#### MARC FORNES & THEVERYMANY™

PRACTICING AT THE INTERSECTION OF ART + ARCHITECTURE ^ COMPUTATION## Archive for January, 2008

## 080130_Exhibition: Aperiodic_Vertebrae

THEVERYMANY has been set up based on a continuum research on explicit and encoded protocols within design – the first implicit consequence of its core is to let traces; those traces – often under the format of simple text files – allow to exactly reproduce or alter the model, eventually share axioms… but it somehow also requires to admit and assume those traces, if so, one can learn from mistakes, errors and/or tolerances of previous stages or generation based on feed back…

Yesterday was the kick start in Berlin of the assembly process for the installation -once again the amount of components generated through a long chaine of various small codes / utilities has directly revealled “dirt”/issues hidden behind a fast/furious seamless process… yet nothing extraordinary beyond the purpose of a physical mock up: large scale test for a complete automate pipe line of form & drawing generation…

DIRTY DIGITAL:

One of the significant issue we came across is related to the nature of tiling and computation – the subdivision algorythm is based on a recursive protocol (or SUBSTITUTION) which is first drawing a primitve pyramide (within a choice of four primitives) which then gets subdivide – the process is repeated many times within itself to generate self-similarity… the issue there is that within each generation the protocol requires to “compare” (points, lenght, areas, etc…) and that matching process needs to determine whether two geometry or parameters are “equal” given an inevitable rounding errors… unfortunately the rounding errors are bound to accumulate whithin each generation…

Yet it wasn’t any special issue except when point connection gets generated and therefore requires to increase the tolerance factor not to miss any neighbors… though applying overal tolerance is triggering other error trapping while small naming or matching utilities code are running as host on the larger protocol…

Anyway – suming up it is yet still triggering slight erros and confusion – though I’d like to be transparent and learn within those error trapping – it is defintively part of a certain material paradigm debugging…

Let see which surprises are we getting tomorrow…

“a chaque jour sa peine…”

## 080124_Exhibition: Aperiodic_Vertebrae

THEVERYMANY (Marc Fornes, Skylar Tibbits) has been kindly invited to exhibit a physical piece at *“Generator.X v2.0: Beyond the screen”* – a workshop and exhibition about digital fabrication and generative systems curated by Marius Watz (http://www.generatorx.no/) in collaboration with Club Transmediale and [DAM] Berlin.

Based onto earlier experimentation (Aperiodic series) the installation is an assembly of nearly 500 flat panels (11 types) all milled within 6 sheets (8 feet by 4 feet) of corrugated plastic (4 colors: black, silver grey, white and translucent) and also nearly 500 assembly details (moreless all unique!) all laser cut onto 7 sheets of transparent acrylic…

Despite mesuring 13 feet long (after been scaled nearly by half for simple reason of space available within the gallery!) all the panels and assembly details are now flying over nested within one suitcase only…

(pictures of the assembly process should come up soon)

It has been quite some intense moments of scripting since last weekend – mainly sequences of utilities codes – in order to perform a complete automaton starting from the first 4 nurbs curve (those ones were drafted!), the generation of the geometries till the production of each components, notches, unroll, color coding, naming, etc… but there were also a lot of discussion on logic, sequence and protocols to be set up in order to PRE-facilitate as much as we can the entire physical re-fold-assembly of nearly a thousand parts…

Illustrated above (top) the layout of one of the acrylic sheet (number 6) with 66 assembly details – all got named with the number of the piece (as text + name of the object) + each notche with the color of the brick it should connect to and the name of its panel it should locked in…

Illustrated above (bottom) the lay out of one of the 11 types of panels onto a sheets of corrugated plastic – the intersting figure is that the nesting of the panels sheets has been the only hand protocols as a simple traight forward array of the same geometry – this is where it is a hughe gain of time and energy as nesting for so many parts if different would take ages (if even only possible) to find an efficient nested solution…

That starting hypothesis of embeded relative simplicity due to the self-similarity (without even counting the labor time saved to look for the right panels when assembling – imagine a pile of 500 panels to pick from?!!) is RE-questioning the complete mass customization fashion and other kit of parts…

Though the amount of components generated which have to be RE-assembled is also RE-questioning the limit of using generative processes without going further down the line using assembly robots…

Generator.x 2.0: Beyond the Screen

24 Jan - 2 Feb 2008, Ballhaus Naunynstrasse / [DAM] Berlin

Credits:

Design: THEVERYMANY (Marc Fornes + Skylar Tibbits)

Scripting: Marc Fornes

Manufacturing protocols: Marc Fornes + Skylar Tibbits

Laser cutting: Skylar Tibbits

CNC & material research: Jared Laucks

Assembling: Skylar Tibbits (+ helpers!)

