A fundamental problem in computer vision is how to determine the 3-D spatial orientation of curves and surfaces appearing in an image. The problem is generally underconstrained, and is complicated by the fact that metric properties, such as orientation and length, are not invariant under projection. Under perspective projection (the correct model for most real images) the transform is nonlinear, and therefore hard to invert. Two constructive methods are presented. The first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines. The second determines the orientation of planes by 'backprojection' of two intrinsic properties of contours: angle magnitude and curvature.