How to calculate other perspectives on amount of points

I have a actually trivial question, but I just can't find a solution yet.
The following problem:
I have a certain set of points in the xy plane. If you plot them (viewed from the direction of the z-axis) they form a circle.
Now I want to change the perspective, i.e. no longer look perpendicular to the xy plane, but at an angle. The result should then be an ellipse and not a circle.
So it's practically the same as what Matlab does for a spin of a 3D scatter. Maybe I just don't know the wright word for searching.

I've already tried something with the rotation matrix by transforming the points with it, but every time something came out in the form of a cross.

See my Matlab Code below:

r=1;
a=10;
Rx=[1,0,0; 0,cosd(a),-sind(a); 0,sind(a),cosd(a)];

x=[];
y=[];
z=[];
for phi=0:10:360
    x=[x; r*cosd(phi)];
    y=[y; r*sind(phi)];
    z=[z; 0];
end
Points = [x,y,z];

Points_new=[];
for p=1:numel(Points)/3
    Points_new = [Points_new; Rx*Points(p)];
end

figure
scatter(Points(:,1), Points(:,2), '+')
hold on
scatter(Points_new(:,1), Points_new(:,2), '+')
axis equal

Your issue is that you apply the rotation matrix wrong. Let's look at this code:

Points_new=[];
for p=1:numel(Points)/3
    Points_new = [Points_new; Rx*Points(p)];
end

In the loop, p is a scalar value, it starts with 1. Now Points(p) will be Points(1), which is 1. Rx*1 is just Rx, the 3x3 matrix. So the loop is adding 3x3 matrices to the array Points_new, not a vector!.

And, indeed, when we look at the sizes of the arrays, Points has 37 rows, whereas Points_new has 111, three rows for each one row in Points.

You can fix this by using proper indexing, Points(p,:) is the row containing the x,y,z coordinates that you want to transform. Now we need to put that in the right shape by transposing, and then transpose the result again:

Points_new=[];
for p=1:numel(Points)/3
    Points_new = [Points_new; (Rx*Points(p,:).').'];
end

But note that this is very inefficient, for two reasons. One, we're increasing the size of the array Points_new every iteration. Instead, allocate the array to its final size first, then assign by indexing into it:

Points_new = zeros(size(Points));
for p = 1:size(Points,1)
    Points_new(p,:) = Rx*Points(p,:).';
end

(Note I also changed numel(...)/3 into size(...,1), which is clearer in intention.)

The second reason it's inefficient is that you're looping where no loop is necessary. MATLAB loops are very fast nowadays, but not using explicit loops is often a bit faster, and a lot cleaner (easier to write, easier to read, easier to maintain):

Points_new = (Rx * Points.').';

Alternatively, apply the rotation matrix by right multiplication:

Points_new = Points * Rx.';

(obviously the same discussion can be had about your first loop, which can be implemented quite simply as an array function).