Formfindung von Freiformflächen
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1 HafenCity Universität Hamburg Structural and Architectural Engineering/ Facade Systems and Building Envelopes December, 13 and 15, Hamburg, Germany Formfindung von Freiformflächen Formfindung von Freiformflächen Dr Stavric Milena, DI arch Institute of Architecture and Media Graz University of Technology, Austria
2 Content: Content: Curves Algebraic Curves Conic section Curves 2. Order Free Form Curves Bezier Curves B Spline Curves NURBS Curves Surfaces Traditional Surfaces Developable Surfaces Double curved Surfaces Geometrical properties Surfaces with negative Gaussian curvature Surfaces with positive Gaussian curvature Free Form Surfaces Bezier Surfaces B Spline Surfaces and NURBS Surfaces Curvature of Surfaces Developable Surfaces How to make Free Form Surfaces buildable Shape optimization Geometric Optimization Discrete form Discrete Free Form Surfaces Grid Generation Discrete component Discretization into curved Components Discretization into planar Components Triangulation Triangle meshes Quadrilateral Meshes with Planar Faces More edges Meshes with planar Faces Supporting structure Layer Structure Offset and Parallel Meshes
3 Free Form Surfaces Bézier surfaces B- Spline Surfaces Nurbs Surfaces
4 Free Form Surfaces Bézier surfaces B- Spline Surfaces Nurbs Surfaces
5 Free Form Surfaces Bézier surfaces B- Spline Surfaces Nurbs Surfaces
6 Free Form Surfaces Bézier surfaces B- Spline Surfaces Nurbs Surfaces
7 Free Form Surfaces Bézier surfaces Bézier surfaces of degree (2,2)
8 Free Form Surfaces Bézier surfaces Bezier surfaces of degree (1,1)
9 Free Form Surfaces Bézier surfaces Bezier surfaces of degree (2,2)
10 Free Form Surfaces Bézier surfaces Bezier surfaces of degree (1,1)
11 Free Form Surfaces Free Form Surfaces NURBS Surfaces
12 Why NURBS? Why NURBS? NURBS curves and surfaces are useful for a number of reasons: They offer one common mathematical form for both standard analytical shapes (e.g., conics) and free form shapes. They provide the flexibility to design a large variety of shapes. Theyreduce the memoryconsumption when storing shapes (compared to simpler methods). They can be evaluated reasonably quickly by numerically stable and accurate algorithms.
13 Free Form Surfaces NURBS Surface parametrisation P (u, v)
14 Free Form Surfaces Curvature Surfaces properties: tangent plane principal curvatures
15 Free form Surfaces Curvature Gaussian curvature
16 Optimisation Howtomakefreeform buildable? 1. Optimisation mathematical optimisation geometrical optimisation geometric shape optimisation 1. Geometric divison into more patches 2. Discretisation of the surfaces panelisation and planarisation Panelisation is a mainaspect of the desing process
17 Optimisation Howtomakefreeform buildable? 1. Optimisation 2. Geometric divison into more surfaces 3. Discretisation of the surfaces panelisation and planarisation Panelisation is a main aspect of the desing process Optimisation: Shape optimisation: 1. approximation i with ihruled ldsurfaces (surface S is ruled ldif through hevery point of S there is a straight line that lies on S) 2. approximation with developable surfaces 3. approximation with translational ti lsurfaces Geometric optimisation Discrete form
18 PLANARIZATION Ti Triangulation
19 PLANARIZATION Quad meshing
20 NURBS Curvature of surfaces
21 Optimisation p Approximation i byruled surfaces Staatsgalerie Stuttgart, James Stirling, 1984
22 Optimisation Approximation i by buildable developable surfaces Bézier Surfaces Space curve and associated developable surfaces
23 Optimisation Developable surfaces Bezier surfaces Walt Disney Concert Hall, Frank Gehry
24 Optimisation Developable surfaces Bezier surfaces
25
26 Optimisation Approximation i bytranslational lsurfaces Discretization quadrilaterial meshes Planar pannels
27 Optimisation Approximation i bytranslational lsurfaces
28 Optimisation Approximation i bytranslational lsurfaces offset problem
29 Non Standard Architektur Non Standard Architektur Mur Turm, Steiermark, arch. Leonhard, 2010
30 Non Standard Architektur Non Standard Architektur Mur Turm, Steiermark, arch. Leonhard, 2010 Problems Complex knots Complex knots Many edges Torsion Offset
