Input data for a 3D cone

A cone that can have both ends open or one end open and the other closed (that is, pointed).

If both ends are open then the two radii must not differ in magnitude by more than a factor of 10.

If one end is closed, making a pointed cone, then a warning messaage invariably comes up saying that the end triangles are too long and thin.  This can be disabled, but only do this temporarily.  Physical cones are never pointed.

The axial direction can be divided evenly or unevenly (except that the uneven distribution is not allowed for a closed cone).

The uneven distribution gives a higher density of segments near the smaller end, so that all the triangular segments have approximately the same shape (in particular, this avoids some of the triangles becoming long and thin). The uneven distribution is recommended unless the larger end of the disc is a critical region (in which case it would probably be better to use a separate section of cone to model the outer edge).

The user specifies:

(1) The radius and the x,y,z coordinates of the centre of the first end of the electrode.

(2) The radius and the x,y,z coordinates of the centre of the second end of the electrode (if the two radii are the same then the 'cone' will be changed to a 'cylinder') (and if the cone is pointed -that is, if one of the radii is zero- then the zero radius should be the second one).

(3) The numbers nv1,nv2 that label the voltages that are applied to the electrode (the values of the voltages will be entered later).

-nv1 and nv2 are the same if the electrode is an equipotential

-they are different if a potential gradient is required in the z direction

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

(5) Either:

(a) The numbers n1 and n2 of divisions along the axis and around the axis respectively, giving 4*n1*n2 triangles for a cone with an open end, and (4*n1-3)*n2 for complete cone (that is, with a closed end). The numbers n1 and n2 might be changed by the program.

Or (for an open ended cone, when it is the usual recommended choice):

(b) The total number N of segments and 0. The 0 will trigger the program to partition N into n1 along the axis and n2 around the axis, in such a way that all the trapeziums formed by pairs of triangles are as nearly square as possible. The final number of triangles will be 4*n1*n2, which might be slightly different (so if greater control is required, use n1 and n2).

For important advice on subdividing please look at section 3.4 of the Users Guide or the general advice on segmentation.

The numbers n1 and n2 (or N) apply to the minimum sector, before reflections in any planes of symmetry. (When the cone 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 make n2 = 8 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 cone. 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.

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.

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.

The axial direction is divided evenly unless there is a 'u' in the 7th position of the line that starts with 'con', eg a line such as:

The uneven distribution is not allowed for a closed cone.

Typical data for a conical surface, taken from shap3d02.dat, are:

cone, uneven distribution axially

1. 0. 0 . 0. radius, centre of 1st end of cone

3. 0. 0. 2. radius, centre of 2nd end

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

5 10 total number of subdivisions and 0, or divisions along axis and around axis

The data required are:

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

(2) radius and x,y,z coordinates of centre of 2nd end of electrode (if 2 radii are the same then 'con' will be changed to 'cyl' -this is necessary for technical reasons) (and if the cone is pointed -that is, if one of the radii is zero- then the zero radius should be the second one)

(3) numbers nv1,nv2 that label voltages that are applied to the electrode

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

(5) 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.

(6) Either:

(a) The numbers n1 and n2 of divisions along the axis and around the axis respectively, giving 4*n1*n2 triangles for a cone with an open end, and (4*n1-3)*n2 for complete cone (that is, with a closed end). The numbers n1 and n2 might be changed by the program.

Or (for an open ended cone, when it is the recommended choice):

(b) The total number N of segments and 0. The 0 will trigger the program to partition N into n1 along the axis and n2 around the axis, in such a way that all the trapeziums formed by pairs of triangles are as nearly square as possible. The final number of triangles will be 4*n1*n2, which might be slightly different.

For important advice on subdividing please look at section 3.4 of the Users Guide or the general advice on segmentation.