Method for computing angle constrained isoptic curves for surfaces

In computer graphics and geometric modeling for good quality displaying of an object it is required that the object must fit on the screen. It often happens, for example when we are using modeling software, that the object we would like to rotate around an axis, or edit from another point of view, is partly out of the screen, and thus some parts are not visible. In two dimensions the isoptic curve of a curve is constructed by involving lines with a given angle intersect each other at a certain point of the isoptic curve. In three dimensions the points of an isoptic curve may be the admissible positions of the camera. So from these points we can watch the object with respect to the given viewing angle. The purpose of this paper is to find a general method and computational algorithm that helps to locate the closest possible position of the camera, which positions form a closed curve around the surface. The developed algorithm produces this curve for a special case.