umbers behave differently from the reals, in that when they are squared they give a negative result. They are written as multiples of the imaginary unit i, which is defined so that:
i*i=-1
Complex numbers are numbers which have two parts (hence the name complex) - a real part and an imaginary part.
For example:
3+4i,
or more generally:
a+bi, where a and b are some real numbers.
Well that's a definition, but I guess you might be wondering what is the point of them - I've not said anything yet about why they are interesting and useful...
Solving cubic equations was one of their first uses, but I doubt that is what most of you are interested in.
Where they really get fun is when you start looking at them geometrically.
The Argand plane is a setting that allows us to treat complex numbers a bit like vectors.
Each complex number a+bi defines a point relative to an origin (0,0), much the same as a vector with an x and y component.
Like vectors we can add and subtract them to get a new point.
But when we multiply them, unlike vectors, we add the angles (measured anti-clockwise from the positive real axis, also called the argument) and multiply the lengths (or the modulus of each number).
This all follows naturally as a consequence of the definition of i as the square root of minus one.
........
That is just dipping a toe into the great depths.
Complex number math, and in particular complex Analysis (calculus with complex numbers) is a vast subject that I obviously can't cover much of here.
If you are interested in learning more :
The Math department at Cal State Fullerton has some very nice Complex Analysis pages.
Chapters 5 and 6 of the film Dimensions covers complex numbers very visually. You can watch it online here, or read the description here.
Complex numbers on Wikipedia
on MathWorld
Hans Lundmark's complex analysis pages
The book Indra's Pearls is about making certain types of fractals with complex numbers, and includes a good introduction, along with lots of pseudocode.
To really engage with some of the true depth and power of complex numbers I particularly recommend the beautiful Visual Complex Analysis. This was the book that made me love this subject.
I'm really looking forward to seeing more designers make use of complex numbers. I think it is a wonderful tool. It is an advanced branch of mathematics, requiring some serious study to understand, but because of its strong geometric connections, I think relatively accessible to those who tend to think more visually. Now that David has included them in Grasshopper, starting to explore them should be easier than ever.…
Added by Daniel Piker at 4:38am on November 25, 2009
can work in any node of a given hierarchy tree (loaded in your work session) by making the node "active". "Nodes" can be other things as well (like workplane, clip definitions etc).
Why to do that weird thing? Well, think any design being "flat" > meaning that all objects are placed in a single file (and in a single layer). Not that good > although the items are present you barely can handle them (because power is nothing without control, he he).
Let's go one step further: we can start classifying objects in "groups" (like a directories/files organization in any O/S). This means, in MCAD speak, creating assemblies (a void thing kinda like a directory) that contain components/entities (kinda like files).
Several steps further we end up with severely nested "arrangements" of entities (an assembly could be parent of something and child of something else).
For instance, it could be rather obvious the logical classification of a "geodetic" (so to speak) structure like this : a 40000m2 "hangar" defining some thematic park.
I mean : a void master that owns 4 equal void segment sets that own 4 "legs" that own various geodesic structural members + cables + membranes + you name it etc etc.
Each "leg" owns the concrete base (Shared) and a rather complex set of objects.
Notice that some tensile membrane "fixture" combos (see above)...act as perimeter light fixtures as well...meaning that the membrane tension plate may could be a child of a void "light" parent...or may could be a "stand alone" assembly etc etc.
These arrangements can be internal (belonging in, say, a x node within the current active file) or external (belonging in a y node within another file). If they deal with the same (topologically speaking) object they define clusters of Shared entities (or variations)- where only the view transformation matrix changes (in the simple scenario, he he). For instance the disk shown above is a Shared Assembly that owns the bolts, the plates, the tension member etc etc. Selective Instancing allows modifying some attributes without affecting the topology (i.e. the geometry).
The whole (terrible) mess is controlled by some tree like "dialog" (in Catia is "transparent") that is called Structure Browser. By controlled I mean (1) display/display mode with regard any tree member combo/selection set (assembly and/or component) in any View (2) clip state control (3) active status (for modifications/variations) (4) workplane control (5) drag and drop ownership control (6) ....
