver Plots)

vx=2; vy=3; vz=10; a=-32; t=(0:.1:1)';
x=vx*t; y=vy*t; z=vz*t+1/2*a*t.^2;
r=[x,y,z]; v=gradient(r')';
axis([0 3 0 4 -10 2]), pbaspect([2 1 1])
hold on, grid on, view([70 18])
arrow3(r,r+v,'b',0.9)
hold off

Example 5.  Velocity Vectors
Example 5.


Cone Plots

Example 6.  (cf. Coneplot)

load wind, wind_speed=sqrt(u.^2+v.^2+w.^2);
xmin=min(x(:)); xmax=max(x(:));
ymin=min(y(:)); ymax=max(y(:));
zmin=min(z(:));
hsurfaces=slice(x,y,z,wind_speed,[xmin,xmax],ymax,zmin);
set(hsurfaces,'FaceColor','interp','EdgeColor','none',...
              'AmbientStrength',0.6)
hold on, daspect([2,2,1]), view(30,40), axis tight
xrange=linspace(xmin,xmax,8);
yrange=linspace(ymin,ymax,8);
[cx cy cz]=meshgrid(xrange,yrange,3:4:15);
ui=interp3(x,y,z,u,cx,cy,cz);
vi=interp3(x,y,z,v,cx,cy,cz);
wi=interp3(x,y,z,w,cx,cy,cz);
m=sqrt(ui.^2+vi.^2+wi.^2); m=m(:)/30;
p1=[cx(:),cy(:),cz(:)]; p2=[ui(:),vi(:),wi(:)];
hcones=arrow3(p1,p2,'r',m,3*m,'cone');
set(hcones,'DiffuseStrength',0.8)
hold off, axis off
camproj perspective, camzoom(1.2)
camlight right, lighting phong

Example 6.  Wind Speed and Direction
Example 6.

 
Example 7.  (cf. Vector Field Displayed with Cone Plots)

load wind, wind_speed=sqrt(u.^2+v.^2+w.^2);
hiso=patch(isosurface(x,y,z,wind_speed,40),...
          'FaceColor','red','EdgeColor','none');
isonormals(x,y,z,wind_speed,hiso)
hcap=patch(isocaps(x,y,z,wind_speed,40),...
          'FaceColor','interp','EdgeColor','none',...
          'AmbientStrength',0.6);
hold on, colormap hsv, daspect([1,1,1]), view(65,45)
[f verts]=reducepatch(isosurface(x,y,z,wind_speed,30),0.07);
cx=verts(:,1); cy=verts(:,2); cz=verts(:,3);
ui=interp3(x,y,z,u,cx,cy,cz);
vi=interp3(x,y,z,v,cx,cy,cz);
wi=interp3(x,y,z,w,cx,cy,cz);
m=sqrt(ui.^2+vi.^2+wi.^2); m=m(:)/40;
p1=[cx(:),cy(:),cz(:)]; p2=[ui(:),vi(:),wi(:)];
h1=arrow3(p1,p2,'b',m,3*m,'cone');
xrange=linspace(min(x(:)),max(x(:)),10);
yrange=linspace(min(y(:)),max(y(:)),10);
[cx,cy,cz]=meshgrid(xrange,yrange,3:4:15);
ui=interp3(x,y,z,u,cx,cy,cz);
vi=interp3(x,y,z,v,cx,cy,cz);
wi=interp3(x,y,z,w,cx,cy,cz);
m=sqrt(ui.^2 + vi.^2 + wi.^2); m=m(:)/50;
p1=[cx(:),cy(:),cz(:)]; p2=[ui(:),vi(:),wi(:)];
h2=arrow3(p1,p2,'g',m,3*m,'cone');
hold off, axis tight, box on
set(gca,'xtick',[],'ytick',[],'ztick',[])
camproj perspective, camzoom(1.2)
camlight(-45,45), lighting phong

Example 7.  Wind Speed and Direction
Example 7.


Feather Plots

Example 8.  (cf. Feather)

theta=(-90:10:90)'*pi/180;
n=length(theta); p1=[1:n;zeros(1,n)]';
r=2*ones(n,1); [u,v]=pol2cart(theta,r);
plot([1 n],[0 0],'r')
axis([0 20 -2 2]), daspect([8 2 1])
hold on, grid on
arrow3(p1,p1+[u,v],'r',0.9)
hold off

Example 8.  Feather Plot
Example 8.

 
Example 9.  (cf. Plotting Complex Numbers)

t=(0:0.5:10)'; s=0.05+i; Z=exp(-s*t);
n=length(Z); p1=[1:n;zeros(1,n)]';
plot([1 n],[0 0],'b')
axis([0 22 -1 1]), daspect([8 1 1])
hold on, grid on
arrow3(p1,p1+[real(Z),imag(Z)],'b',0.8)
hold off

Example 9.  Complex Number Plot
Example 9.


Compass Plots

Example 10.  (cf. Compass Plots)

wdir =[45 90 90 45 360 335 360 270 335 270 335 335];
knots=[ 6  6  8  6   5   9   8   8   9  10  14  12];
[x,y]=pol2cart(wdir*pi/180,knots);
polar(0,15), axis(15.9*[-1 1 -1 1])
hold on
arrow3(zeros(length(x),2),[x',y'],'r',1.25)
hold off

Example 10.  Wind Speed and Direction
Example 10.

 
Example 11.  (cf. Compass)

Z=eig(randn(20)); m=abs(Z);
R=ceil(max(m)); r=R+0.3;
polar(0,R), axis(r*[-1 1 -1 1])
hold on
arrow3(zeros(length(Z),2),[real(Z),imag(Z)],'b',1.75*m/R)
hold off

Example 11.  Complex Number Plot
Example 11.


