Input data for an elliptical cylindrical rectangle.

A rectangle on an elliptical cylindrical surface (and the same effect can also be produced by stretching). a rectangle on a cylindrical surface

The user specifies:

(1) the x,y,z coordinates of the corners

(2) the minor (that is, smaller) radius

(3) the x,y,z coordinates of the first end of the axis of the parent cylinder

(4) the x,y,z coordinates of any other point on the axis of the parent cylinder

(5) 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

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

(7) Either:

(a) The numbers n1 and n2 of divisions along the axis and around the axis respectively.

Or (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 rectangles are as nearly square as possible. The final number of segments, n1*n2, might be slightly different from N (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.

It is not possible in this program to specify a part of a cylindrical surface that is larger than one quadrant.

The formula that the program uses for the elliptical shape is

(x/a)**2 + (y/b)**2 = 1,

where a and b are the minor and major radii respectively, and where x and y are local orthogonal axes. The area of this ellipse is pi*a*b.

The user has to enter the length of the minor radius and the coordinates of the end points of an elliptical arc. In the present example, a = 1 and the arc is a quadrant from (x,y) = (0,1.5) to (1,0). Reflections are used here to give a complete cylinder.

To obtain only a middle part of the above arc, for example starting at y = 0.5 and finishing at y = 1.0, the equation is solved to give the end points (0.9428,0.5) and (0.7454,1.0). The program will calculate the major radius.

To check that the resulting arc coincides with the full quadrant given above, add a further electrode with the coordinates:

0.9428 0.5 0.5

0.9428 0.5 1.5

0.7454 1.0 1.5

0.7454 1.0 0.5

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

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 rectangle on an elliptical cylindrical surface, taken from shap3d04.dat, are:

ecr rectangle on elliptical surface

0.0 1.5 0.5 corners

0.0 1.5 -0.5

1.0 0.0 -0.50

1.0 0.0 0.5

0. 0. -0.5 1st point on axis

0. 0. 0.0 2nd point on axis

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

4 10 number of subdivisions, along axis and around axis (0 0 cancels)

The data required are:

(1) x,y,z coordinates of corners

(2) minor radius -to disable the 'inscribing correction' if it has been requested (see the relevant note and the second relevant note), enter a negative radius

(3) x,y,z coordinates of first end of axis of parent cylinder

(4) x,y,z coordinates of any other point on axis of parent cylinder

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

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

(7) Either:

(a) The numbers n1 and n2 of divisions along the axis and around the axis respectively.

Or (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 rectangles are as nearly square as possible. The final number of segments, n1*n2, might be slightly different from N (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.