ANYONE IN BERLIN INTERESTED TO HELP ASSEMBLING IS HIGHLY WELCOME!!

PLEASE COME OVER AT THE [DAM] GALLERY

(starting on the Jan 29th till February 2nd)

## 080121_Consulting: polyhedrons frame structure 02

following up on some side escapism while running on more “rational” automaton for an exhibition in berlin (more to come soon)

here the previous code developped for the course of a friend at Knowlton School of Architecture has been applied onto some random polyhedrons.

## 080118_Consulting: polyhedrons frame structure 01

I recently happen to write few codes for Aurel Von Richtofen who is teaching a course/seminar based on rhinoscript at the Knowlton School Of Architecture (Ohio State University) like: select points within closed polygones, points relaxation/explosion, frame along the edge of polygons, etc…

Whenever I have here or there an hour to kill I often happen to re-read a previous code, clean it and often push it slightly further to render few frames – here are some random fast track results…

PROTOCOL (original version):

– for each closed polygons

– for each faces

– extract edges

– add polylines: array(edge start pt, end pt,face centroide)

– offset the curve (on face – toward the centroide)

Many “quick fix” upgrades are possible:

recursive subdivision according to face aera, membrure thickness according to edge length, etc…

## 080115_”SunCare”

Tooling development (in progress) for SOM – different codes:

– Panels: honeycomb subdivision of a nurbs surface based on the UV coordinates of an host nurbs surface (here a sphere) – each cells is re-subdivided into planar panels (triangles) which are able to rotate onto the edge they share with the original cell.

– “SUNCARE” : the facade panels are rotating based on a Sun path “analysis” – in that exemple a random arc inclined 45 degree – though can easily be ploted based on the GPS coordinates of the site and the sun data using as parameters the azimuth and elevation (thx to Neil Katz).

– Animation: rhino animation (number of frame according to sun data sampling) where the honeycomb panels open whenever directly exposed to the sun (with decay)…

AZIMUTH AND ELEVATION – an angular coordinate system for locating positions in the sky. Azimuth is measured clockwise from true north to the point on the horizon directly below the object. Elevation is measured vertically from that point on the horizon up to the object. If you know the azimuth of a constellation is 135° from north, and the elevation is 30°, you can look toward the southeast, about a third of the way up from the horizon to locate that constellation. Because our planet rotates, azimuth and elevation numbers for stars and planets are constantly changing with time and with the observer’s location on earth.

## 080114_Boolean_Series002

Since my very traditionalist architectural educational background in France – the Sphere has been unfortunatly very early on associated my history & theory course and french Neo-classical (though utopist) architects such as “Nicolas Ledoux” – and therefore temporally banished from my formal language ever since; so what is it that suddenly brings it back? was it the Star Wars “baby boom”? is it Rem Koolhaas and his (re-)recent fascination for the icone as primitives like in his recent proposal for the Ras al Khaimah Convention and Exhibition Centre in the UAE?

PROTOCOL:

– pick a closed surface or polysurface

– plot random points within that solid

– assign a sphere to each of the points; its radius being either the same for each or weighted according to the color of the point

– for every point boolean its sphere with his neighbours

“SIDE TRACK” : ELEVEN PROPERTIES OF A SPHERE (ie wikipedia.org)

In their book Geometry and the imagination David Hilbert and Stephan Cohn-Vossen describe eleven properties of the sphere and discuss whether these properties uniquely determine the sphere. Several properties hold for the plane which can be thought of as a sphere with infinite radius. These properties are:

The points on the sphere are all the same distance from a fixed point. Also, the ratio of the distance of its points from two fixed points is constant.

The first part is the usual definition of the sphere and determines it uniquely. The second part can be easily deduced and follows a similar result of Apollonius of Perga for the circle. This second part also holds for the plane.

The contours and plane sections of the sphere are circles.

This property defines the sphere uniquely.

The sphere has constant width and constant girth.

The width of a surface is the distance between pairs of parallel tangent planes. There are numerous other closed convex surfaces which have constant width, for example Meissner’s tetrahedron. The girth of a surface is the circumference of the boundary of its orthogonal projection on to a plane. It can be proved that each of these properties implies the other.

A normal vector to a sphere, a normal plane and its normal section. The curvature of the curve of intersection is the sectional curvature. For the sphere each normal section through a given point will be a circle of the same radius, the radius of the sphere. This means that every point on the sphere will be an umbilical point.

All points of a sphere are umbilics.

At any point on a surface we can find a normal direction which is at right angles to the surface, for the sphere these on the lines radiating out from the center of the sphere. The intersection of a plane containing the normal with the surface will form a curve called a normal section and the curvature of this curve is the sectional curvature. For most points on a surfaces different sections will have different curvatures, the maximum and minimum values of these are called the principal curvatures. It can be proved that any closed surface will have at least four points called umbilical points. At an umbilic all the sectional curvatures are equal, in particular the principal curvature’s are equal. Umbilical points can be thought of as the points where the surface is closely approximated by a sphere.

