Techniques to rapidly model local spaces, using 3D range data, can enable implementation of: (1) real-time obstacle avoidance for improved safety, (2) advanced automated equipment control modes, and (3) as-built data acquisition for improved quantity tracking, engineering, and project control systems. The objective of the research reported here was to develop rapid local spatial modeling tools. Algorithms for fitting sparse range point clouds to geometric primitives such as spheres, cylinders, and cuboids have been developed as well as methods for merging primitives into assemblies. Results of experiments are presented and practical usage and limitations are discussed.