Choosing shapes of 3D triangles and rectangles

The user has already specified (see the note on consistency checks) the maximum permitted aspect ratio of a triangular or rectangular segment.

It is unwise in general to let this ratio exceed about 5. The number acts as an important safeguard. The recommended value is 5. (For more details and information on disabling, see the note on consistency checks).

The program makes the assumption that each segment has a uniform charge density over its surface, which is probably not be a good assumption when the segments are long and thin.  But sometimes triangles that are long and thin are unavoidable, for example when the users equations option is used.  Rectangles that are long and thin can be justified 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. So it is possible to disable this check (see the note on consistency checks).

Thin triangles.

CPO3D usually subdivides triangles into 2 parts by bisecting the longest side. This action is repeated for each sub-triangle, until the required number of segments has been reached.  But a different method is used when the triangle is judged to be ‘thin’, which is when the aspect ratio of the base (the longest side) to the height is greater than 5. Then the triangle is divided into 4 parts, using one of two methods, to minimise the aspect ratios of the sub-triangles and to give the sub-triangles the same area if possible.

Examples of all the different types of triangles are given in shap3d28.dat.