--- Elements of Parametric Design --- by Robert Woodbury (2010)
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Driven by new computer and digital fabrication tools, the architectural designs that are being built are pushing boundaries of form, customization and construction. Pushed by practices wanting and needing to produce novelty, computer-aided design systems are increasingly parametric - that is, they represent designs that change with their input data. Such systems give more control and capability to designers, but require much more comprehensive understanding if they are to be used effectively.
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Animated hyperboloid
December 2012
Gif by: Cmapm
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Copenhagen Elephant House A Case Study of Digital Design Processes
. . . by Brady Peters
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9 - GenerativeComponents (software) : https://communities.bentley.com/products/products_generativecomponents/w/generative_components_community_wiki
11 - parametric modeling (or constraint modeling)
11 - relating and repairing . . . . . . . . 11 - merge operator.
12 - propagation-based systems - graph based
22 - geometric construction . . . . . . . 23 - copy, cut and paste
24 - designing relationships
27 - near-hierarchies for objects (such as a car)
34 - a parametric design is (or as?) a graph
35 - CAD - "relegates programming to the background"
30 - "throw away code is a fact of parametric design" . . . . . 41 - recursion (fractal)
47 - parametric craft
40 - sections cut from a torus
61 - vector spaces (normal) and affine spaces (coordinate)
62 - parametric model construction, update method programming, module development & meta-programming
69 - New Elephant House by Brody Peters. Architect : Foster & Patrners (2008) - location : Denmark Zoo
71 - the torus - thus defines an array of planar faces suitable for manufacture
71 - torus swatch - part of a torus surface
72 - structure generator
74 - geometry method statement
81-170 - geometry
82 - Gaspard Munge - 1795 - descriptive geometry
83 - CAD - shaping and intersection operations
86 - vector and points
88 - homogenous coordinates ( for points p[3] = 1 and for vectors v[3] = 0 )
89 - arithmetic of vectors
92 - linear combinations
93 - linear dependence and independence, span, vector basis
95 - scalar product of two vectors - or the dot product
97 - converse projection
98 - lines in 2d . . . . . . 98 - explicit & implicit equations
99 - line operator (matrix)
101 - parametric line equation - is constructive (can generate points)
102 - projecting a point to a line . . . . . . . 103 - lines in 3D
106 - coordinate systems / frames
103 - right-hand rule (for rotation)
108 - cross product
110 - Gram-Schmit orthonormalization process
123 - intersections . . . . . . . . . 132 - closest fitting object . . . . 134 - curves
137 - interpolating vs approximating curves
138 - linear interpolation or tweening . . . . . . . . 138 - systolic array
139 - tangent vector (and normalized)
140 - normal vector
141 - osculating circle, evolute
141 - binormal vector, Frenet frames
143 - hodograph - https://en.wikipedia.org/wiki/Hodograph
146 - bezier curves - cubic form, four control points
148 - deCasteljau algorithm
152 - non-uniform rational b-splines or NURBS - have projective invariance
154 - joining bezier curves - continuity and smoothness
155 - B-spline curves
156 - knot vector
157 - blossom values
170 - lines of principle curvature
172 - white magnolia tower - Shanghai
185 - patterns for parametric design
294 - Wang (2010) - design patterns .... Grasshopper reference
199 - hyperboloid - of one sheet
201 - jigs - lower detail models. abstracting a specific design
203 - curve literature - degree elevation
204 - tube. . . . . . . . . . . 205 - sheet
206 - scallop
209 - helix - circular and conic
212 - point collection
219 - hedgehog - tile surface with splines
249 - Jordan curve theorem
253 - affine map
260 - recursion - squares (nested), trees
266 - Sierpinski carpet . . . . . . . 268 - Hilbert curve
276 - solidworks configuration manager and Autodesk Showcase - multiple variations of a single model
276 - design space
279 - generative components (software)
282 - metaballs
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35 - "Conceiving data flow; dividing to conquer; naming and thinking abstractly; mathematically and algorithmically form the base for designers to build their parametric craft."
75 - "Variable openings in the glass canopy controlled natural airflow. Fritting patterns printed on gas reduced solar radiation received and thus helped maintain a comfortable temperature."
85 - "Learning about parametric tools involves bringing together four distinct ways of understanding the mathematics of spatial objects : geometric, visual, symbolic and algorithmic. We will call each of these a view onto the toolbox."
92 - "The overall structure of a typical arithmetic calculation in space is to start with points, use point-point subtraction to convert to vectors, do the serious work with vectors and convert back to points with point-point addition."
96 - "Geometrically, the scalar product is a measure of the projection of one vector onto another."
139 - "The very big lesson here his that parametric and geometric space are different. It is easy to work in parametric space, but designs are built in geometric space. The difference between the two bedevils much work."
152 - "A big disadvantage of Bezier curves is that they are not projectively invariant, that is, they change with perspective. Of course all CAD systems use perspective. Section 6.9.13 outlines Non-Uniform Rational B-Splines (NURBs), the main purpose of which is to ensure perspective invariance."
287 - "Furthermore, parametric proximity does not imply geometric similarity of designs. Conversely, two very close values of the parameters may result in quite a distinct model."
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