We present methods for the global reconstruction of some classes of special surfaces. The contour ending (cusp on the apparent contour) is tracked under a dynamic monocular perspective observer. The classes of surfaces considered are surfaces of revolution (SOR), canal surfaces and ruled surfaces. This paper presents theoretical methods for surface reconstruction and error analysis of reconstruction under noise. We find the techniques used exhibit stability even under large noise. This work has added to the accumulating body of work that has arisen in the computer vision community, concerning the differential geometric aspects of special surface classes.