Rotate About an Arbitrary Axis

This example shows how to rotate an object about an arbitrary axis.

Translate to Origin Before Rotating

Rotations are performed about the origin. Therefore, you need to perform a translation so that the intended axis of rotation is temporarily at the origin. After applying the rotation transform matrix, you then translate the object back to its original position.

Rotate Surface

This example shows how to rotate a surface about the y-axis.

Create Surface and Transform

Parent the surface to the transform object.

t = hgtransform;
surf(peaks(40),'Parent',t)
view(-20,30)
axis manual

Create Transform

Set a y-axis rotation matrix to rotate the surface by -15 degrees.

ry_angle = -15*pi/180; 
Ry = makehgtform('yrotate',ry_angle);
t.Matrix = Ry;

The surface rotated -15 degrees about the y-axis that passes through the origin.

Translate the Surface and Rotate

Now rotate the surface about the y-axis that passes through the point x = 20.

Create two translation matrices, one to translate the surface -20 units in x and another to translate 20 units back. Concatenate the two translation matrices with the rotation matrix in the correct order and set the transform.

Tx1 = makehgtform('translate',[-20 0 0]);
Tx2 = makehgtform('translate',[20 0 0]);
t.Matrix = Tx2*Ry*Tx1;