The Art Of Transformation

To transform is to change in composition or structure.  In its simplest terms the word transform, as it applies to 3D graphics, is to handle scenes changing from one frame to the next.  Moving an object is a transformation referred to as translation.  Other types of transformations include moving the point of view, zooming, scaling (changing an objects size) and rotation.

As objects are transformed in a 3D world, their positions must be calculated at rates of millions of times per second.  The calculations are based on linear algebra (in particulare matrix multiplication operations).

The math required to compute transforms is straightforward, but the number of operations neeed to compute a single transform consists of 16 multiplication and 12 addition operations.

Matrix Multiplication To Compute Transforms

In this example, different transformations are combined on NVIDIA's Porsche Boxter - rotation, scaling, and translation, into one fluid scene: