Many spatial datasets and spatial problems can be described with reference to regular lattice frameworks rather than continuous space. Examples include: raster scan and digital elevation model data, digital images, cost surfaces, cellular automata models, swarm models, and many others. This raises the question as to how distances should be measured in such cases and to what extent these relate to continuous space metrics. In this paper I show that a set of image processing algorithms known as distance transforms (DTs) may be applied to such datasets and can be extended to solve a wide range of 2D and 3D optimisation problems. These extended versions of the standard DT procedure have applications in many areas including location theory, path determination, planning, and decision support. As such I argue that they warrant consideration for inclusion as a standard set of tools within modern GIS and spatial analysis software packages. Sample pseudo-code for the transforms discussed is included in an appendix.