Transformations: Translation

Introduction to Translation:

Translation is a fundamental transformation in computer graphics that involves displacing objects from one position to another within a three-dimensional coordinate space. It plays a crucial role in repositioning graphical elements to achieve desired visual effects.

Translation in 3D Space:

In 3D graphics, the translation of a point (x, y, z) involves moving it along the x, y, and z axes by specific amounts represented by the translation vector (v_x, v_y, v_z). The new coordinates (x', y', z') after translation can be expressed mathematically using matrix multiplication.

Matrix Representation of Translation in 3D:

The translation operation in 3D space can be efficiently represented using a 4x4 matrix T as follows:

Matrix Multiplication for Translation:

To apply the translation matrix T to a point (x, y, z), the matrix multiplication is performed as follows:

The resulting vector (x', y', z', 1) contains the translated coordinates. The additional fourth element, 1, ensures compatibility with the homogeneous coordinate system.