Disk out of an arc

I was wondering how to create a matrix of points inside an arc of a specific radius R. My goal is my matrix to have a sufficient number of elements, so that when creating a 2D/3D plot, the shape appear as a surface. My idea is to create a set of many arcs, so that the shape appears as continuous. I used a fairly easy code to create arcs of angle pi/8:

R = 0;

theta = pi/8;

x = linspace(R*cos(theta),R,100);

y = sqrt (R^2 - x.*x);

plot(x,y)

xlim([0 5])

ylim([0 5])

hold on

R = 1;

x = linspace(R*cos(theta),R,100);

y = sqrt (R^2 - x.*x);

plot(x,y)

hold on

R = 2;

x = linspace(R*cos(theta),R,100);

y = sqrt (R^2 - x.*x);

plot(x,y)

hold on

R = 3;

x = linspace(R*cos(theta),R,100);

y = sqrt (R^2 - x.*x);

plot(x,y)

hold on

R = 4;

x = linspace(R*cos(theta),R,100);

y = sqrt (R^2 - x.*x);

plot(x,y)

hold on

R = 5;

x = linspace(R*cos(theta),R,100);

y = sqrt (R^2 - x.*x);

plot(x,y)

hold on

How can I continue a similar procedure with a function that avoids writing so many values of R manually? I thought using R = linspace (0,Rmax,N), where Rmax is the radius of the disk, N the number of arcs, but his doesn't appear to work; there is an error with the functions I am using.

[Jan]

"doesn't appear to work" and "there is an error" is less useful to clarify the problem. Please post a copy of the complete error message.

What about using a surface to display a surface?

[Minas Emiris]

Let me start by specifying the purpose I need this 2D sketch for. I recognise 3d sketching is easier with Autocad, but I wanted to create a 3D sketch of a wheel's rim. For the front part which I will attach on a photo below, the way I thought I could create it was firstly to create a 2D sketch of the surface, then create a 3D. For this surface, I figure it will be easier to split it in small parts which repeat in a circular pattern as shown (16 times).

Now, to create the plot I figured I could firstly create a matrix of points inside the arc, then delete the points of the matrix which lie below the curve formed by the holes of the rim (shown as curve C1). This is the reason why I think the function surface might not work.

Moving onto my attempt, I am attempting to use the function of linspace to create a set of radii (R = linspace(0,5,100) for example), but I am using linspace for x as well in terms of R, so the error message is that the input of linspace must be scalar.

Answer 1

[Are Mjaavatten]

Is this what you want?

R = 5;
x = linspace(R*cos(theta),R,100);
y = sqrt (R^2 - x.*x);
x = [0,x];
y = [0,y];
patch(x,y,'b')

Alternatively, by plotting one arc at a time, as you proposed:

figure;
hold on
N = 300;
Rmax = 5;
R = linspace (0,Rmax,N);
for i = 1:N
    x = linspace(R(i)*cos(theta),R(i),100);
    y = sqrt (R(i)^2 - x.*x);
    plot(x,y,'b');
end

[Minas Emiris]

I have thought of the first solution, if you read my comment above, you will see I would have problems with my issue later.

The second solution is what I was looking for, thank you very much!

[Minas Emiris]

How do we though create a matrix with all the values of X and Y of this plot?

[Are Mjaavatten]

To collect all x and y values in large matrices X and Y in pretty straight-forward:

N = 300;
M = 100;
Rmax = 5;
theta = pi/8;
R = linspace (0,Rmax,N);
X = zeros(N,M);
Y = zeros(N,M);
figure;
hold on
for i = 1:N
    X(i,:) = linspace(R(i)*cos(theta),R(i),M);
    Y(i,:) = sqrt (R(i)^2 - X(i,:).*X(i,:));
    plot(X(i,:),Y(i,:),'b');
end

I am not sure that this is what you want, though.

[Minas Emiris]

This does provide us with two matrices of X and Y, but it would be easier if the matrix of X was firstly turned into a row of values in ascending order, and Y was accordingly rearranged as well, so that each element of X corresponds to an element of Y.

[Are Mjaavatten]

This does what you ask for:

[x,ix] = sort(X(:));
y = Y(ix);
plot(x,y,'.')

But somehow I doubt that this is what you want.

I really hate this this damn machine,

I wish that they would sell it.

It never does quite what I mean

but only what I tell it!

The programmer's lament ( from the time before PCs):

[Minas Emiris]

Thank you very much!! Nice poem!