Now...what if I would chan…
this occasion, but it could be converted for DT in no time). Requires some minutes more as regards ... some things, but the usual update is due to some days.
Bad news: it's C#
Good news: User's Manual :
1. That thing (the C#, not me) after sorting (in a "sequential way", so tho speak) the panels (their order was chaotic) allows you to start the massacre by locating a focus of interest (and the user controllable +/- Range derived from it).2. The Range is variable (obviously) and takes care not to exceed the indices of the panel list (OK, that's elementary).
3. If you click the right button (Sadistic Q: where is it? he he) things are deleted and a new constantly self-updating list is your new List. Thus the massacre of panels is totally controllable. An autoZoom thing is also included (free of charge, but it's a bit nerve braking). Zoom factor is variable as well.
4. Then you move over (via the index slider) and start the massacre again. Notice the change of Range.
5. If you turn begin to false (initialization) and then begin to true > start all over again.
6. The other C# thing allows you to increment the index slider in a rather more convenient way. It's a bit weird: it uses delegates (A delegate is an object that knows how to call a method) and events (An event is a construct that exposes just the subset of delegate features required for the broadcaster/subscriber model - but don't ask what this means, he he) in order to talk with your slider (with a defined NickName) and perform the required value control.
NOTE: without realizing it you've just (indirectly) asked one of the most important questions even exposed in this Noble Forum. I hear you : what question? Well ... wait some days for the mother of all threads: "Total control in collections on a per Item basis"
may the Force (the dark option) be with you (and me)
best, Peter…
Rubicon (ii.e. some programming language [I would strongly recommend C#] > the Dark Side > years of pain + tears > hell or heaven?).
Back to that pile or worms of yours (I hate "simple" cases, he he).
0. if you want rounded lips ... Styrofoam is the only solution (+ sanding [buy a mask and some decent cigars ... path is long and hilly]). if not > goto 5/6.
1. by what means you think that you can shape Styrofoam? Do you have access to some CNC foam cutter? Or the only tools that you have are ... 2 hands and a knife? (or a thermal cutter). Accuracy is a BIG issue here: chances are that panels won't "fit". Solution is available in the forthcoming V3.
2. male "protrusions" on Styrofoam is kinda 3rd marriage > AVOID at any cost > this would end up in tears.
3. female ones are safe ... thus we need a proper "insert stripe" that must be compatible with the Styrofoam adhesive and strong enough to hold the pieces until the glue cures (it takes time, there's no instant Styrofoam adhesives around). Maybe aluminum (hard to cut by hand) or balsa (very expensive) or plywood (best option).
4. Some CNC foam cutters they can't shape the female "crevices" > be prepared (a thermal tool may(?) cut the mustard).
Note: panels made with Styrofoam look miserable because reality and theory differ. They also look miserable as well (and kitsch and miserable).
5. making the panels with (marine) plywood ... well this yields far superior accuracy and therefor aesthetics but (a) yields max panel thickness constrains, (b) introduces max panel dimensions constrains (c) yields packing issues [waste material] and (d) requires a totally different "connection" approach: it doesn't make sense to do some female crevice ... unless the plywood is very thick (expensive + heavy).
Note: Designing (pro option) self supporting "rib" reinforced sandwich composite panels ... well this is a bit far and away from what you can handle at present time.
So ... I've suspended the male/female thingy until you decide the final policy: it's the material/detailing that should dictate the method(s) AND the whole design and not the other way.
This is what we call bottom-top design approach (dinosaur Architects follow the top-bottom: disastrous + naive + naive + naive + avoid).
6. Plan ZZTop: make a stand alone autonomous perimeter frame per panel (marine plywood: imagine "thickening" these abstract beams shown inwards per panel) then join these frames by means of bolts (easy) and fill the "gaps" with Styrofoam (hmm). Note: you can reinforce the frames by a variety of means (say: a secondary "beam" sub-structure) achieving a rather elegant all overall solution.
