This paper is devoted to analytical approaches to path planning with obstacles. Two analytical modeling principles are compared for obstacles in a scene: the methods of potentials and R-functional modeling. The functional voxel design principle of complex computational processes is presented on an illustrative example of modeling of the R-function for the union/intersection of the domains of two functions. The fundamentals of arithmetic operations over local geometrical characteristics describing the components of a homogeneous unit vector of a local function are discussed. The denormalization principle of such components is demonstrated for application in arithmetic operations constituting an R-function. The scene is modeled by the layout of concentric objects and a local function describing the target by a funnel surface at a given point. A dynamic formation algorithm is considered for the final local function of the union of the funnel and scene surfaces at a current point. The final local function is used to determine the components of the direction vector of gradient-based motion to the target.