  We present a novel metric to analyze the similarity between the physical
environment and the virtual environment for natural walking in virtual reality.
Our approach is general and can be applied to any pair of physical and virtual
environments. We use geometric techniques based on conforming constrained
Delaunay triangulations and visibility polygons to compute the Environment
Navigation Incompatibility (ENI) metric that can be used to measure the
complexity of performing simultaneous navigation. We demonstrate applications
of ENI for highlighting regions of incompatibility for a pair of environments,
guiding the design of the virtual environments to make them more compatible
with a fixed physical environment, and evaluating the performance of different
redirected walking controllers. We validate the ENI metric using simulations
and two user studies. Results of our simulations and user studies show that in
the environment pair that our metric identified as more navigable, users were
able to walk for longer before colliding with objects in the physical
environment. Overall, ENI is the first general metric that can automatically
identify regions of high and low compatibility in physical and virtual
environments. Our project website is available at https://gamma.umd.edu/eni/.
