Mon, 05 Feb 2024 22:35:32 +0000 Mon, 05 Feb 2024 22:35:32 +0000 https://www.grasshopper3d.com/photo/inflated-in-kangaroo?context=user by Mårten Nettelbladt High resolution meshes (based on Polyline typeface) inflated with Kangaroo and rendered with the built-in environmental map ‘Sunroom’. Each mesh was left for about 5 minutes (on my old laptop). Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/bening-book-cover?context=user by Mårten Nettelbladt Dear grasshoppers, this is the cover of my new book "The Geometry of Bending". It has plenty of Grasshopper examples. More info here: http://martennettelbladt.se/bending-book/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/bending-book-pages-40-41?context=user by Mårten Nettelbladt Some Grasshopper examples from my new book. Kangaroo hinge force. More info here: http://martennettelbladt.se/bending-book/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/bending-book-pages-34-35?context=user by Mårten Nettelbladt Some Grasshopper examples from my new book. Developing the concept of "flat approximation". More info here: http://martennettelbladt.se/bending-book/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/bending-book-pages-20-21?context=user by Mårten Nettelbladt Some Grasshopper examples from my new book. Creating a parametric helix. More info here: http://martennettelbladt.se/bending-book/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/bending-book-pages-16-17?context=user by Mårten Nettelbladt Some Grasshopper examples from my new book. Kangaroo bending force and curvature analysis. More info here: http://martennettelbladt.se/bending-book/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/bending-book-pages-06-07?context=user by Mårten Nettelbladt One of my first investigations and the starting point for the whole process. I traced a saw blade and tried to figure out its geometry. More info here: http://martennettelbladt.se/bending-book/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/welcome-to-the-release-party-for-my-book?context=user by Mårten Nettelbladt Welcome to the release party for my new book "The Geometry of Bending"! Wednesday 12 June 2013, 17-21. FFAR Forum för arkitektur, Ringvägen 141, Stockholm (Sweden) RSVP as a message or comment. I hope to see you there! The book is based on the material from my blog http://thegeometryofbending.blogspot.se/ and includes plenty of grasshopper examples. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/gr-shoppa?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/kangaroo-shrink-wrap?context=user by Mårten Nettelbladt http://www.grasshopper3d.com/group/kangaroo/forum/topics/shrink-wrap-trouble Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mn-comparison?context=user by Mårten Nettelbladt Comparing digitized geometry with results from Kangaroo. Download here: http://dl.dropbox.com/u/20386776/MN-comparison.zip NB: You need Kangaroo & WeaverBird installed. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/marten1-1?context=user by Mårten Nettelbladt Me at the opening of the exhibition. Top screen shows Tapeworm surface in Rhino window, bottom screen shows Grasshopper window. Hardware sliders below and plywood model above. It's all run by a Mac Mini hidden under the table. Exhibition hosted, curated and designed by Fritz Halvorsen. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/screen1-1?context=user by Mårten Nettelbladt Download Rhino file + Grasshopper definition here: http://dl.dropbox.com/u/20386776/Graph.3dm http://dl.dropbox.com/u/20386776/Tapeworm_no_firefly.ghx The firefly stuff has been omitted in this version since not everyone have their hardware sliders... Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/exhibition1-1?context=user by Mårten Nettelbladt FFAR, Forum for Architecture, at Ringvägen 141 in Stockholm. Run by Fritz Halvorsen. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/exhibition2-1?context=user by Mårten Nettelbladt Opening of the exhibition 'function', showing works by Ulrika Karlsson & Marcelyn Gow, Pablo Miranda Carranza & Åsmund Gamlesæter and Mårten Nettelbladt (me). Exhibition hosted, curated and designed by Fritz Halvorsen. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/exhibition3-1?context=user by Mårten Nettelbladt Searching for the obvious Mårten Nettelbladt When you bend a thin strip of plywood you get a beautifully shaped curve. What geometry does this curve follow? There is a peaceful simplicity to the shape, and yet, it doesn't fall into the normal categories of basic geometric shapes as we know them. The exhibition shows two different ways to approach this challenge. Part one: A plywood strip, twelve meters long, curled and twisted into a double loop shape. This geometry is a result of the material trying to resist, and thereby minimize, the forces of bending and torsion. Part two: A computer generated surface, curling and twisting according to user input. Two lists of values control the curvature and the direction of the surface. The resulting single-curved surface will always be developable and unroll to a straight strip. Question: Is there a simple mathematical solution that will produce the same geometry as in the plywood loop? The search continues. Special thanks to David Rutten, McNeel Andy Payne & Jason K. Johnson, Firefly Experiments Grasshopper Forum Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/exhibition4-1?