Essential Means for Urban Computing; Specification of Web-Based Computing Platforms for Urban Planning, a Hitchhiker's Guide

Mon, 01 Jan 0001 00:00:00 +0000

Authors: Pirouz Nourian, Carlos Martinez-Ortiz, Ken Arroyo Ohori

Abstract:

This article provides an overview of the specifications of web-based computing platforms for urban data analytics and computational urban planning practice. There are currently a variety of tools and platforms that can be used in urban computing practices, including scientific computing languages, interactive web languages, data sharing platforms and still many desktop computing environments, e.g., GIS software applications. We have reviewed a list of technologies considering their potential and applicability in urban planning and urban data analytics. This review is not only based on the technical factors such as capabilities of the programming languages but also the ease of developing and sharing complex data processing workflows. The arena of web-based computing platforms is currently under rapid development and is too volatile to be predictable; therefore, in this article we focus on the specification of the requirements and potentials from an urban planning point of view rather than speculating about the fate of computing platforms or programming languages. The article presents a list of promising computing technologies, a technical specification of the essential data models and operators for geo-spatial data processing, and mathematical models for an ideal urban computing platform.

Voxel Graph Operators; Topological Voxelization, Graph Generation, and Derivation of Discrete Differential Operators from Voxel Complexes

Mon, 01 Jan 0001 00:00:00 +0000

Authors: Pirouz Nourian and Shervin Azadi

Abstract:

In this paper, we present a novel workflow consisting of algebraic algorithms and data structures for fast and topologically accurate conversion of vector data models such as Boundary Representations into voxels (topological voxelization); spatially indexing them; constructing connectivity graphs from voxels; and constructing a coherent set of multivariate differential and integral operators from these graphs. Topological Voxelization is revisited and presented in the paper as a reversible mapping of geometric models from $\mathbb{R}^3$ to $\mathbb{Z}^3$ to $\mathbb{N}^3$ and eventually to an index space created by Morton Codes in $\mathbb{N}$ while ensuring the topological validity of the voxel models; namely their topological thinness and their geometrical consistency. In addition, we present algorithms for constructing graphs and hyper-graph connectivity models on voxel data for graph traversal and field interpolations and utilize them algebraically in elegantly discretizing differential and integral operators for geometric, graphical, or spatial analyses and digital simulations. The multi-variate differential and integral operators presented in this paper can be used particularly in the formulation of Partial Differential Equations for physics simulations.

Spatial Computing | Genesis Lab

Essential Means for Urban Computing; Specification of Web-Based Computing Platforms for Urban Planning, a Hitchhiker's Guide

Voxel Graph Operators; Topological Voxelization, Graph Generation, and Derivation of Discrete Differential Operators from Voxel Complexes