Scaling (geometry)
Using homogeneous coordinates

In projective geometry, often used in computer graphics, points are represented using homogeneous coordinates. To scale an object by a vector v = (v, v, v), each homogeneous coordinate vector p = (p, p, p, 1) would need to be multiplied with this projective transformation matrix:

As shown below, the multiplication will give the expected result:

Since the last component of a homogeneous coordinate can be viewed as the denominator of the other three components, a uniform scaling by a common factor s (uniform scaling) can be accomplished by using this scaling matrix:

For each vector p = (p, p, p, 1) we would have

which would be equivalent to
combination:two_responses