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/exhibition5-1?context=user by Mårten Nettelbladt Using the remote control! Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/catalog-1?context=user by Mårten Nettelbladt Searching for the obvious Mårten Nettelbladt When you bend a thin strip of plywood you get a beautifully shaped curve. What geometry does this curve follow? There is a peaceful simplicity to the shape, and yet, it doesn't fall into the normal categories of basic geometric shapes as we know them. The exhibition shows two different ways to approach this challenge. Part one: A plywood strip, twelve meters long, curled and twisted into a double loop shape. This geometry is a result of the material trying to resist, and thereby minimize, the forces of bending and torsion. Part two: A computer generated surface, curling and twisting according to user input. Two lists of values control the curvature and the direction of the surface. The resulting single-curved surface will always be developable and unroll to a straight strip. Question: Is there a simple mathematical solution that will produce the same geometry as in the plywood loop? The search continues. Special thanks to David Rutten, McNeel Andy Payne & Jason K. Johnson, Firefly Experiments Grasshopper Forum Update: Please contact Fritz Halvorsen at Forum för Arkitektur, to get a copy: info@ffar.se Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/invitation-exhibition-opening?context=user by Mårten Nettelbladt Welcome to the opening of the exhibition 'function' at FFAR forum for architecture 6.00-10.00 p.m. April 14, 2011. The exhibition presents works by servo, Omkrets arkitektur and gran on the theme mathematics and architecture. R.S.P.V to info@ffar.se before April 10, 2011 FFAR forum for architecture is an event and debate space presenting a broader perspective on contemporary architecture. Founded in 2010, FFAR invites both theorists and practitioners to engage in, and thereby forward, contemporary architectural debate. Information on upcoming events on www.ffar.se Ringvägen 141, Stockholm, Sweden. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnkangaroocurvature-1?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnkangaroobending-1?context=user by Mårten Nettelbladt This is the closest approximation I have found so far in my quest for finding the Geometry of bending. It's a fairly simple setup in Kangaroo. Pretty amazing how well it works! Thanks Daniel... Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/are-you-sure-you-want-to-do?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/hardware-remote-control-v2?context=user by Mårten Nettelbladt Hardware "sliders" (knobs) for Grasshopper. Arduino board inside. See this post for more info: (http://www.grasshopper3d.com/photo/hardware-remote-control-in-gh). Firefly connects between arduino and GH. The grey plastic case is 14 x 11 cm. Tomasz Gancarczyk made one too: http://www.grasshopper3d.com/photo/knob-controller and so did bingg http://www.grasshopper3d.com/photo/arduino-in-use Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnbendinganalysis-1?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/hardware-remote-control-in-gh?context=user by Mårten Nettelbladt These 4 knobs are each connected to a 10 kohm potentiometer and then wired into an Arduino Uno board. Via USB cable into my computer where the Firefly component in GH reads the values. It works great and it's very fun to adjust a 3d model in this rather "direct" way... Update: If you want to try this at home, please check out http://www.fireflyexperiments.com/ and download the Primer. You'll find almost everything explained in there. I ordered an Arduino Starter Kit from a Swedish site http://www.electrokit.se/moduler-mikroprocessor-arduino-starter-kit-mah-uno_12200001 and then I got some more potetiometers and some knobs. I've put this in a case now, see here http://www.grasshopper3d.com/photo/hardware-remote-control-v2 Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnmyfirstarduinohardwareslider-1?context=user by Mårten Nettelbladt Arduino UNO plus a 10kohm potentiometer. (The extra LED has no real function here). Connects to GH with the Firefly component. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapewormchain01-1?context=user by Mårten Nettelbladt Both the Amount and the Direction of bending are controlled by a Cosine function. This is ONE long developable surface that can be unrolled to a straight strip. