Cornell University
BioNB 441
Using Graphics

Introduction.

Graphics covers a huge area of different techniques. I will attempt to provide examples of all the Matlab high-level graphics functions I have found, as well as some examples of lower level functions. Graphics might be used in neurobiology for:

• Generation of visual stimuli.
• Presenting point data and fitting a model to it.
• Plotting the trajectory (in 2D or 3D, cartesian or radial) of an animal.
• Depicting experimental apparatus.
• Animation.

The following examples will use Matlab base functions (no toolboxes). Each of the examples represents a typical graphics use, but there are many options which are not explained below. Use Matlab help to investigate each of the functions.

### 2D High-level Function Examples

Simple x-y plot.

```x=0:.1:2*pi;
y1=sin(x);
y2=cos(x);
plot(x,y1,'bx-',x,y2,'r.','linewidth',2);
```

X-y plot with error bars

```x=0:.4:2*pi;
y1=sin(x);
e=.3 .* y1 .* rand(size(x));
errorbar(x,y1,e)
set(findobj('type','line'),'linewidth',2)
```

Area plot

```x=0:.4:2*pi;
y1=sin(x);
y2=sin(x)/2;
area(x',[y1' y2'])
```

Log-log and semilog plots.

```x=0:.1:4;
y1=exp(-x)+.01*randn(size(x));
y2=x.^2;
figure(1)
semilogy(x,y1,'bx-');
figure(2)
loglog(x,y2,'ro-')
```

Histograms and bar charts

```clf
data=randn(10000,1);
hist(data,30)
hold on
x_fit=-4:.1:4;
plot(x_fit, 1000*exp(-(x_fit.^2)/2),'r','linewidth',2)
```
```x=0:.4:2*pi;
y1=sin(x);
y2=sin(x)/2;
figure(1)
bar(x',[y1' y2'],2)
figure(2)
bar(x',[y1' y2'],'stacked')
```

Simple polar plot

```x=0:.1:2*pi;
y1=sin(x).^2;
y2=cos(x).^2;
polar(x,y1,'r-');
```

Angle histogram

```theta=randn(1000,1);
rose(theta,30)
```

Vector plot at origin

```x=0:.4:2*pi;
y1=sin(x);
y2=cos(x)+rand(size(x));
compass(y1,y2,'r')
set(findobj('type','line'),'linewidth',2)
```

2D vector field as arrows

```[x,y]=meshgrid(0:.2:1, 0:.2:1.5);
Vx=sin(x);
Vy=cos(x);
quiver(x,y,Vx,Vy)
set(findobj('type','line'),'linewidth',2)
```

### 2.5D High-level Function Examples

Contour plots, meshes and surfaces

```[x,y]=meshgrid(0:.1:3, 0:.1:5);
z= sin(2*x) .* cos(y);
figure(1)
contour(x,y,z,10);
set(findobj('type','patch'),'linewidth',2)
figure(2)
meshc(x,y,z);
set(gca,'color',[.5 .5 .5])
figure(3)
meshz(x,y,z);
set(gca,'color',[.5 .5 .5])
```

```[x,y]=meshgrid(0:.1:3, 0:.1:5);
z= sin(2*x) .* cos(y);
figure(1)
surf(x,y,z);
figure(2)
h=surfl(x,y,z)
colormap(pink)
set(h,'edgecolor','none')
set(gca,'color',[.5 .5 .5])
figure(3)
surfc(x,y,z);
set(gca,'color',[.5 .5 .5])
```

Bar chart

```[x,y]=meshgrid(0:6, 0:10);
z= sin(x) .* cos(y/2);
figure(1)
bar3(z);
```

### 3D High level functions

Simple x-y-z plots

```t=0:.01:2*pi;
x=1.2*sin(2*t);
y=1.2*cos(2*t);
z=t/6;
plot3(x,y,z, 'linewidth',2)
grid on
box on
axis equal
```

Isosurface determination of a 3D scalar field

```clf
r=-1:.05:1;
[x,y,z]=meshgrid(r,r,r);
w=sqrt(x.^2 + y.^2 + z.^2)+0.02*randn(size(x));
isosurface(w,.5);
figure(1)
p=patch(isosurface(w,.5));
set(p,'facecolor',[1,1,.5],'edgecolor','none')
light
daspect([1,1,1])
axis off
view(30,30)
figure(2)
clf
w=smooth3(w);
p=patch(isosurface(w,.5));
set(p,'facecolor',[1,1,.5],'edgecolor','none')
light
daspect([1,1,1])
axis off
view(30,30)
```

