Question about plots using meshgrids.

2015 11 24
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更新时间：2015 11 25
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I've created a plot which can show the range of the tip's movement from a 2-armed robotic arm and I hope to add one more arm.
The correct code which can plot 2 arms shows as follows:
l1 = 10; % length of first arm
l2 = 7; % length of second arm
theta1 = 0:0.1:pi/2;% all possible theta1 values
theta2 = 0:0.1:pi;% all possible theta2 values
[THETA1, THETA2] = meshgrid(theta1, theta2); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) ;
for theta1 = 0:0.1:pi/2;
for theta2 = 0:0.1:pi;
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2); % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2);
plot (X,Y);
hold on
end
end
The result after running shows as the figure
And here's the incorrect one with 3 arms:
l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
theta1 = 0:0.1:pi/2;% all possible theta1 values
theta2 = 0:0.1:pi;% all possible theta2 values
theta3 = 0:0.1:pi;
[THETA1, THETA2, THETA3] = meshgrid(theta1, theta2,theta3); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3) ;
for theta1 = 0:0.1:pi/2;
for theta2 = 0:0.1:pi;
for theta3 = 0:0.1:pi;
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3); % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3);
plot (X,Y);
hold on
end
end
end
The error is that" Error using plot Data cannot have more than 2 dimensions."

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 采纳的回答

Walter Roberson
Walter Roberson 2015-11-25

0 个投票

You do not need those three nested for loops: you calculate the same thing in every iteration of the loop. You can just use
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3); % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3);
with no loops.
But then you end up with X and Y both three dimensional; what it means to plot that is not well defined. But you could try
X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));
plot(X1, Y1)

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Ercong Shang
Ercong Shang 2015-11-25
编辑：Walter Roberson 2015-11-25
I've just modified the code as you said
l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
theta1 = 0:0.1:pi/2;% all possible theta1 values
theta2 = 0:0.1:pi;% all possible theta2 values
theta3 = 0:0.1:pi;
[THETA1, THETA2] = meshgrid(theta1, theta2); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) ;
for theta1 = 0:0.1:pi/2;
for theta2 = 0:0.1:pi;
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2); % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2);
X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));
plot(X1,Y1)
hold on
end
end
But the result is the same of the previous, I hope to add another length and angle to it.
Walter Roberson
Walter Roberson 2015-11-25
No loops!
l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
theta1 = 0:0.1:pi/2;% all possible theta1 values
theta2 = 0:0.1:pi;% all possible theta2 values
theta3 = 0:0.1:pi;
[THETA1, THETA2, THETA3] = meshgrid(theta1, theta2,theta3); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3) ;
X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));
plot(X1, Y1);
Ercong Shang
Ercong Shang 2015-11-25
编辑：Ercong Shang 2015-11-25
Thanks a lot! By the way , where do I need to modify in order to add as many arms as I can ? Just take 4 arms as an example if possible.
Walter Roberson
Walter Roberson 2015-11-25
编辑：Walter Roberson 2015-11-25
What is the generalized expression for X and Y ? All cos for X and all sin for Y ? That does not sound like it would achieve all possible locations.
Assume that you have a numeric vector L that contains the lengths for each arm. Assume that you have a cell array thetas of the same length, each entry of which contains the list of theta values for the corresponding arm.
n_arm = length(L);
clear THETAS
[THETAS{1:n_arm}] = ndgrid(thetas{:});
X = 0;
Y = 0;
theta_sum = 0;
for arm_num = 1 : n_arm
theta_sum = theta_sum + THETAS{arm_num};
X = X + L(arm_num) * cos(theta_sum);
Y = Y + L(arm_num) * sin(theta_sum);
end
X1 = reshape(X, size(X,1), []);
Y1 = reshape(Y, size(Y,1), []);
plot(X1, Y1);

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