Rhomboaster - Explanation of the models

Morphological model
The figure below illustrates the morphological model used to construct all the drawings shown on the main page. The practical process of model construction is:
  1. The x-y-z co-ordinates of each vertex of the model are calculated in an Excel spreadsheet. Within the spreadsheet these co-ordinates are simple functions of the five parameters shown in the diagram, derived using basic trigonometry. Changing the values of any of the four parameters creates modified models.
  2. The spreadsheet is saved as a text file, consisting of a sequence of x-y-z co-ordinate locations, together with a fourth value (c) indicating the how the successive vertices should be joined.
  3. This text file is used by the program Rotater to produce rotatable wireframe models.
  4. A succession of views from Rotater are then saved (using AppleScript routines included with Rotater 3.5) and joined together as an animated GIF (using the shareware program GifBuilder).

Parameter values used in the models
Nannolith thickness 1010101010
Central body radius 1010101010
Ray angle 1515202015
Ray length 11.515306030
Interlayer angle 6060606030

Note that not all parameters were varied. In particular for the rhomb->cuspis->bramlettei->calcitrapa sequence only ray angle and ray length were vried. The values for these parameters were first set by creating a model of bramlettei which modelled realistically the available SEMs. Modified versions were then produced for the other species and for a simple rhomb. This process resulted in the ray angle varying between the rhomb and the bramlettei model, a more parsimonious hypothesis might be that only ray length varies, but without rather precise anglar measurements on real specimens we cannot test whether this actually is the case. Also we would note that the inter-ray angle certainly does decrease during the transition from contortus to orthostylus.

Investigating further:

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