# Advanced Level

The advanced level of learning formex configuration processing involves the learning of the theory and applications of a number of advanced concepts, as described in the sequel. This level of learning also requires the study of Section 6 of the ‘Basics of Formian-K’, referred to in the description of the intermediate level of learning.

Of course, it should not be assumed that once one has studied the advanced topics, then one would have no more need for any further studies in configuration processing. The process of increasing one’s knowledge in any discipline is ‘unending’. Thus, one would never reach a point where there is nothing more to learn and the process of ‘learning’ does not effectively come to an end. Now, with this though in mind, the list of recommended advanced topics are:

**Tractation function:**The effect of the tractation function is to ‘project’ a given form onto a specified surface. Where, the form to be projected will appear as the argument of the function in terms of a formex expression and the projection surface will be specified by the canonic parameters of the function. The projection may be central, axial or parallel and the projection surface may be chosen from a variety of different surfaces. The study material for the tractation function is Chapter 5 of the PhD Thesis:

1. Champion, O C,

**Polyhedric Configurations**, PhD Thesis, Chapter 5, University of Surrey, 1997, Download

**Pellevation functions:**The effect of a pellevation function is to reshape a given surface by superimposing a specified surface on it. The given surface will appear as the argument of the function in terms of a formex expression and the surface to be superimposed on it will be specified by the canonic parameters of the function. For example, using pellevation functions, one can create a surface that is 35% saddle shaped, 40% conical and 25% spherical.

The study material for the pellevation function consists of two documents. Namely:

2. Nooshin, H,

**' A Technique for Surface Generation '**, Proceedings of the International Symposium on Conceptual Design of Structures, Edited by K U Bletzinger et al, Published by Institute fur Konstruktion und Entwurf II, Stuttgart, Germany, October 1996, pp 331-338 Download

3. Hofmann, I S,

**' The concept of Pellevation for Shaping of Structural forms '**, Proceedings of the 5th International Conference on Space Structures, University of Surrey, Edited by G A R Parke and P Disney, Thomas Telford, August 2002, pp 433-442, ISBN: 07277 31734 Download

The first document is the initial paper that introduced the idea and the second one is a summary of the results of a PhD Thesis that explores the concept of pellevation.

**Scallop Forms:**The term ‘scallop form’ is used to refer to an ‘enveloping surface structure’, such as a dome or a barrel vault that, in addition to its own general curviance, has raised (or depressed) sectors. Here, the word ‘scallop’ is in reference to the marine creature whose shell has raised sectors. The study material for the scallop forms has two parts, namely:

4. Nooshin, H, Tomatsuri, H, and Fujimoto, M,

**' Scallop Domes '**, Proceedings of the IASS International Symposium on Shell and Spatial Structures, Edited by S P Chiew, November 1997, Singapore, pp 651-660, ISBN: 981-00-8905-8 Download

5. Nooshin, H, Kamyab, R and Samavati O A,

**' Exploring Scallop Forms '**, International Journal of Space Structure, Special Issue on Configuration Processing, 2017 Download

**Novation function:**The novation function is a convenient conceptual tool for reshaping of configurations. Where, the required manner of reshaping is specified by one or more movements (relocations) of points on or around the configuration. The function will then reshape the configuration in ‘conformity’ with the indicated relocations. The configuration to be reshaped will appear as the argument of the function in terms of a formex expression and the required relocations and the ‘conformity rule’ will be specified by the canonic parameters of the function. Novation functions are powerful tools for shaping of forms, and in particular, for creation of freeforms.

The study material for the novation function are:

6. Nooshin, H, Albermani, F G A and Disney P L,

**' Novational Transformations '**, Proceedings of the IASS International Colloquium on Structural Morphology, Edited by J C Chilton, B S Choo, W J Lewis and O Popovic, August 1997, Nottingham, UK, pp 36-50, ISBN: 0-85358-064-2 Download

7. Nooshin, H and Samavati, O A,

**' Exploring the Concept of Novation '**, Asian Journal of Civil Engineering (BHRC), Vol 15, No 6 (2014), pp 869-895, ISSN: 1563-0854. [Available in Researchgate

**Link**]

The first document is the initial publication that introduced the idea. It discusses the theory with some examples of applications. The second document has a more practical approach and it is suggested that the Reader starts with this document first.

**Polymation, Antipolymation, Basiretian and Pod functions:**This group of functions are for configuration processing tasks involving polyhedra. The effect of the polymation function is to map an object (given as the argument) on selected faces (or edges or vertices) of a chosen polyhedron. The effect of the antipolymation function is the reverse. That is, an object that has been mapped by a polymation function on a face (or edge or vertex) of a polyhedron, is transformed back to its original form in the global coordinate system. The Basiretian function is a mechanism that allows creation of configurations involving item from different polyhedra. Finally, the pod function is an ‘information provider’ (database) for all aspects of polyhedra.

The study material for the above four functions is contained in Chapter 4 of the PhD Thesis:

8. Champion, O C,

**' Polyhedric Configurations '**, PhD Thesis, Chapter 4, University of Surrey, 1997 Download

**Geodesic Domes:**One of the major attractions of the programming language Formian is its ability to generate geodesic domes based on all types of Platonic and Archimedean polyhedra and this is achieved with ease and elegance.

The study material for the geodesic domes is contained in Chapter 6 of the PhD Thesis:

9. Champion, O C,

**' Polyhedric Configurations '**, PhD Thesis, Chapter 6, University of Surrey, 1997 Download

**Positation function:**The Positation function is a ‘replicator’. To elaborate, given a configuration (as argument) with one, two, or three specified ‘anchor’ points (reference points related to the configuration) and with a number of specified groups of ‘trellis’ points (indicating the required places for replication), the positation function replicates the configuration with the anchor points being positioned at the corresponding trellis points.

The study material for the positation function is Appendix V of the same PhD Thesis which is given as the study material for tractation, polymation, antipolymation, basiretian and pod functions, as well as the geodesic domes, namely:

10. Champion, O C,

**' Polyhedric Configurations '**, PhD Thesis, Appendix V, University of Surrey, 1997 Download