This paper presents a linear algorithm for the simultaneous computation of 3D points and camera positions from multiple perspective views, based on having four points on a reference plane visible in all views. The reconstruction and camera recovery is achieved, in a single step, by finding the null-space of a matrix using singular value decomposition. Unlike factorization algorithms, the presented algorithm does not require all points to be visible in all views. By simultaneously reconstructing points and views the numerically stabilizing effect of having wide spread cameras with large mutual baselines is exploited. Experimental results are presented for both finite and infinite reference planes. An especially interesting application of this method is the reconstruction of architectural scenes with the reference plane taken as the plane at infinity which is visible via three orthogonal vanishing points. This is demonstrated by reconstructing the outside and inside (courtyard) of a building on the basis of 35 views in one single SVD.