We introduce an intuitive method, called Marionette, for the modelling of free-form architecture with planar facets. The method takes inspiration from descriptive geometry and allows to design complex shapes with one projection and the control of elevation curves. The proposed framework achieves exact facet planarity in real time and considerably enriches previous geometrically constrained methods for free-form architecture. A discussion on the design of quadrilateral meshes with a fixed horizontal projection is first proposed, and the method is then extended to various projections and patterns. The method used is a discrete solution of a continuous problem. This relation between smooth and continuous problem is discussed and shows how to combine the marionette method with modelling tools for smooth surfaces, like non-uniform rational basis spline or T-splines. The result is a versatile tool for shape modelling, suited to engineering problems related to free-form architecture.
GlymphJSheldenDCeccatoCet al. A parametric strategy for free-form glass structures using quadrilateral planar facets. Automat Constr2004; 13(2): 187–202.
2.
PottmannHAsperlAHoferMet al. Architectural geometry. Exton, PA: Bentley Institute Press, 2007.
3.
SchoberH.Geometrie-prinzipien für wirtschaftliche und effiziente schalentragwerke (teil 1). Bautechnik2002; 79(1): 16–24.
4.
BagnerisMMotroRMaurinBet al. Structural morphology issues in conceptual design of double curved systems. Int J Space Struct2008; 23(2): 79–87.
5.
MesnilRDoutheCBaverelOet al. Isogonal moulding surfaces: a family of shapes for high node congruence in free-form structures. Automat Constr2015; 59: 38–47.
6.
BobenkoAHuhnen-VenedeyE.Curvature line parametrized surfaces and orthogonal coordinate systems: discretization with Dupin cyclides. Geometriae Dedicata2012; 159(1): 207–237.
7.
MesnilRDoutheCBaverelOet al. Generalised cyclidic nets for shape modelling in architecture. Int J Architect Comput2017; 15(2): 148–168.
8.
KleinF.Vergleichende Betrachtungen über neuere geometrische Forschungen. Math Ann1893; 43(1): 63–100.
9.
AdriaenssensSNeyLBodarweEet al. Finding the form of an irregular meshed steel and glass shell based on construction constraints. J Architect Eng2012; 18(3): 206–213.
10.
LiuYWangWPottmannHet al. Geometric modeling with conical meshes and developable surfaces. ACM T Graphic2006; 25(3): 681–689.
LeroyC.Traité de stéréotomie, comprenant les applications de la géométrie descriptive à la théorie des ombres, la perspective linéaire la gnomonique, la coupe des pierres et la charpente, avec un atlas composé de 74 planches in folio. Paris: Mallet-Bachelier, 1857.
20.
BlockPOchsendorfJ.Thrust network analysis: a new methodology for three-dimensional equilibrium. J Int Ass Shell Spat Struct2007; 48: 167–173.
21.
RippmannMLachauerLBlockP.Interactive vault design. Int J Space Struct2012; 27(4): 219–230.
22.
MikiMIgarashiTBlockP.Parametric self-supporting surfaces via direct computation of Airy stress functions. ACM T Graphic2015; 34(4): 89.
23.
BobenkoASurisYB.Discrete differential geometry: integrable structure. American Mathematical Society, 2008, http://bookstore.ams.org/gsm-98
24.
AlinhacS.Hyperbolic partial differential equations. New York: Springer Science+Business Media, 2009.
25.
TariniMPuppoEPanozzoDet al. Simple quad domains for field aligned mesh parametrization. ACM T Graphic2011; 30(6): 142.
26.
TakayamaKPanozzoDSorkine-HornungAet al. Sketch-based generation and editing of quad meshes. ACM T Graphic2013; 32(4): 97.
27.
MesnilRDoutheCBaverelOet al. Structural morphology and performance of plated structures with planar quadrilateral facets. J Int Ass Shell Spat Struct2017; 58(1): 7–22.
28.
RobellerCStiticAMayencourtPet al. Interlocking folded plate: integrated mechanical attachment for structural wood panels. In: BlockPKnippersJMitraNet al. (eds) Advances in architectural geometry 2014. Cham: Springer, 2015, pp. 281–294.
29.
LebéeA.From folds to structures, a review. Int J Space Struct2015; 30(2): 55–74.
30.
NocedalJWrightS.Numerical optimization. New York: Springer Science+Business Media, 2006.
31.
TakayamaKPanozzoDSorkine-HornungO.Pattern-based quadrangulation for N-sided patches. Comput Graph Forum2014; 33: 177–184.
32.
PreisingerCHeimrathM.Karamba – a toolkit for parametric structural design. Struct Eng Int2014; 24(2): 217–221.
33.
FirlMBletzingerKU.Shape optimization of thin walled structures governed by geometrically nonlinear mechanics. Comput Method Appl M2012; 237–240: 107–117.
