MonarchIP develops and distributes ACGL™, the Analytical Computational-Geometry Library for scientists and engineers. ACGL is a groundbreaking software-library that provides analytical computational-geometry capabilities by seamlessly integrating constructive elements of computational-geometry with curved shapes and analytical elements of analytical-geometry. ACGL makes it possible to easily use analytical methods, commonly employed in science and engineering, to directly and efficiently design and analyze complex and dynamic geometric-systems, composed of curved and polygon shapes, in a natural and intuitive manner. Scientist and engineers routinely encounter complex and dynamic geometric-systems as components of larger systems. Unfortunately, the traditional tools of computational geometry and the methods of analytical geometry are of limited value in an analytical environment where the analysis and design of a system is performed in terms of the system’s characteristic functions and their derivatives. Specifically, while computational geometry tools are well suited for constructing complex geometric-systems, they are algorithmic in nature and are, at best, difficult to integrate into analytical methods and in many cases are fundamentally incompatible with them. Further, they work primarily with polygons and do not provide any significant capabilities to work with curved shapes. Conversely, while the methods of analytical geometry work well in an analytical environment and support curved shapes, they only work on a small number of relatively simple shapes, limiting their use to only the simplest systems. ACGL is a C++ class-library that starts to substantially eliminate these limitations by using a mathematical approach, consisting of objects and operations, to construct complex geometric-systems. This, in turn, allows for the design and analysis of a geometric-system to be performed in terms of its characteristic functions and their derivatives.