Parametric design is a versatile decision-making methodology that allows multi-criteria optimization. However, it is not as common for addressing aspects such as the cultural heritage of a given community. In this context, qualitative research proposes linking a cultural heritage classification with parametric design algorithms that include a stage of “design thinking” methodology, which culminates in community validation. This paper aims to demonstrate the potential of parametric and low-tech design as a multi-criteria decision strategy. Algorithms were developed with the mechanical properties of a given material, with meteorological information as input data, geometry as response, and with a simultaneously integrated multi-criteria decision-making process to improve the design. Most algorithms take as input variables such as size, function, or geometry and, as output, the structural material that best fits them, but not the opposite. This methodology was tested on a case study with the Misak community in Colombia, using Guadua (Guadua angustifolia), a subfamily of the bamboo, but which is little used. These criteria provided multiple design alternatives that were constantly debated to adjust and test the parameters of the prototype. The principal outcome is that an existing cultural heritage classification allows for the parametric model’s generalization ability.

This is part II (of the two-parts paper) dedicated to the development of a pre-rationalization approach that provides favorable constructive properties for the low-tech construction of doubly curved structures. In this second part, we utilize the geometric constructs developed in part I, specifically patches with one direction of their coordinate curves being planar (PU-property) and the other direction generating developable strips (V-strips), to address site constraints. More precisely, we articulate a design process based on these constructs that allows for the low-tech construction of a doubly curved bamboo structure without falsework.

This paper investigates the generation and utilization of Isothermic Surfaces (IS), which are distinguished by their unique geometric properties of admitting conformal and conjugate patches, or CC-patches. These properties facilitate planarity of faces, orthogonality of joints, and square-like proportionality of sub-divisions, among others. Our pre-rationalization approach leverages CC-patches across six surface types to develop a design tool that enables the generation of a wide range of variations, i.e. design possibilities. More precisely, reparemetrizations as well as transformations—including Christoffel, B¨acklund- Darboux-Ribaucour (BDR), Goursat and M¨obius—are applied to generate and transform the different IS types. While each transformation preserves the CC-patch property, it can alter other geometric properties of the surface. Thus, allowing the designer to choose transformations with more architectural shape variety, while maintaining the mentioned fabrication advantages of CC-patches.

This two-parts paper is dedicated to the development of a pre-rationalization approach that provides favorable constructive properties for the low-tech construction of doubly curved structures. In part I, we provide methods for generating geometric constructs (patches) with two essential properties: One family of coordinate curves are planar (PU-property), while the other generating singly curved strips (develpable V-strips). The geometric constructs are done on three levels of geometric properties, of being: conjugate, orthogonal-conjugate (principal), and orthogonal-conjugate with negative constant Gaussian curvature (principal Tchebyshef nCGC). The main contribution of part I, is the articulation of a space of design variants within the pre-rationalization of the three levels, by introducing transforms leaving the geometric properties invariant, namely, Projective, Mo ̈bius, and Ba ̈cklund transforms.

Pré-rationalisation des structures courbes : exploration des constructions géométriques avec des matériaux à faible impact environnemental: Cette thèse explore comment des structures courbes—appréciées pour leur potentiel spatial, structurel et esthétique—peuvent être conçues et construites de manière faisable à l’aide de matériaux à faible impact environnemental et de techniques de construction traditionnelles, dans des contextes low-tech. Alors que les stratégies de rationalisation existantes reposent souvent sur des méthodes postérieures à la conception, des matériaux synthétiques et des technologies de fabrication avancées, cette recherche propose une approche alternative : intégrer la constructibilité dès les premières étapes du design, à travers une méthodologie ancrée dans la géométrie.Nous commençons par identifier les paramètres architecturaux influençant la configuration des composants pour deux stratégies d’assemblage : par éléments squelettiques et par blocs. Ces paramètres sont ensuite analysés selon leurs propriétés constructives, en particulier leur complexité de fabrication dans des contextes low-tech. Ils sont reformulés en propriétés géométriques, ouvrant la voie à l’introduction du concept de “constructs géométriques”, Un ensemble de surfaces, de patchs et de transformations caractérisés par des propriétés géométriques spécifiques dérivées de la géométrie différentielle et sélectionnées pour leur capacité à générer des variantes morphologiques tout en préservant la constructibilité. Nous mettons ensuite en pratique cette méthodologie à travers trois démonstrateurs à l’échelle 1:1. Ceux-ci montrent qu’il est possible de réaliser des formes complexes à l’aide de matériaux locaux et de techniques artisanales, dès lors que les propriétés géométriques sont intégrées au processus de conception. Cette approche démontre qu’une complexité formelle peut coexister avec des pratiques durables et accessibles. En proposant une logique de pré-rationalisation, cette recherche redonne une place centrale aux savoir-faire traditionnels tout en les outillant pour des explorations formelles contemporaines, à la croisée de l’architecture, des mathématiques et de la construction