Mark Weiser described ubiquitous computing as "invisible, everywhere comput
ing that does not live on a personal device of any sort, but is in the wood
work everywhere." [1] The EasyLiving project at Microsoft Research is focus
ed on those aspects of ubiquitous computing relevant to smart environments,
including work in distributed computing, geometric world modeling, compute
r vision, and user interfaces. Though the need for research in distributed
computing, perception, and interfaces is widely recognized, the importance
of an explicit geometric world model for ubiquitous computing has not been
well-articulated. This article elucidates the role of geometry in ubiquitou
s computing, offering example scenarios that require or benefit greatly fro
m geometric knowledge, and describing four primary benefits of a geometric
model.