How to rotate a curve in the xz-plane around z axis?

I have a curve difined in a vector M with values in x and z position. I use "plot3" to plot this but now I want to rotate this curve around some axis, preferable z-axis so that it creates a body. In my case it will have a shape of a mountain.

Is this possible?

Answer 1

[Jan]

Rotation around the Z-axis by the angle a:

R = [ cos(a), sin(a), 0; ...
     -sin(a), cos(a), 0; ...
     0,       0,      1];
Points        = rand(3, 100);
RotatedPoints = R * Points;

[Per]

Thank you! How do I define the start point of the rotation? In this case it rotates around z-axis with [0;0;0] fixed. What if I want the curve to rotate around z-axis but with start in say [11;0,0]?

What I want to achive is a rotation of the black curve around the red axis is this picture:

[Jan]

Subtract the translation before rotating and add the translation afterwards again.

[Per]

I dont see it. How do I subtract the translation? say it's 3 in x-dir and 5 in y-dir, will it look like:

R = [ cos(a), sin(a), 0; ...
     -sin(a), cos(a), 0; ...
     -3,       -5,      1];

and then after the Curve*R I then add +3 and +5 ?