Streamlines and coneplot of a 3D vector field (and a stereo viewer)

```clf
r=-1:.1:1;
[x,y,z]=meshgrid(r,r,r);
%generate a spiral velocity field
ux=5*y;
uy=-5*x;
uz=ones(size(x));

%=======================
subplot(1,2,2)

%make some streamlines
hs=streamline(stream3(x,y,z,ux,uy,uz,...
r,zeros(size(r)),zeros(size(r))));
set(hs,'linewidth',2);

%attach some cones to the streamlines
spacing=30;
for i=1:length(hs)
sx=get(hs(i),'xdata');sx=sx(1:spacing:end);
sy=get(hs(i),'ydata');sy=sy(1:spacing:end);
sz=get(hs(i),'zdata');sz=sz(1:spacing:end);
hc=coneplot(x,y,z,ux,uy,uz,sx,sy,sz,2);
set(hc,'facecolor','red','EdgeColor', 'none')
end

axis([-1 1 -1 1 -1 1])
box on
light('position',[10 10 10])
set(gca,'projection','perspective')
view(30,30)

%positions of the right eye
from=get(gca,'cameraposition');
to=get(gca,'cameratarget');
up=get(gca,'cameraupvector');

ax1=gca;

%===========================
subplot(1,2,1)

%copy the whole data structure to a new axis
copyobj(get(ax1,'children'),gca);

axis([-1 1 -1 1 -1 1])
box on
light('position',[10 10 10])
set(gca,'projection','perspective')

d=.5; %eye spacing
%get the position of the left eye
lefteye=from+d*cross((from-to),up)...
/sqrt(sum((from-to).^2)) ;

set(gca,'cameraposition',lefteye);
```

### Some specialized applications

A stereo camera.
Draw all the objects you want in a view for the right eye, then copy the objects into another axis and compute the view for the left eye. Only the computer graphic camera position changes.

```%define a 3D line
t=0:.01:2*pi;
x=0.9*sin(2*t);
y=0.9*cos(2*t);
z=t/6;

%===========================
subplot(1,2,2) %The right eye

plot3(x,y,z, 'linewidth',2)

% make the plotted region look nice
grid on
box on
axis([-1 1 -1 1 0 1])
set(gca,'projection','perspective')
view(30,30)

%positions of the right eye
from=get(gca,'cameraposition');
to=get(gca,'cameratarget');
up=get(gca,'cameraupvector');

ax1=gca;

%===========================
subplot(1,2,1) %The left eye

%copy the whole data structure to a new axis
copyobj(get(ax1,'children'),gca);

grid on
box on
axis([-1 1 -1 1 0 1])
set(gca,'projection','perspective')

d=.5; %eye spacing
%get the position of the left eye
lefteye=from+d*cross((from-to),up)...
/sqrt(sum((from-to).^2)) ;

set(gca,'cameraposition',lefteye);
```

A hierarchical modeler.
Most of the information for this modeler is on a another web page. The modeler allows you to construct elaborate 3D models and animate them. One example image is shown below.

Computing and displaying trajectories.
The program below is a simple simulation of a 'butterfly' randomly searching for regions of rich food sources. The trajectory is plotted as a series of dots representing the butterfly. The butterfly has state variables of position and velocity and is subject to small random accelerations. The butterfly is confined to a 'cage' by reflective boundary conditions. The food distribution for this simulation was periodic and is displayed as coutour lines of food density.

```clf;

%initial butterfly position
x=0; y=0;

%initial butterfly velocity
vx=0; vy=0;
maxspeed=3;

%time step
dt=.1;

plot(x,y,'.')
s=10
axis([-s s -s s]);
hold on
set(gcf,'doublebuffer','on')

%build a food distribution and contour it
[foodx,foody]=meshgrid(-s:s,-s:s);
foodarray=((sin(foodx/2).^2+sin(foody/2).^2)/2).^4;
contour(foodx, foody, foodarray);
drawnow

for t=1:dt:1000

%assume random accelerations
vx = randn+vx;
vy = randn+vy;

%calculate current food and slow down if
%food is plentiful
food=((sin(x/2).^2+sin(y/2).^2)/2).^4;
vx=vx*(1-food/2);
vy=vy*(1-food/2);

%impose a maximum flying speed
speed=sqrt(vx^2+vy^2);
if speed>maxspeed
vx=vx*maxspeed/speed;
vy=vy*maxspeed/speed;
end

%update positions and check for out-of-cage
%reverse the velocity at the edges
x = x + vx*dt;
y = y + vy*dt;
if x>s | x<-s
vx=-vx;
end
if y>s | y<-s
vy=-vy;
end

plot(x,y,'.');
%text(0,-11,['t=',num2str(t)])
axis([-s s -s s])
drawnow
end
```