In this paper a linear algorithm for synthesizing new views of piecewise planar objects without making an explicit 3D reconstruction is proposed together with a simple algorithm for 3D reconstruction of the scene. It is shown how this can be done using only one image and information about the projection of the intersection lines between the object planes. These could either be estimated manually or more automatically using at least one more image. No calibration information is needed.A main idea in the paper is to work with textured planes. A patch in one image, corresponding to a planar surface in the scene, is transformed to a patch in another image by a homography. The generalized eigenvectors and eigenvalues of the homographies have geometrical interpretations that are used in the algorithms.To generate a new image we calculate the homographies for each plane to the new image. The textures can then easily be mapped to the new image. The reconstruction is given as the equation of each plane in the corresponding homography to a certain image.