Range sensors capable of continuous free motion during surface-geometry measurement have limited access to complex surfaces or must operate in a restricted environment. This is due to the use of secondary sensors to track the range-sensor head. Other free-motion sensors require a complex range-data acquisition process. This paper presents a method of measuring surface geometry by a laser-camera range-sensor head that is permitted continuous unconstrained motion in six degrees of freedom, without requiring measurement of the sensor-head position and orientation by additional sensors. Numerous range views, each containing several profiles captured in a single camera image, are acquired with little motion between viewpoints. This form of range data provides sufficient information at each laser-camera viewpoint, to generate overlap for registration of successive views while minimizing redundant data. Transformations between pairs of adjacent views are computed using a transformation-parameter optimization to minimize the distance between view surfaces. Global registration of all views is carried out by sequentially applying the local transformations. In simulations of the range-sensing method using noiseless and noisy range views, global registration of an open 49-view sequence yielded mean absolute global registration errors that are acceptable for many surface-modeling applications. The method is applicable when the range-sensor head and object have independent continuous unknown motion.