Aims

• To describe and explain the use of homogeneous transformation matrices.
• To describe in outline how to superpose sets of points.
• To introduce C code for working with three-dimensional transformations.

Objectives

After this lecture you will:

• understand the form and use of homogeneous transformation matrices;
• understand, in outline, how structure superposition is performed;
• understand how to implement programs for fitting and transforming structural fragments.

Supplementary Material

Part of the lecture handout, featuring some of the lecture slides, is available on-line. (PDF)

The source code introduced in this lecture is available on-line.
/users/mdstud/kemp/3Dstructure/examples
/users/mdstud/kemp/3Dstructure/src

Kearsley's method for finding the rotation matrix that minimses the average distance between sets of atoms is described in:

Kearsley, S.K. (1989) "Structural Comparisons Using Restrained Inhomogeneous Transformations", Acta Cryst., A45, 628-635. (PDF)