The method of this invention, and the apparatus which implements it, provides a way of sampling points on the surface of a portion of a rigid or semi-rigid object, which might be an anatomical body. Points are sampled by a moveable contact probe which emits a sonic waveform under the direction of a control unit. Multiple fixed sonic transducers in contact with the object at diverse locations detect the waveform, the arrival of which is timed for each transducer by the control unit. Given the speed of sound in the object and the coordinates of the transducers, a digital computer can compute the location of the probe. Two ways are presented to calibrate the locations of the transducers. Provision is made for mitigating possible distortion of soft object surfaces due to the contact force of the probe. During the sampling of probe contact locations, at least one physical or physiological attribute is also acquired. Sampling sufficient points allows 3-d geometric construction of a model of the portion, which includes both the surface shape geometry and the distribution of the values of the attribute thereon. Finally a view of the model may be rendered on a graphical display medium.