The present disclosure is directed toward systems and methods that facilitate scanning an object (e.g., a three-dimensional object) having custom mesh lines thereon and generating a three-dimensional mesh of the object. For example, a three-dimensional modeling system receives a scan of the object including depth information and a two-dimensional texture map of the object. The three-dimensional modeling system further generates an edge map for the two-dimensional texture map and modifies the edge map to generate a two-dimensional mesh including edges, vertices, and faces that correspond to the custom mesh lines on the object. Based on the two-dimensional mesh and the depth information from the scan, the three-dimensional modeling system generates a three-dimensional model of the object.