Input data for a 3D spherical surface

The hemisphere or a smaller part of a sphere that lies between two parallel planes.

The user is asked to specify:

(1) The radius of the sphere and the x,y,z coordinates of its centre.

(2) The x,y,z coordinates of the centre of the first bounding circle (see below for what is meant by a bounding circle).

(3) The x,y,z coordinates of the centre of the second bounding circle.

(4) The numbers nv1,nv2 that label the voltages that are applied to the sphere (the values of the voltages will be entered later) -nv1 and nv2 are the same if sphere is an equipotential -they are different if a potential gradient is required in the z direction.

(5) If nv1 and nv2 are different, then the user specifies the values of z at which these 2 voltages are applied.

(6) The number n of divisions into triangles. For important advice on subdividing please look at section 3.4 of the Users Guide or the general advice on segmentation. The triangles all have approximately the same area, and are all approximately right-angled isosceles triangles, except for those that are near to a closed end. The number n might be changed by the program. The number n applies to the minimum sector, before reflections in any planes of symmetry. (When the sphere is on the z axis and the x=0, y=0 and x=y symmetry planes have not been called and n is small the program might increase n to give 8-fold symmetry about the z axis, in case other parts of the system have this symmetry.)

There is no need to worry about any planes of reflection symmetry when entering the above information -you can enter a whole hemisphere. The program will test for consistency with those planes and will remove the unnecessary parts (and this will be done before the subdivision into the more basic shapes). The total number of segments starts at the number given by the user but is then doubled for each reflection.

A whole sphere is not allowed -it must be entered as 2 hemispheres.

Bounding circles (on end boundary planes):

The program allows a section of a sphere to be created by cutting a whole sphere with two parallel planes.

The two parallel cuts create edges that are circles. These circles are referred to as the bounding circles in the present program.. They are always parallel to each other.

For example, if a sphere has a radius of 1 and is centred at (0,0,0) and if the first cut passes through the centre, then the bounding circle would have a radius of 1. If the second cut passes through (0,0,0.8) then the second bounding circle would have a radius of 0.6 (=square root of 1**2 - 0.8**2). The slice would have a thickness of 0.8. If on the other hand the second cut passes through (0.0.1) then the second bounding circle would have a radius of 0 and the slice would be a hemisphere.

A slice of a sphere can also be created with the 'clipping' option, but the edges might then be ragged.

All types of electrodes can be scaled and/or shifted and/or reflected and/or rotated.

A spherical electrode can also be made solid, with a zero internal field -but be careful.

There is an option to make an off-centred sphere.

For users who are editing or constructing an 'input data file' without the use of the data-builder -that is, pre-processor:

But Manual editing is certainly not recommended -it is a relic from the time when the databuilder was not available All users are strongly encouraged to use the databuilder, which always gives the correct formats and which has many options for which the formats are not described or easily deduced.

Typical data for a spherical surface, taken from test3d01.dat, are:

spherical electrode -

0.75 0. 0. 0. radius, centre of sphere -

0. 0. 0. centre of 1st bounding circle

0. 0. 0.75 centre of 2nd bounding circle

1 1 numbers of 2 applied voltages (can be same)

37 number of subdivisions into triangles (0 cancels)

The data required are:

(1) radius of sphere and x,y,z coordinates of its centre -to disable the 'inscribing correction' (see the relevant note and the second relevant note), enter a negative radius

(2) x,y,z coordinates of centre of 1st bounding circle (see below for what is meant by a bounding circle)

(3) x,y,z coordinates of centre of 2nd bounding circle

(4) numbers nv1,nv2 that label voltages that are applied to the sphere

(5) if nv1 and nv2 are different, then enter values of z at which these 2 voltages are applied

(6) an optional 'address', which is an integer and which can always be 0 -it is non-zero only when information on a large number of curved electrodes is being entered and when the user wants to reduce the number of lines of data -see the relevant note.

(7) number n of divisions into triangles.