This is the best solution by roughly 666 miles.
…
make-this-form-...
Other than that:
1. Tensegrity is a "static" thingy in the sense that you use some module (let's call it "mode") and repeat. Creating some code that does INVENT new modes for T trusses (Pulitzer/EMMY/Nobel on sight, he he) ... I would strongly suggest to forget that THIS VERY MOMENT.
2. Applying some T "mode" on something (see my examples in the above thread where I use surfaces for the T nodes) is another animal. If you intend to use Kangaroo to "relax" that something (NOT the T itself) well ... you can do it but has nothing to do with T.
3. The Kangaroo def provided is a "way" to test the "rigidity" of the T in use. It's a "post-processing" thing NOT a T solving thing.
4. I have a terrible feeling: are you saying that (a) without knowing a thing (or two) from C#, (b) without knowing K1/K2, (c) with a limited GH experience ... your goal is to write down from scratch a FEA ("Femap") thingy that ALSO does node "relaxation" ? If so ... well ... what about sky diving (without parachute) or that classic Russian roulette "game"?
PS: shown double tetra (classic) and XFrames (classic) T trusses applied in open and closed surfaces.
But of course these are abstract stupid "arrangements" utterly out of question in real-life: read CAREFULLY the discussion in the thread provided above AND also study the 3dPDF attached (with a system out of many available) in order to get the gist about what real-life means (Note: EVEN if no real-parts are used ... the node calculation is different from the abstract "star" connections pictured above - by "star" I mean that cables meet at a single point in space without any "offset" etc etc).
Moral: Seppuku
Plan Z: Skype ASAP
…
a machine that is light and very sturdy. I have taken my Macbook Pro all around the world, carry it with me every day, even dropped it a few times and its still totally fine. Its thin and light.
2) You get some actual support for your hardware even a few years down the line. My Macbook Pro is from 2012 and I can still walk in to any Apple Store and get help with it, which I have done many, many times in different places around the world - I never had to show a receipt or was charged any money for help. There is no PC/Laptop manufacturer in the world with anything close to that, because companies like Asus, Dell, etc. bring out dozens of new versions of laptops every year, so its much harder to service them after a few years.
3) This is the most important one, which usually people forget when they say that Macbooks are overpriced: Resale Value. If you have ever tried to sell an old PC/Laptop (I have a few times), you will know how little value they have even after just 2-3 years. Macbooks retain their value very well and even after 4 years you can still get 50% of your original price.
4) Of course you can install Windows on it and it runs perfectly. I have MacOS and Windows on it and both run absolutely fine. On the Windows side I have Rhino+GH, Maya and a few others. Having Windows is good, because some software still only runs on Windows (looking at you, 3DSMax!). Most other software also runs on MacOS. In the interest of sanity it is great to have an alternative to Windows for all the day to day stuff, like Mail, Calender, Photos, Presentations, etc. that just always works.
5) As for performance: Yes, Macbook Pros dont necessarily have the latest and greatest in graphics cards (the rest is on par with PC laptops), but unless you want to play games you will not need it. VRay RT can do GPU rendering, but you wont get great performance from a Notebook GPU anyways and it doesnt make sense to do rendering on a laptop (especially since you have a workstation). You could get one of the older Macbook Pro Retina Late 2013 or Mid 2014 models with the GTX750M by Nvidia, which will be usable to render using VRay RT, but of course not huge performance. Better to invest in a good used graphics card for your workstation like an Nvdia GTX980ti, which is the best value for money for GPU rendering right now (lots of used ones available).
So at least consider also getting a Macbook Pro. You can buy refurbished models (depending where you are) and they are like new, but a lot cheaper or even get an older one thats used. It will be a worthwile investment.
Take it from someone who has used dozens of PCs and Macs in my lifetime and have to do the IT support here at work (where we also use both).
