Figure. The underlying coordinate system is always the rectangular cartesian coordinate system.
In ProTOp new optimization coordinate systems are always derived from the world coordinate system or WCS, which is a cartesian coordinate system. The type of the new system can be changed to cylindrical or spherical. Furthermore, its position and orientation can be changed by applying adequate transformations.
In ProTOp any coordinate system type is drawn in a similar way because the underlying coordinate system is always the rectangular cartesian coordinate system as shown in the figure. However, the cylindrical and spherical coordinate systems are decorated by curvilinear lines indicating the correct interpretation of engaged position parameters.
Figure. The underlying coordinate system is always the rectangular cartesian coordinate system.
What is changed by choosing another type is the definition of the position parameters, in the following way:
where the radius R is assumed to be non-negative, while the range of Theta is [-180, +180] and the range of Phi is [-90, +90] measured in degrees.
Figure. Position parameters for all three coordinate system types.
This means that a change of the coordinate system type will change the interpretation of any position parameters that reference the considered coordinate system.
NOTE. Angular parameters (Phi and Theta) have to be specified in degrees (not radians).
A coordinate system data row is flagged by an error status in the following situations:
Various coordinate system types are most useful in configuring the optimization domain. The figures below show the same solid structure configured by various cell and coordinate system types.
Figure. A solid dome structure configured by the Cross3D cell and using a cartesian coordinate system.
Figure. A solid dome structure configured by the HComb2D cell and using a spherical coordinate system.