Conference material: "Proceedings of the International Conference on Computer Graphics and Vision “Graphicon” (19-21 September 2022, Ryazan)"
Authors:Tolok A.V., Petukhov P.A.
Functional-voxel Modeling of the Dynamic Solution of the Path Search Problem by the Gradient Method
The paper considers an algorithm for gradient motion on a surface that simulates a scene with target objects and obstacles. To implement the gradient descent algorithm, the principles of functionalvoxel modeling are used, which allow organizing a region of gradient characteristics for a given scene space. The mathematical apparatus of R-functions is chosen as a tool for describing a scene with obstacles. Approaches for obtaining the inverse expression of the R-function, i.e. removing an object from the scene to solve problems of dynamic rearrangement of obstacles and goals, are investigated. A functional-voxel approach to solving the procedure for the inverse expression of an R-function without loss of the sign of the function value is shown, which does not allow performing an algebraic expression of an R-function directly. The result of the inverse decomposition into objects is demonstrated by the example of the application of the R-intersection function. The principle of functional-voxel modeling of the area of the intersection law of two specific objects is implemented, which allows solving the direct and inverse problem of R-functional modeling.