CONFIGURATIONS, CONSTRAINTS, AND CSG
Adrian Bowyer, DAVID EISENTHAL, Dan Pidcock, Kevin D. Wise · International Journal of Shape Modeling · 2000
This paper presents a multidimensional CSG geometric modeller. It then shows how this modeller can be used to produce a compact representation of the complete configuration-space map of a mechanism composed of polyhedral parts. The map is derived directly from the three-dimensional geometric model that describes the mechanism, and allows more degrees of freedom than any other current system. Methods of exploring the map to give the kinematics of the mechanism will also be described and examples will be given. We will then go on to show how geometric constraints can be reformulated as a multidimensional CSG expression describing the constraints problem in a space similar to the configuration space above. Geometric constraints representing mechanisms will be described and the resulting mechanisms shown. Finally we will show how the two techniques, which are both coded using the same multidimensional modeller, can be combined. This allows parts of a machine that are known (such as slides and hinges) to be described explicitly using constraints, and parts that are unknown (such as interferences between moving parts) to be coded as a configuration-space map. The entire mechanism can then be simulated and its behaviour examined.