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnanalysingconicplankline-1?context=user by Mårten Nettelbladt For a conic plank line, curvature seems to vary in a parabola like way (not starting at zero). The direction of the curvature (twist) varies in a linear fashion. When curvature is at max, twisting is at zero. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapewormcurls2-1?context=user by Mårten Nettelbladt Developable surface. Twisting according to Sine Summation GraphMapper. Unrolls to straight strip. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapewormpinkcurls-1?context=user by Mårten Nettelbladt Five twisted surfaces. Amount of twist controlled by GraphMapper. See also: http://www.grasshopper3d.com/video/tapeworm-twisting Surfaces are developable and possible to unroll to straight strips Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapeworm10foldedloop-1?context=user by Mårten Nettelbladt Developable surface. Unrolls to a straight strip. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapewormweaving2-1?context=user by Mårten Nettelbladt Constant curvature. Twist varying with sine, but transposed to be mainly on the negative side (below zero). Developable surface that will unroll to a straight strip. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapewormweaving-1?context=user by Mårten Nettelbladt Constant curvature. Twist varying with sine, but transposed to be mainly on the positive side (above zero). Developable surface that will unroll to a straight strip. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mntapewormskein-1?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/merry-christmas-1?context=user by Mårten Nettelbladt Ribbons made with Tapeworm script. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/parametric-tagliatelle-2?context=user by Mårten Nettelbladt One developable surface that will unroll to a straight strip. Similar setup in this image but the "Shift List" component is set to "0" here. As you can see it gets very symmetrical. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/parametric-tagliatelle?context=user by Mårten Nettelbladt Again, this is a (one) developable surface that will unroll to a straight strip. The curvature is controlled by Sine and Cosine functions with a lot of sliders attached. The "shift list" component provides necessary distortion between "bend" and "twist" values. Otherwise, the curvature of the strip gets very repetitive, see example here. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/developable-strips?context=user by Mårten Nettelbladt Developable surfaces that will unroll to straight strips. Thanks to Graph Mappers (one for bending and one for twisting) the shape is relatively easy and intuitive to adjust. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/big-nono?context=user by Mårten Nettelbladt Can grasshopper deal with self-intersecting surfaces in a clever way? Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/guitar-string-gh-scripting?context=user by Mårten Nettelbladt Trying to mimic the loop shape of a curved guitar string. The scripted curve has linear increasing/decreasing curvature (like a Clothoid or Cornu Spiral). Pretty good fit?! (Gray line is a shadow) Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/paper-model-1?context=user by Mårten Nettelbladt Sorry, no grasshopper, but investigating an important subject: what curves can be joined by a developable surface? Related to this one: http://www.grasshopper3d.com/photo/2985220:Photo:130248 Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/paper-model?context=user by Mårten Nettelbladt Sorry, no grasshopper, but investigating an important subject: what curves can be joined by a developable surface? Related to this one: http://www.grasshopper3d.com/photo/2985220:Photo:130249 Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/2985220:Photo:128022?context=user by Mårten Nettelbladt what a mess (scripting gone wrong) Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/grasshopper-toolbar-icon-32x32?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/inflatedprincipalcurvature-1?context=user by Mårten Nettelbladt Using GH to display the principal curvature (white lines) on a surface. The surface is a digitized inflated plastic bag. Black lines were drawn manually. Dot "1" shows star point. See more here: http://www.omkrets.se/inflated/ Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/two-circles?context=user by Mårten Nettelbladt This is a strange relationship. When bending curves are aligned at their centre points, the curve endpoints lay on two circles! Circle diameter = 4/5 of curve length. Download .ghx file: UPDATED WITH CORRECT FILE http://www.omkrets.se/grasshopper/MN-cornu-script.zip Early test here:http://thegeometryofbending.blogspot.com/2008/11/arranging-curves.html Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/tracing-a-saw-blade?context=user by Mårten Nettelbladt Tracing a bent saw blade with ink. Obviously this is NOT grasshopper, but it relates to THIS image and THIS ONE. From my blog The Geometry of Bending. