  Convex polytopes have compact representations and exhibit convexity, which
makes them suitable for abstracting obstacle-free spaces from various
environments. Existing methods for generating convex polytopes always struggle
to strike a balance between two requirements, producing high-quality polytope
and efficiency. Moreover, another crucial requirement for convex polytopes to
accurately contain certain seed point sets, such as a robot or a front-end
path, is proposed in various tasks, which we refer to as manageability. In this
paper, we show that we can achieve generation of high-quality convex polytope
while ensuring both efficiency and manageability simultaneously, by introducing
Fast Iterative Regional Inflation (FIRI).FIRI consists of two iteratively
executed submodules: Restrictive Inflation (RsI) and computation of the Maximum
Volume Inscribed Ellipsoid (MVIE) of convex polytope. By explicitly
incorporating constraints that include the seed point set, RsI guarantees
manageability. Meanwhile, the iterative monotonic optimization of MVIE, which
serves as a lower bound of the volume of convex polytope, ensures high-quality
results of FIRI. In terms of efficiency, we design methods tailored to the
low-dimensional and multi-constrained nature of both modules, resulting in
orders of magnitude improvement compared to generic solvers. Notably, for 2-D
MVIE, we present a novel analytical algorithm that achieves linear-time
complexity for the first time, further enhancing the efficiency of FIRI in the
2-D scenario. Extensive benchmarks conducted against state-of-the-art methods
validate the superior performance of FIRI in terms of quality, manageability,
and efficiency. Furthermore, various real-world applications showcase the
generality and practicality of FIRI. The high-performance code of FIRI will be
open-sourced for the reference of the community.
