Geometrical tracking and pose estimation using the homogeneous UVW inverse spherical coordinate system, directly from range data obtained from a triangulation based range sensor, are demonstrated. The method is shown to be more accurate, reliable, and computationally faster than using the more conventional XYZ Cartesian coordinate system. This is presented through a practical application, by comparing the accuracy and resolution of a 3D laser scanner prototype that geometrically tracks and computes the relative pose of objects in 3D space. The system uses real-time geometrical surface fitting and intensity processing for the detection and tracking of planar targets on an object. A dual-axis laser scanner is used for this demonstration that combines optical triangulation, Lissajous scanning patterns, geometrical tracking, and photogrammetry (spatial resection), to calculate the relative pose of objects in the 3D space.