Lecture GK-3

Transformations and superpostion

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

Some of the lecture slides are available on-line (PDF). Notes on transformations are also available on-line (local access).

The source code introduced in this lecture is available on-line:

/chalmers/users/kemp/TDA506/practical1/question2
/chalmers/users/kemp/TDA506/src
/chalmers/users/kemp/TDA506/include

For those who are interested in the mathematics of fitting point sets, Kearsley's method for finding the rotation matrix that minimses the average distance between sets of atoms is described in:

Kearsley, S.K. (1989) "On the orthogonal transformation used for structural comparisons", Acta Cryst., A45, 208-210. (PDF)