Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions [1] by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended to continuous integrands via the Gauss–Bonnet theorem. [2] It was introduced independently by Pierre Schapira [3] [4] [5] and Oleg Viro [6] in 1988, and is useful for enumeration problems in computational geometry and sensor networks. [7]
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions [1] by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended to continuous integrands via the Gauss–Bonnet theorem. [2] It was introduced independently by Pierre Schapira [3] [4] [5] and Oleg Viro [6] in 1988, and is useful for enumeration problems in computational geometry and sensor networks. [7]