This paper considers the problem of finding the shortest tour to cover a given set of inverted cone views with apex angle alpha and height H when their apex points lie on a planar surface. This is a novel variant of the 3D Traveling Salesman Problem with intersecting Neighborhoods (TSPN) called Cone-Tspn. When the cones are allowed to tilt by an angle epsilon we have the tilted Cone-Tspn problem, to which we present an algorithm that returns a solution with an approximation ratio of Oleft(frac 1+tanalpha 1-tanepsilontanalpha left(1+logfrac max(H) min(H) right)right). We demonstrate through simulations that our algorithm can be implemented in a practical way and by exploiting the structure of the cones we can achieve shorter tours. Finally, we present results from covering a reflective surface (lake area) that shows the importance of selecting different view angles under strong sunlight specularities.