Difference between revisions of "MOVING REFERENCE MODELS"
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These constraints can be overcome by abandoning a fixed-reference frame in favor of a moving-reference system. In general, the moving reference model is based on simple principles of motion and stepwise growth. At each growth step, the aperture migrates to a new position, according to locally defined rules (Ackerly 1989). Such models have been employed in simulating ammonite growth. Okamoto (1988) proposed a tube model for all types of shell coiling, including heteromorph forms with abrupt changes of coiling patterns. His approach integrates accretional growth of the aperture (opening of the shell) without defining any fixed coordinate system. A similar moving-reference frame has been used in simulating radiate accretive growth of marine sessile organisms, such as corals and sponges, where the growth axis is associated with the local maximum of growth (e.g., Kaandorp 1994; Hammer, 1998; Kaandorp and Kuebler 2001). A comparable approach was used in simulating plant growth (Lindenmayer 1968; Prusinkiewicz and Lindenmayer 1990). CITED AFTER [[OUR PUBLICATIONS|Tyszka & Topa, 2005]]. | These constraints can be overcome by abandoning a fixed-reference frame in favor of a moving-reference system. In general, the moving reference model is based on simple principles of motion and stepwise growth. At each growth step, the aperture migrates to a new position, according to locally defined rules (Ackerly 1989). Such models have been employed in simulating ammonite growth. Okamoto (1988) proposed a tube model for all types of shell coiling, including heteromorph forms with abrupt changes of coiling patterns. His approach integrates accretional growth of the aperture (opening of the shell) without defining any fixed coordinate system. A similar moving-reference frame has been used in simulating radiate accretive growth of marine sessile organisms, such as corals and sponges, where the growth axis is associated with the local maximum of growth (e.g., Kaandorp 1994; Hammer, 1998; Kaandorp and Kuebler 2001). A comparable approach was used in simulating plant growth (Lindenmayer 1968; Prusinkiewicz and Lindenmayer 1990). CITED AFTER [[OUR PUBLICATIONS|Tyszka & Topa, 2005]]. | ||
| − | == Model [[ | + | == Model [[parameters]] == |
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[[Image:Model_parameters.jpg|thumb|left|222px|<font size="2">Moving-reference model parameters <font size="1">(Tyszka, 2006, modified)</font>]] | [[Image:Model_parameters.jpg|thumb|left|222px|<font size="2">Moving-reference model parameters <font size="1">(Tyszka, 2006, modified)</font>]] | ||
| − | The model includes 6 parameters, representing morphospace dimensions: | + | The model includes 6 parameters, representing [[MORPHOSPACE|'''morphospace''']] dimensions: |
* Chamber scaling ratios defined in 3-dimensional space by 3 parameters: | * Chamber scaling ratios defined in 3-dimensional space by 3 parameters: | ||
| − | + | ** '''kx''' - chamber width ratio, | |
| − | + | ** '''ky''' - chamber height ratio, | |
| − | + | ** '''kz''' - chamber depth ratio. | |
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If all chamber scaling ratios equal each other, i.e., kx = ky = kz, a new chamber is isometric to the previous one. Any differences in chamber scaling ratios cause allometric growth of successive chambers. | If all chamber scaling ratios equal each other, i.e., kx = ky = kz, a new chamber is isometric to the previous one. Any differences in chamber scaling ratios cause allometric growth of successive chambers. | ||
| + | * '''TF''' (translation factor) controls an overlap of successive chambers (see Fig.); the “0” TF value places the centre of a new chamber directly at the aperture of the last chamber. This parameter ranges from “-1” to “+1” values. Higher values detach a new chamber from the existing shell that represents a “forbidden zone” sensu Berger (1969) | ||
| + | * '''φ''' as a deviation angle (deflection angle) an angle between the local reference line and the line defining the centre of a new chamber; it ranges from -180° to 180°. Higher or lower out of range values can be recalculated to the values from the given range | ||
| + | * '''β''' as a rotation angle; this parameter is necessary in 3-dimensional space. It ranges from -180° to 180°; higher or lower values can also be recalculated. | ||
== [[Simulation steps]] == | == [[Simulation steps]] == | ||