For the sphere the curvatures of all normal sections are equal, so every point is an umbilic. The sphere and plane are the only surfaces with this property.

The sphere does not have a surface of centers.

For a given normal section there is a circle whose curvature is the same as the sectional curvature, is tangent to the surface and whose center lines along on the normal line. Take the two center corresponding to the maximum and minimum sectional curvatures these are called the focal points, and the set of all such centers forms the focal surface.

For most surfaces the focal surface forms two sheets each of which is a surface and which come together at umbilical points. There are a number of special cases. For canal surfaces one sheet forms a curve and the other sheet is a surface; For cones, cylinders, toruses and cyclides both sheets form curves. For the sphere the center of every osculating circle is at the center of the sphere and the focal surface forms a single point. This is a unique property of the sphere.

All geodesics of the sphere are closed curves.

Geodesics are curves on a surface which give the shortest distance between two points. They are generalisation of the concept of a straight line in the plane. For the sphere the geodesics are great circles. There are many other surfaces with this property.

Of all the solids having a given volume, the sphere is the one with the smallest surface area; of all solids having a given surface area, the sphere is the one having the greatest volume.

These properties define the sphere uniquely. These properties can be seen by observing soap bubbles. A soap bubble will enclose a fixed volume and due to surface tension it will try to minimize its surface area. Therefore a free floating soap bubble will be approximately a sphere, factors like gravity will cause a slight distortion.

The sphere has the smallest total mean curvature among all convex solids with a given surface area.

The mean curvature is the average of the two principal curvatures and as these are constant at all points of the sphere then so is the mean curvature.

The sphere has constant positive mean curvature.

The sphere is the only surface without boundary or singularities with constant positive mean curvature. There are other surfaces with constant mean curvature, the minimal surfaces have zero mean curvature.

The sphere has constant positive Gaussian curvature.

Gaussian curvature is the product of the two principle curvatures. It is an intrinsic property which can be determined by measuring length and angles and does not depend on the way the surface is embedded in space. Hence, bending a surface will not alter the Gaussian curvature and other surfaces with constant positive Gaussian curvature can be obtained by cutting a small slit in the sphere and bending it. All these other surfaces would have boundaries and the sphere is the only surface without boundary with constant positive Gaussian curvature. The pseudosphere is an example of a surface with constant negative Gaussian curvature.

The sphere is transformed into itself by a three-parameter family of rigid motions.

Consider a unit sphere place at the origin, a rotation around the x, y or z axis will map the sphere onto itself, indeed any rotation about a line through the origin can be expressed as a combination of rotations around the three coordinate axis, see Euler angles. Thus there is a three parameter family of rotations which transform the sphere onto itself, this is the rotation group, SO(3). The plane is the only other surface with a three parameter family of transformations (translations along the x and y axis and rotations around the origin). Circular cylinders are the only surfaces with two parameter families of rigid motions and the surfaces of revolution and helicoids are the only surfaces with a one parameter family.

## 080110_Boolean_Series001

“SIDE TRACK” : CONSTRUCTIVE SOLID GEOMETRY (CSG) (ie wikipedia.org)

Constructive solid geometry (CSG) is a technique used in solid modeling. CSG is often, but not always, a procedural modeling technique used in 3D computer graphics and CAD. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine objects. Often CSG presents a model or surface that appears visually complex, but is actually little more than cleverly combined or decombined objects. (In some cases, constructive solid geometry is performed on polygonal meshes, and may or may not be procedural and/or parametric.)

The simplest solid objects used for the representation are called primitives. Typically they are the objects of simple shape: cuboids, cylinders, prisms, pyramids, spheres, cones. The set of allowable primitives is limited by each software package. Some software packages allow CSG on curved objects while other packages do not.

It is said that an object is constructed from primitives by means of allowable operations, which are typically Boolean operations on sets: union, intersection and difference.

A primitive can typically be described by a procedure which accepts some number of parameters; for example, a sphere may be described by the coordinates of its center point, along with a radius value. These primitives can be combined into compound objects using operations like these:

– boolean union: the merger of two objects into one.

– boolean difference: the subtraction of one object from another.

– boolean intersection: the portion common to both objects

Combining these elementary operations it is possible to build up objects with high complexity starting from simple ones.

EXTEND:

in the case of spheres as primitives – if all have the same exact radius, the complex composite object -resultant from a set of boolean operations- can be describe out of one spherical mould from which all the different parts are trimmed: the challenge here will be to describe and catalogue all the parts not as geometry but rather as 3d trim paths for robotic arm…