Separating topology and geometry in space planning

Separating topology and geometry in space planning

2 We are here dealing with the problem of space layout planning. We present an architectural conceptual CAD approach. Starting with design specifications in terms of constraints over spaces, a specific enumeration heuristics leads to a complete set of consistent conceptual design solutions named topological solutions. These topological solutions which do not presume any precise definitive dimen...

Path planning and the topology of configuration space

| This work considers the path planning problem for planar revolute manipulators operating in a workspace of polygonal obstacles. This problem is solved by determining the topological characteristics of obstacles in connguration space, thereby determining where feasible paths can be found. A collision-free path is then calculated by using the mathematical description of the boundaries of only t...

Controlled Topology in Geometry

The purpose of the present note is to announce some finiteness theorems for classes of Riemannian manifolds (cf. A, B and D below). Let ^*$(n) denote the class of closed Riemannian «-manifolds with sectional curvatures between k and K, diameter between d and D, and volume between v and V. Here k < K are arbitrary, 0 < d < D, and 0 < v < V, THEOREM A. For n ^ 3,4 the class ^£%'y{n) contains at m...

The Effect of Planning State Space Topology on Search Performance

The topological characteristics of the state space graph for a planning problem are related to the internal structure of the underlying problem, and can affect the efficiency of planning. We outline a proposed approach for using this knowledge to build a novel type of plan library (which we call a planning backbone) that organizes states hierarchically based on their

Editorial: Brain Extracellular Space: Geometry, Matrix and Physiological Importance