Transformations

Overview

A transformation is any function that we can apply to a set of geometric primitives, such as points or edges. Some examples of transformations include moving points by a scalar value, scaling them by a value, rotating, mirroring them across an axis, and more.

Translation, rotation, and scaling are three types of transformations with great importance in the world of 3D design. They belong to a special set of transformations called affine transformations. They’re essential in assembling 3D scenes, and nearly every major 3D design software has tools for these three transformations.

The affine transformations

Any transformation that preserves parallel lines is said to be an affine transformation. When we apply transformations to an object, those transformations are said to be affine if parallel lines on the object remain parallel after the transformation.

Affine transformations preserve two properties:

• Collinearity: When we transform an object, all points along a line must remain along that line, regardless of whether that line is rotated, translated, stretched, etc.

• Ratios of distances: All points must maintain the same relative distance from one another following the transform. For example, if a set of points in a line are all scaled by the same amount, then the relative distance between points should not change.