Stone sculpture from equations

Two hybrid, human-machine interface systems have been developed jointly by the NIST Intelligent Systems group and the author's sculpture studio. Both systems have been operated extensively in a hazardous environment for carving stone, and allow the operator direct access to spatial coordinates from mathematical equations describing the ultimate form. Three features unique to these hybrid systems are: 1) the operator has access to quantitative spatial information in real time; 2) registration is accomplished with three ordered non-collinear points; and 3) the operator has great freedom to solve the tool trajectories. Several different types of stone sculpture projects are described which took advantage of the unique capabilities of these hybrid systems.