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Sensor deployment is a fundamental issue in a wireless sensor network, which often dictates the overall network performance. Previous studies on sensor deployment mainly focused on sensor networks on 2D plane or in 3D volume. In this paper, we tackle the problem of optimal sensor deployment on 3D surfaces, aiming to achieve the highest overall sensing quality. In general, the reading of a sensor node exhibits unreliability, which often depends on the distance between the sensor and the target to be sensed, as observed in a wide range of applications. Therefore, with a given set of sensors, a sensor network offers different accuracy in data acquisition when the sensors are deployed in different ways in the Field of Interest (FoI). We formulate this optimal surface deployment problem in terms of sensing quality by introducing a general function to measure the unreliability of monitored data in the entire sensor network. We present its optimal solution and propose a series of algorithms for practical implementation. Extensive simulations are conducted on various 3D mountain surface models to demonstrate the effectiveness of the proposed algorithms.