This disclosure describes methods for determining if arrangements of shapes satisfy boundary distance constraints among those shapes. The first embodiment includes constructing 110 a function which is an exact or approximate analytical representation of the constraint between two shapes. Further, this embodiment includes evaluating 120 the function constructed in 110 to determine if the constraint between the two shapes is exactly or approximately satisfied.The second embodiment includes constructing 210 a function which is an exact or approximate analytical representation of the constraint between two shapes. In addition, this embodiment includes assigning 215 values to variables and/or parameters of the function constructed in 210. Further, this embodiment includes evaluating 220 the function constructed in 210 using the assignments of 215 to determine if the constraint between the two shapes is exactly or approximately satisfied.