In this chapter the development of a model of a growth in three dimensions is discussed. In the first section it is demonstrated how the modelling system for iterative geometric constructions (see also Sect. 2.6) can be extended to 3D. In Sect. 5.2, a discussion follows on the 3D structure of an organism with radiate accretive growth. In Sects. 5.3 and 5.4 it is discussed how this 3D structure can be represented in a model. The results of these sections, a suitable data representation for a 3D object developing in the radiate accretive growth process, is used in the final Sect. 5.6, in which the development of a model of a radiate growth process in three dimensions is presented. Most of the rules discussed in Sect. 3.6, on the iterative geometric constructions for simulating this growth process, will be extended to 3D. In Sect. 3.6 the biological examples used as a case-study were the sponge Haliclona oculata and the stony coral Montastrea annularis. For reasons which will become clear in the next sections, the sponge Haliclona simulans (see Fig. 3.15) is used as an example in this chapter. The biological significance of the rules will be indicated only briefly in this chapter, since most of them were already discussed in Sect. 3.6. The extension to 3D of the simulation model is an essential one, since many aspects of the growth process (e.g. a larger possibility for the branches to avoid each other, the formation of flattened forms influenced by the flow direction) can only be adequately described with a 3D model. For convenience the symbols used in the sections on the 3D model of radiate accretive growth (Sects. 5.3–5.7 are listed separately in Sect. 5.8).
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- 3D Models of Growth Forms
Jaap A. Kaandorp
- Springer Berlin Heidelberg
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