Framed isophote curves on the framed surface

The isophote curve on surfaces is an important consequence of Lambert reflect law in optical research. In this paper, we define the framed isophote curve along a surface which original curve and surface may be singular. We give a condition of the framed isophote curve, and the expression of the light vector with different conditions. The relationship between the framed isophote curve and the framed helix is expounded. Moreover, we get the relationship between the framed isophote curve and the framed slant helix. Finally, we give the theorem for singularities recognition of framed isophote curves and two examples.