Reference Frames

Example 12.  Coordinate Axes

p=[4 2 1]; axis([-6 6 0 5 -1 1])
pbaspect([2 1.5 1]), view(55,15)
hold on
arrow3(repmat([p(1:2),0],4,1),...
  [0 p(2) 0;p(1) 0 0;p;0 0 0],'--o',0,0,0.5)
arrow3(zeros(3),diag([7,5,1]),'o')
arrow3([0 0 0],p,'2.5s',1.5,[],0)
hold off, axis off, camlight left
set(gca,'CameraViewAngle',4)
text(7.1,0,0,'X'), text(0,5.05,0,'Y')
text(0,0,1,'Z','VerticalAlignment','bottom',...
  'HorizontalAlignment','center')

Example 12.  Coordinate Axes
Example 12.

 
Example 13.  Eigenvectors

n=500; % generate test data
newz=[ 1  1 1]/sqrt(3);
newy=[ 0 -1 1]/sqrt(2);
newx=cross(newy,newz);
R=[newx;newy;newz]; % rotation matrix
U=randn(n,3)*diag([1,2,3])*R;
u=U(:,1)+10; v=U(:,2)+20; w=U(:,3)+30;
% plot eigenvectors with mean origin
plot3(u,v,w,'r.')
axis([0 20 10 29 20 40]), daspect([1 1 1])
view([-70,15]), set(gca,'CameraViewAngle',8)
hold on, grid on
mu=repmat(mean([u,v,w]),3,1);
[V,D]=eig(cov([u,v,w]));
p=9*V'+mu;
arrow3(mu,p,[],1.25,[],0)
p=p+ones(3);
text(p(1,1),p(1,2),p(1,3),'\bfU')
text(p(2,1),p(2,2),p(2,3),'\bfV')
text(p(3,1),p(3,2),p(3,3),'\bfW')
hold off

Example 13.  Eigenvectors
Example 13.

 
Example 14.  (cf. Frenet)

z=(0:2/99:2)'; t=2*pi*z; r=2+z;
x=r.*cos(t); y=r.*sin(t);
R=[x,y,z]; dR=gradient(R')';
m=repmat(sqrt(sum(dR.*dR,2)),1,3);
T=dR./m; dT=gradient(T')';
m=repmat(sqrt(sum(dT.*dT,2)),1,3);
N=dT./m; B=cross(T,N);
plot3(x,y,z,'color',0.5*[1 1 1])
axis([-4 4 -4 4 0 2.5])
hold on, grid on, pbaspect([1 1 1])
set(gca,'CameraViewAngle',7)
plot3(0,0,0,'r'), plot3(0,0,0,'color',[0 0.5 0])
plot3(0,0,0,'b')
legend('Curve','Tangent','Normal','Binormal',2)
ndx=1:4:length(x); R=R(ndx,:);
arrow3(R,R+1.4*T(ndx,:),'r',0.9)
arrow3(R,R+1.4*N(ndx,:),'e',0.9)
arrow3(R,R+0.4*B(ndx,:),'b',0.9)
hold off, view(-50,5)
set(gcf,'renderer','zbuffer')

Example 14.  Frenet Frames
Example 14.


Named Colors

Example 15.  Named Color Table

arrow3('colors',0.4)     % 24 named colors with 44 adjustable shades

Example 15.  Named Color Table
Example 15.


Color Equivalencies
ColorOrder               Arrow3 Simulink               Arrow3
Color1       Blue LightBlue       aZure
Color2       Evergreen DarkGreen       Asparagus
Color3       Red Orange       kumQuat
Color4       Sky blue Gray       Light gray
Color5       Violet  
Color6       Pear  
Color7       Dark gray  


Update (Modify and Restore)

Example 16.  Modify and Restore

% Arrow3 draws surfaces that appear to be right circular cones and
% spheres, but arrowheads and initial point markers retain their
% appearance only so long as the data aspect ratio remains unchanged.
daspect([1 1 2]), view([-40,24])
axis([-1 4 -1 4 0 6])
hold on, axis off
p1=[0,0,0;2,1,0;2.5,3,0;0,2,0];
p2=[-1,2,6;3,-1,3;2.5,1.5,5;-1,3.5,2];
global LineWidthOrder, LineWidthOrder=[2,3,3,3];
global ColorOrder, ColorOrder='rvbe';
w=[3,8,6,4]; h=[9,12,12,8]; ip=[3,5,5,4];
set(gca,'LineStyleOrder',{'--','-','-.',':'},...
  'position',get(gca,'position')+[0,0.075,0,0])
arrow3(p1,p2,'o*/',w,h,ip)
hold off
camlight left

Example 16.  (a) Original plot
Example 16.

 
% Changing the data aspect ratio distorts the appearance of
% arrowheads and initial point markers.
daspect([1 1 1])

Example 16.  (b) Aspect ratio distortion
Example 16.

 
% Restore appearance of arrowheads and initial point markers.
arrow3('update')
% Modify colors of arrowheads, initial point markers, and lines to
% conform with magnitude coloring in the current colormap.
h=arrow3('update','colors');
% Change line style to continuous.
set(h(strcmp(get(h,'type'),'line')),'LineStyle','-')
% Reduce arrowhead width by 25%, retain arrowhead height, and reduce
% initial point marker diameter by 50%.
h=arrow3('update',[0.75,1,0.5]);
% Reduce opacity to 70%.
set(h,'FaceAlpha',0.7)
camlight head

Example 16.  (c) Updated plot
Example 16.

 
See also Arrow3 Messes Up My Plots!