Optimal control problems are formulated and solved in which the manipulation is distributed over a three-dimensional (3D) spatial field with constraints on the spatial variation. These spatial field control problems that arise in applications in acoustics, structures, epidemiology, cancer treatment, and tissue engineering have much higher controllability than boundary control problems, but have vastly higher degrees of freedom. Efficient algorithms are developed for computing optimal manipulated fields by combination of modal analysis and least-squares optimization over a basis function space. Small minimum control error is observed in applications to distributed parameter systems with reaction, diffusion, and convection.