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Clustering spatial data is a well-known problem that has been extensively studied. Grouping similar data in large 2-dimensional spaces to find hidden patterns or meaningful sub-groups has many applications such as satellite imagery, geographic information systems, medical image analysis, marketing, computer visions, etc. Although many methods have been proposed in the literature, very few have considered physical obstacles that may have significant consequences on the effectiveness of the clustering. Taking into account these constraints during the clustering process is costly and the modeling of the constraints is paramount for good performance. In this paper, we investigate the problem of clustering in the presence of constraints such as physical obstacles and introduce a new approach to model these constraints using polygons. We also propose a strategy to prune the search space and reduce the number of polygons to test during clustering. We devise a density-based clustering algorithm, DBCluC, which takes advantage of our constraint modeling to efficiently cluster data objects while considering all physical constraints. The algorithm can detect clusters of arbitrary shape and is insensitive to noise, the input order and the difficulty of constraints. Its average running complexity is O(NlogN) where N is the number of data points.