This thesis analyzes procedure of generation of hyperbolic grids formulated by two constraints, which specify grid orthogonality and cell volume. The procedure was applied on a wide range of geometries and high quality two and three dimensional hyperbolic grids were generated by using grid control and smoothing procedures, which supply grid clustering in all directions and prevent grid deformation (grid shock), respectively.

This architectural thesis challenges the conventional perception of cities as horizontally sprawling realms dominated by towering edifices and skyscrapers. Inspired by Rem Koolhaas' influential book "Delirious New York," which argues that each block represents an independent fantasy, which creates a more cohesive and united version of the city (Koolhaas, 1994). This thesis introduces a groundbreaking outlook that envisions cities as complex networks of functions, neighborhoods, and pathways within an immersive three-dimensional framework. The proposed approach seeks to merge the established city of Manhattan with a new counterpart, driven by enhancing residents' quality of life and addressing the challenges of metropolitan areas. Three key factors underscore the significance of this approach. Firstly, there is a current dearth of connections between buildings and floors, impeding the cohesive fabric of urban life and hindering social interaction and community engagement. Secondly, the rapid population growth in Manhattan has strained the city's surface, leading to challenges in space availability. Additionally, there is a significant lack of public spaces that cater to the community's needs for socializing, outdoor recreation, and access to nature. Moreover, the looming threat of rising sea levels amplifies the urgency of these challenges. By addressing these key factors, the proposed approach aims to revolutionize the urban fabric, creating a more interconnected, sustainable, and resilient cityscape that elevates the well-being of residents and harmonizes with the dynamic nature of urban life. To address these issues, the thesis examines specific components such as existing voids, the street network, and building elements. Through reimagining and redesigning these elements, the goal is to create a unified and sustainable urban environment that aligns with current trends and harnesses emerging technologies. The ultimate aspiration is to achieve a cohesive urban milieu that enhances and reshapes the well- being of residents while adapting to the dynamic nature of urban life / Master of Architecture / This architectural thesis challenges our traditional view of cities as sprawling landscapes dominated by tall buildings. Taking inspiration from Rem Koolhaas' exploration of Manhattan's unique block fantasies in "Delirious New York,". This thesis presents an exciting new perspective. It envisions cities as vibrant hybrid networks, blending various functions, neighborhoods, and pathways within a three-dimensional grid. The proposed approach seeks to merge and integrate the existing city of Manhattan with a new one, aiming to improve the overall quality of life for its residents while addressing the challenges of metropolitan areas. Three significant factors justify this approach. First, there is a lack of connections between buildings and floors, which limits the cohesiveness of urban life. Second, Manhattan's surface is strained due to population growth, demanding innovative solutions. Public spaces encouraging socializing, outdoor activities, and access to natural environments are also insufficient. The rising sea levels add an extra layer of concern. To tackle these complex issues, the thesis explores specific components such as underutilized spaces within the city, streets, and existing buildings. Through imaginative redesign and reimagining, the goal is to create a more harmonious and sustainable urban environment that responds to current trends and technologies. By integrating these elements, the thesis aims to shape cities into vibrant, inclusive, and interconnected spaces that cater to the needs of their communities.

Given a grid of cells, each having a value indicating its cost per unit area, a variant of the least-cost path problem is to find a corridor of a specified width connecting two termini such that its cost-weighted area is minimized. A computationally efficient method exists for finding such corridors, but as is the case with conventional raster-based least-cost paths, their incremental orientations are limited to a fixed number of (typically eight orthogonal and diagonal) directions, and therefore, regardless of the grid resolution, they tend to deviate from those conceivable on the Euclidean plane. Additionally, these methods are limited to problems found on two-dimensional grids and ignore the ever-increasing availability and necessity of three-dimensional raster based geographic data. This thesis attempts to address the problems highlighted above by designing and testing least-cost corridor algorithms. First a method is proposed for solving the two-dimensional raster-based least-cost corridor problem with reduced distortion by adapting a distortion reduction technique originally designed for least-cost paths and applying it to an efficient but distortionprone least-cost corridor algorithm. The proposed method for distortion reduction is, in theory, guaranteed to generate no less accurate solutions than the existing one in polynomial time and, in practice, expected to generate more accurate solutions, as demonstrated experimentally using synthetic and real-world data. A corridor is then modeled on a threedimensional grid of cost-weighted cubic cells or voxels as a sequence of sets of voxels, called ‘neighborhoods,’ that are arranged in a 26-hedoral form, design a heuristic method to find a sequence of such neighborhoods that sweeps the minimum cost-weighted volume, and test its performance with computer-generated random data. Results show that the method finds a low-cost, if not least-cost, corridor with a specified width in a threedimensional cost grid and has a reasonable efficiency as its complexity is O(n2) where n is the number of voxels in the input cost grid and is independent of corridor width. A major drawback is that the corridor found may self-intersect, which is often not only an undesirable quality but makes the estimation of its cost-weighted volume inaccurate. / Med tanke på ett rutnät av celler, som vart och ett har ett värde som indikerar dess kostnad per areaenhet, är en variant av det billigaste banproblemet att hitta en korridor med en specificerad bredd som förbinder två terminaler så att dess kostnadsviktade område minimeras. Det finns en beräkningseffektiv metod för att hitta sådana korridorer, men som är fallet med konventionella rasterbaserade lägsta kostnadsspår är deras inkrementella orienteringar begränsade till ett fast antal (vanligtvis åtta ortogonala och diagonala) riktningar, och därför, oavsett nätupplösning tenderar de att avvika från de tänkbara på det euklidiska planet. Dessutom är dessa metoder begränsade till problem som finns i tvådimensionella nät och ignorerar den ständigt ökande tillgängligheten och nödvändigheten av tredimensionell rasterbaserad geografisk data. Denna avhandling försöker ta itu med problemen som belyses ovan genom att utforma och testa korridoralgoritmer till lägsta kostnad. Först föreslås en metod för att lösa det tvådimensionella rasterbaserade problemet med billigaste korridorer med minskad förvrängning genom att anpassa en distorsionsminskningsteknik som ursprungligen utformades för billigaste vägar och tillämpa den på en effektiv men distorsionsbenägen billigaste korridoralgoritm. Den föreslagna metoden för distorsionsminskning är i teorin garanterad att generera inte mindre exakta lösningar än den befintliga i polynomtid och i praktiken förväntas generera mer exakta lösningar, vilket demonstreras experimentellt med syntetiska och verkliga data. En korridor modelleras sedan på ett tredimensionellt rutnät av kostnadsvägda kubikceller eller voxels som en sekvens av uppsättningar av voxels, kallade "stadsdelar", som är ordnade i en 26-hedoral form, designar en heuristisk metod för att hitta en sekvens av sådana stadsdelar som sveper den lägsta kostnadsviktade volymen och testar dess prestanda med datorgenererade slumpmässiga data. Resultaten visar att metoden hittar en låg kostnad, om inte minst kostnad, korridor med en specificerad bredd i ett tredimensionellt kostnadsnät och har en rimlig effektivitet eftersom dess komplexitet är O (n2) där n är antalet voxlar i ingångskostnadsnätet och är oberoende av korridorbredd En stor nackdel är att korridoren som hittas kan korsa sig själv, vilket ofta inte bara är en oönskad kvalitet utan gör uppskattningen av dess kostnadsviktade volym felaktig. / <p>QC 20210309</p>