This paper studies the reconstruction of unknown curved surfaces through finger tracking. A patch can be generated from tactile data points along three concurrent surface curves under the Darboux frame estimated at the curve intersection point. Surface fitting while minimizing the total (absolute) Gaussian curvature effectively prevents unnecessary folds otherwise expected to result from the use of such "1-D" data. The implementation involves a two-axis joystick sensor, a three-fingered 4-DOF BarrettHand, and a 4-DOF Adept SCARA robot. Experiments have demonstrated good accuracy of reconstruction.