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
        rhombcuspisbramletteicalcitrapacontortus
        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:
        • Rotater is a shareware program produced by Craig Kloeden for the Apple MacIntosh that "reads a set of 3-dimensional points and lines and plots them in a window. The image can then be rotated with the mouse in real time". It is a very convenient program for visualising 3D data, although of course it is essential that you can mathematically describe an object before you can use it.
        • Windows equivalent - Rotate this is a Windows version of Rotater. I do not know how well it works, but to help here are zippped versions of my files.
        • Rotater files for the rhomboaster models are available here (N.B. they are of no use without the Rotater program).
        • The Excel spreadsheet used to calculate them is available here (N.B. You need to save this link as source then open from inside Excel).
        • Other examples of coccoliths and nannoliths modelled with this program are available elsewhere on the INA site.

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