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mncurvature-analysis?context=user by Mårten Nettelbladt The drawing is related to THIS one and they are both based on this scanned drawing (that you see in the background). They are part of a little project of mine called "The Geometry of Bending" that aims to understand the shape of elastically bent materials. So, those three drop-like shapes are attempting to describe this geometry. The underlying scan are curves drawn along a bent sawblade. The rhino-curve to the right is just a trace of one of those drawn curves. The middle one is something I created in Grasshopper and its geometry is related to the Cornu spiral (the curvature increases linearly until it reaches the midpoint). The curve to the left is an elastica curve, also created in Grasshopper, it's commonly believed that this is the shape of a bent material. I put those 3 curves back into GH to plot their curvature as a graph. I think it's clear that the traced saw-blade has more in common with the Cornu-spiral curve than with the elastica curve... Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mncurvature-analysis2?context=user by Mårten Nettelbladt The drawing is related to this one and they are both based on this scanned drawing (that you see in the background). They are part of a little project of mine called "The Geometry of Bending" that aims to understand the shape of elastically bent materials. So, those three drop-like shapes are attempting to describe this geometry. The underlying scan are curves drawn along a bent sawblade. The rhino-curve to the right is just a trace of one of those drawn curves. The middle one is something I created in Grasshopper and its geometry is related to the Cornu spiral (the curvature increases linearly until it reaches the midpoint). The curve to the left is an elastica curve, also created in Grasshopper, it's commonly believed that this is the shape of a bent material. I put those 3 curves back into GH to plot their curvature as a graph and the image above is from that process. So the red curves are Curvature circles from the Elastica curve and the points are centre points of those circles. I think it is clear that the traced saw-blade has more in common with the Cornu-spiral curve than with the elastica curve... Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mngalapagoscircles-1?context=user by Mårten Nettelbladt I played around a little with Galapagos, I love it already! The attached definition is placing circles around another circle. It tries to minimize the gaps between the circles and at the same time it tries to get the total area of the outer circles equal to the area of the inner circle. It usually ends up on 15 circles but not always. The further it goes, the more reluctant will it be to change the number of circles. There is a slider called "Koefficient" to adjust the priority between the two goals. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnlampshadev2-1?context=user by Mårten Nettelbladt Download definition here: http://www.omkrets.se/grasshopper/MN-lamp-shade_2010-02-27.zip Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnlampshade-1?context=user by Mårten Nettelbladt (Also posted in the Curved Folding Network http://www.curvedfolding.com/) I made this test in august 2008 and it's probably my only test until now with curved folding (converted from .wrm). All surfaces bend in a "cylindrical" fashion so it's quite basic. It's mimicking a lamp shade that I saw somewhere. Looking at the definition now it seems so complex for achieving something rather simple! There must be a much easier way to do this even without scripting. Download definition: http://www.omkrets.se/grasshopper/MN-lamp-shade_2008-08-20.zip Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/mnprimenumbers-1?context=user by Mårten Nettelbladt This is in response to Daniels image http://www.grasshopper3d.com/photo/geometric-prime-number-finder and it's something i tried in Rhino in July 2001. (No Grasshopper involved obviously, just Array command... Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/grasshopper-icon?context=user by Mårten Nettelbladt Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/conic-plank-lines-3?context=user by Mårten Nettelbladt Conic plank lines (single curved this time) generated directly from Grasshopper without a base surface. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/conic-plank-lines-2?context=user by Mårten Nettelbladt Created with David Ruttens ToyCar Script. When I used Grasshopper to create surfaces, the strips didn't turn out single curved. Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt https://www.grasshopper3d.com/photo/conic-plank-lines-1?context=user by Mårten Nettelbladt The green strips of paper are "conic plank lines". Mårten Nettelbladt https://www.grasshopper3d.com/profile/MNettelbladt