Allowed reading error and aspect ratio checks

In ‘CPO2D/databuilder/printing levels and checks’ the user is asked to specify a number, while in ‘CPO3D/databuilder/printing levels and ratio checks’ the user is asked to specify 2 numbers.

The CPO2D and CPO3D programs both need a number to be specified for a wide variety of consistency checks that it carries out, such as whether centres of curvature are consistent with other coordinates. It also represents an allowed fractional error in entering the values of coordinates, and it must be non-zero.

A suitable value for this number is usually 0.01.

Make the number smaller than 0.01 if the electrodes that are being specified are narrow and closely spaced, so that the coordinates need to be more precise than 1%. The program will not allow the value to be larger than 0.05.

For example, if a circle is centred at (0,0) and one point on the circumference is at (1,0) the user might want to specify another point at (sqrt(0.5),sqrt(0.5)). Now sqrt(0.5) = 0.7071068…, so if the user enters (0.71,0.71) and the ‘allowed reading error’ is 0.01 then the errors in this are 0.0028932, which are less than 0.01, so then the program will accept this and automatically adjust the coordinates to (0.7071068,0.7071068). On the other hand if the allowed reading error is 0.001 the program will give an error message. The allowed reading error is used in several other ways, for example to see if the 4 corners of a rectangle lie in the same plane, or if the corners of a ‘conical triangle’ lies on the specified cone.

Aspect ratio check.

In CPO3D a second number is required. For a rectangle, it is the maximum permitted ratio of the longest to the shortest side. For a triangular it is the ratio of the base (the longest side) to the height.

If a segment is long and thin then it is unlikely that the surface charge on it would be approximately uniform, as required in the Boundary Element Method. It is therefore unwise in general to let this ratio exceed about 5 unless it is known that the charge density in the region of the segment is sufficiently uniform. The number acts as an important safeguard. The recommended value for general use is 5.

Disabling aspect ratio check

The program normally limits the number to 20. One situation in which such a large ratio might be justified is when the potential distribution on a rectangular electrode is constant in one direction, say x, but varies in the other direction, say y. Then subdivisions that are much longer in the x direction than in the y direction would still be approximately uniformly charged. There are other situations (see note on thin segments) in which a larger ratio is justified. But this must be done with great care. A large ratio (eg 100) can be entered (that is, the test can be disabled) by entering the negative of the number (that is, -100).

For further information see the note on choosing shapes of 3D triangles and rectangles.