Take Plot Data and Turn Into Animation - matlab

Question

I have written code that simulates the rolling of a triangle and gives the output as a trace plot of the three vertices and the centroid for a specified number of rotations.
I would like to turn this plot into an animation and add a circle at each of the triangle vertices to represent wheels.
Can anyone suggest an efficient method to do this?
I am looking to make an animation something like this, except in my case I am not using a ruleaux traingle and just need an animation, not something interactive:
http://demonstrations.wolfram.com/ARollingReuleauxTriangle/
close all
clear
%functions to create rigid body transform matrix---------------------------
hat = #(w) [0,-w(3),w(2); w(3),0,-w(1); -w(2),w(1),0];
rotMatrix = #(th,w) eye(3) + hat(w)*sind(th) + hat(w)*hat(w)*(1-cosd(th));
rbTrans = #(th,w,q) [rotMatrix(th,w), (eye(3) - rotMatrix(th,w))*q(1:3); 0 0 0 1];
%arguments: th=rotation angle, w=rotation axis, q=center of rotation (column vector)
nTurns=5;
degPerTurn=120; %degrees
nStepsPerTurn=1000; %resolution of each "turn". number of points
d = 5.2; %distance from centroid to a vertex
r = 4;
w = [0;0;1;0]; %rotation vector=z-axis
X0 = [0;0;0]; %initial position of centroid
%initialize vertices
v=[0;1;0];
p1 = X0 + [0;d;0];
p2 = X0 + d*rotMatrix(-120,w)*v;
p3 = X0 + d*rotMatrix(120,w)*v;
P(1,1,:) = p1;
P(2,1,:) = p2;
P(3,1,:) = p3;
P(4,1,:) = X0;
rotVertex=2;
thStep=-degPerTurn/nStepsPerTurn;
for i=1:nTurns
for j=1:nStepsPerTurn
%center of rotation
q = squeeze(P(rotVertex,end,:));
q = q + [0; -r; 0];
%transform is a rotation of 120/nSteps about z-axis centered at a
%particular vertex
g = rbTrans(thStep, w, q);
I=size(P,2)+1; %add new element by inserting to (end+1)
for k=1:size(P,1) %for each point we're following-- vertices and centroid
pt = g*[squeeze(P(k,I-1,:)); 1]; %apply transform to last existing value of this point
P(k,I,:) = pt(1:3); %and add it to the end
end
end
%vertices are numbered clockwise around the triangle
rotVertex=rotVertex-1;
if rotVertex<1
rotVertex=rotVertex+3;
end
end
%extract data from 3D array
P1=squeeze(P(1,:,:));
P2=squeeze(P(2,:,:));
P3=squeeze(P(3,:,:));
C=squeeze(P(4,:,:));
figure
plot(P1(:,1),P1(:,2),'b'),hold on
plot(P2(:,1),P2(:,2),'r')
plot(P3(:,1),P3(:,2),'g')
plot(C(:,1),C(:,2),'k')
xlabel('Horizontal Distance (inches)')
ylabel('Vertical Distance (inches)')
axis equal
legend('Vertex 1','Vertex 2','Vertex 3','Centroid', 'Location','Best')
figure
subplot(4,1,1),plot(P1(:,1),P1(:,2)),axis equal,ylabel('P1')
subplot(4,1,2),plot(P2(:,1),P2(:,2)),axis equal,ylabel('P2')
subplot(4,1,3),plot(P3(:,1),P3(:,2)),axis equal,ylabel('P3')
subplot(4,1,4),plot(C(:,1),C(:,2)),axis equal,ylabel('C')
xlabel('Horizontal Distance (inches)')
figure
plot(P3(:,1),P3(:,2),'b'),hold on
plot(C(:,1),C(:,2),'k')
axis equal
xlabel('Horizontal Distance (inches)')
ylabel('Vertical Distance (inches)')
legend('Vertex 3','Centroid', 'Location','Best')

Answer 1

I would encapsulate the drawing of your points in a for loop, drawing each triple of points individually then placing a pause command for a few milliseconds accompanied with a drawnow. If you want this to be an animation, I'm assuming you only want to show one triangle per "frame", and so what you can do is when you want to plot the next set of points, take the previous points and plot them as white to artificially clear them without clearing the entire frame.
Do something like this. Bear in mind I'm only targeting the code where I think is where you want the animation to occur:
figure;
for i = 1 : size(P1, 1)
if (i > 1)
plot(P1(i-1,1), P1(i-1,2), 'w.', P2(i-1,1), P2(i-1,2), 'w.', ...
P3(i-1,1), P3(i-1,2), 'w.', C(i-1,1), C(i-1,2), 'w.');
end
plot(P1(i,1), P1(i,2), 'b.', P2(i,1), P2(i,2), 'r.', ...
P3(i,1), P3(i,2), 'g.', C(i,1), C(i,2), 'k.');
axis equal;
xlabel('Horizontal Distance (inches)');
ylabel('Vertical Distance (inches)');
legend('Vertex 1','Vertex 2','Vertex 3','Centroid', 'Location','Best');
drawnow;
pause(0.1); %// Pause for 0.1 seconds
end