31 Non Standard Architektur Non Standard Architektur Problems Complex knots Complex knots Many edges Torsion Offset
32 Architecture Free form surface Burnham Pavillon, Chicago Zaha Hadid, 2009,
33 Architecture Burnham Pavillon, Chicago Zaha Hadid, 2009, Architecture Free form surface
34 Architecture Burnham Pavillon, Chicago Zaha Hadid, 2009, Architecture Free form surface
35 Architecture Burnham Pavillon, Chicago Zaha Hadid, 2009, Architecture Free form surface
36 Architecture Burnham Pavillon, Chicago Zaha Hadid, 2009, Architecture Free form surface
37 Architecture Free form surface Burnham Pavillon, Chicago Zaha Hadid, 2009,
38 Architecture Free form surface Burnham Pavillon, Chicago Zaha Hadid, 2009,
39 Architecture Free form surface Burnham Pavillon, Chicago Zaha Hadid, 2009,
40 Architecture Free form surface Burnham Pavillon, Chicago Zaha Hadid, 2009,
41 Architecture Freeforms Discretization into curved segments Kunsthaus Friendly Alien, Graz Peter Cook and Colin Fournier, 2003
42 Architecture Freeforms Kunsthaus Friendly Alien, Graz Peter Cook and Colin Fournier, 2003
43 Architecture Freeforms Kunsthaus Friendly Alien, Graz Peter Cook and Colin Fournier, 2003
44 Architecture Freeforms Kunsthaus Friendly Alien, Graz Peter Cook and Colin Fournier, 2003
45 Architecture Triangulation Discretization into planar segments BMW Welt, München Coop Himmelb(l)au, 2007
46 Architecture From idea to realisation...
47 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
48 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
49 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
50 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
51 Free Form Surfaces NURBS
52 Free Form Surfaces NURBS
53 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
54 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
55 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
56 Free Form Surfaces Free Form Surfaces NURBS
57 Free Form Surfaces NURBS Heydar Aliyev Centre, Baku, Azerbaijan Zaha Hadid
58 Free Form Surfaces Free Form Surfaces NURBS
59 Special curves Art and City Museum by MAD architects, Ordos, China, 2011
60 Special curves
61 Special curves Art and City Museum by MAD architects, Ordos, China, 2011
62 Special curves Geodesics Art and City Museum by MAD architects, Ordos, China, 2011
63 Special curves Special curves Geodesics
64 Special curves Special curves Art and City Museum by MAD architects, Ordos, China, 2011
65 Special curves Special curves Art and City Museum by MAD architects, Ordos, China, 2011
66 Special curves Geodesics Art and City Museum by MAD architects, Ordos, China, 2011
67 Architecture Free form surface or not? Yas Hotel, arch. Asymptote, Abu Dhabi,2009
68 Architecture Yas Hotel, arch. Asymptote, Abu Dhabi,2009
69 Architecture Yas Hotel, arch. Asymptote, Abu Dhabi,2009
70 Architecture Yas Hotel, arch. Asymptote, Abu Dhabi,2009
71 Architecture Yas Hotel, arch. Asymptote Abu Dhabi,2009
72 Architecture Yas Hotel, arch. Asymptote Abu Dhabi,2009
73 Free Form Surfaces Nurbs Tori Tori Restaurant Rojkind Architectosmexico City, 2011
74 Free Form Surfaces Nurbs Tori Tori Restaurant Rojkind Architectosmexico City, 2011
75 Free Form Surfaces Nurbs Tori Tori Restaurant Rojkind Architectos mexico City, 2011
76 Discrete Form Pi Principali curvatures lines
77 Special Geodesics curves
78 Special curves Geodesics
79 Special curves p Geodesics Geodesic Lines on Free Form Surfaces Optimized Grids for Timber Rib Shells Ecole Polytechnique Fédérale de Lausanne (EPFL)
80 Special Geodesics curves
81 Special curves Geodesics Centre Pompidou Metz France, 2010 by Shigeru Ban
82 Speci Geodesics al Centre Pompidou Metz France, 2010 by Shigeru Ban curve s
83 Speci Geodesics al Centre Pompidou Metz France, 2010 by Shigeru Ban curve s
84 Special curves Geodesics HAESLEY NINE BRIDGE CLUB HOUSE, 2010 by Shigeru Ban
85 PLANARIZATION 2D Ornament > double curved surface uv parameter lines
86 PLANARIZATION Why tangent planes method? no Problems Complex knots Many edges Torsion Offset Because of aestethic reasons 2D Ornaments > > on a curved surface in space We can vary the tangent planes
87 Vary the points
88 Hyperbolic surface points Butterfly panels
89 EXAMPLES
90 EXAMPLES
91 EXAMPLES
92 EXAMPLES
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