Abstract: A corridor in a target area is designed so as to minimize an environmental, economic, behavioral or any other cost caused by implementing the corridor in a grid of cells. Translation costs caused by straight-line translations of an optimized arrangement of cells through the grid are calculated using locations and values of the swept cells. The optimized arrangement is characterized by a reduced variation of translation width with a translation direction.

Abstract: A corridor in a target area is designed so as to minimize an environmental, economic, behavioral or any other cost caused by implementing the corridor in a grid of cells. Translation costs caused by straight-line translations of an optimized arrangement of cells through the grid are calculated using locations and values of the swept cells. The optimized arrangement is characterized by a reduced variation of translation width with a translation direction.

Abstract: A graphic editing apparatus allows a user to edit graphic objects in a drawing space. The graphic objects are subject to constraints to have specified dimensional properties and/or relationships that need not be Euclidean geometric or topological but may be dependent on spatial variation of selected conditions represented by maps, each of which assigns values to locations in the drawing space. The apparatus also allows the user to edit the constraints. If one or more attributes of a graphic object or of a constraint are modified, then affected graphic objects are selected and modified automatically. If any constraints are violated due to these modifications, the initial and subsequent modifications are undone and information is generated to notify which constraints are violated and how they are violated.