Robot path-planning is a central task for navigation and most path-planners perform well in mapped environments with explicit obstacle boundaries. However, many obstacle fields are better defined by the probability of obstacles and obstacle geometries rather than by explicit locations. Few tools and data structures exist, other than repeated simulations, to predict robot mobility in these situations. Previously, it was shown that geometric obstacle properties could be used to estimate properties of paths routing around these obstacles, looking only at maps and avoiding the task of path planning [1]. This required knowing obstacle geometries relative to travel direction. This work presents a method for representing obstacle geometry, at arbitrary orientations and positions, and therefore a probabilistic model for determining if space near an obstacle is occupied. This paper explains the theory behind this method, uses this method to calculate the portion of a straight path overlapped by obstacles, called linear occupancy ratio, from simulated obstacle fields, and compares these results to measured occupancy ratio values to validate the probabilistic model.