10.2.4.3 How to Use a Point3D Lattice to Complement the Geometry of a 2D Grid Representation

The lattice itself defines the X,Y location of each point. Using this method is very efficient and allows the selection of an offset and a spacing in each direction.

To implement such a lattice:

• The writer may declare that all directions are orthogonal (which allows the reader to avoid some unnecessary checking).
• The writer must define an origin for this lattice.
• The dimensionality of the lattice is given by the number of “offsets” defined. If you write an instance with one offset only, your lattice will be one dimensional.
• For a multi-dimensional lattice, the ordering of the offsets follows their dimension, i.e., the first offset in the XML instance is the first dimension of the lattice array.

For a grid 2D representation, you must declare two instances of point 3D offsets. The dimension of each is the number of offset points declared for each point 3D offset.

To implement, you must know that a lattice of N offset points is described by a spacing array of size N-1. The offset between points is given by the spacing value multiplied by the offset vector. For example, the first offset is 0. The second offset is the first spacing offset. The third offset is (first spacing + second spacing) offset, etc.

The spacing may be regular, in which case, a count and only one spacing value is given. In other cases, the number of spaces between points is inferred from the dimension of the offset.