High-dimensional models of pattern formation in visual cortex can be replaced by low-dimensional feature models provided that relations among the features reflect the high-dimensional structure. We consider orientation columns in a simplified at high-dimensional setting and show that an exact derivation of a Riemannian-curved low-dimensional model is possible. Further evidence to the curved model is provided by the fact that the number of pinwheels is shown to stay non-zero in coincidence with finding in animals though in contrast to other models.