Systems and methods for radiation treatment for determining a dose of radiation. Determining, for a tumor voxel, a value for maximum and minimum constraints, for treating the tumor voxel based on a distance function of a distance field of the tumor and distance fields of organs at risk (OARs). Each constraint on each tumor voxel is a function of a distance from the tumor voxel to a boundary of the tumor, and distances to boundaries of OARs. Determining, for an OAR voxel, a value of a maximum constraint based on the distance field of the tumor. Each constraint on each OAR voxel is a function of a distance from the OAR voxel to the boundary of the tumor. Determining a tumor constraint and a corresponding OAR constraint according to a threshold constraint set, to obtain the constraint set. Determine the dose of radiation, according to the constraint set.
