We present an approach for building an affine representation of an unknown curved object viewed under orthographic projection from images of its occluding contour. It is based on the observation that the projection of a point on a curved, featureless surface can be computed along a special viewing direction that does not belong to the point's tangent plane. We show that by circumnavigating the object on the tangent plane of selected surface points, we can (1) compute two orthogonal projections of every point projecting to the occluding contour during this motion, and (2) compute the affine coordinates of these points. Our approach demonstrates that affine shape of curved objects can be computed directly, i.e., without Euclidean calibration or image velocity and acceleration measurements.