I still have my Macbook Pro Retina from 2012 and its still running perfectly, super fast, and I can use Rhino and GH for huge files, do GPU Rendering with Octane Render and all sorts of other heavy computing stuff.
Hope that helps.…
Added by Armin Seltz at 11:12am on September 19, 2016
hat differ in shapes, sizes and height the facade would be a mess. Some spaces need some light while other can't have any. I would like to have full freedom of creation inside the building, to make it as functional as possible. Thats why i decided the parametric "skin" solution would be best. Since the location has industrial past (factories made of brick) i decided that brick would give interesting result.
I tried creating the definition on my own but since i lack skill in GH i got some problems (especially multiplication of bricks and the diffrence between each "level" (half a brick on y axis) caused problems for me.
I post my simple sketch explaining the idea of definition i would like to create (sorry about quality):
1 - Brep - I would like to use 25x12x6cm (classic brick) but as well experiment with diffrent shapes - like the one on the right with hole inside - that would give more light. Thats why i think the best solution would be using brep for this definition.
2- Multiplication - biggest problem for me - I don't know how tall the wall would be, what will be the final shape of Brep (brick) and that's why i would like to manipulate this with sliders as well. All the walls are flat (maybe it would be easier to use surface?). As i managed to multiply the bricks easy way i don't know how to gain control over height of the wall - for example that it is 30 bricks high, but has each second row moved on x axis by the distance of 1/2 brick. I tried using Series but with no success. Could you help me with that please?
3 - Rotation - i would like to use image sampler for that so i can "paint" where i want more sun and where i dont need it at all (black and white). The rotation has to be limited to 180 degrees as well. Obviously i didn't get here yet, but i never used image sampler so if you could give me some advice how to use component and how to create such images i would be really grateful.
4 - More of a concept thing - since the connection angles differ from 90 degrees i will have to figure out how to connect the parts of the wall at sides ;).
I would like to ask you for help with the defintion, since i am totally stuck at step 2. I post what i came up with so far. Thank you for your time and help!
PS. I post an image that is pretty similar to one of options i would like to check for my building.
…
phere with the maximum number of triangles but not much than a defined threshold.
I scaled that mesh just to fit Rhino grid, but it is not mandatory. What is useful, is to scale not uniformly the mesh (Scale NU). It could be done after cellular modifier applied or before or before and after. The 3 options are possible in the script. If you don’t need them just put 1 in scale sliders.
Ellipsoid mesh is the populated with points, I put 2 independents populations to randomize a bit further. For each vertices of the mesh the closest distance from the populated points is calculated.
Here is an illustration in color of this distance.
This distance is then used to calculate a bump. If domain for bump is beginning with negatives values to 0, it carves the mesh. Instead it bumps/inflates it.
Some images to illustrate the difference with populating 100 points with one or two populations.
Here some images to illustrate the application of scale before carving or after.
Next phase apply noise. At the moment I don't find it good.…
rce=activity
Basically, I want to create a workflow to automatically subdivide a building mass envelope geometry into different floors which will be further subdivided as perimeter zones and core zones.
But I encountered an error for a particular building mass geometry (a quite regular form) which doesn't work with the split building mass component (see item 4&5 below):
The workflow is:
1. import building mass geometry:
2. divide the building mass into floors (one zone per floor) using one of the two different methods depending on whether the floor surface has holes or not:
3. use the split building mass component to further divide the zone for each floor into perimeter zones and core zone:
4. I tested several building forms which work for this workflow as shown below, except for one form C05 which is a courtyard block with small tower blocks on top of it:
5. in the last step, there is an error from the split building mass component saying that "solution exception: index out of range: 0" ...
So, I wonder if this is error is related to the split building mass component or related to the way the building mass geometry is created.
Appreciate your kind advice!
Thank you!…
d simulate the bending process of a flat stell sheet in order to get the same shape. This can be really interesting so we can evaluate the material beheaviour, the deformation on the cross section a
nd explore big deformations in mecanics analysis of materials.
I am not a mecanical engineer nor a civil engineer, I´m an Architect and my interest is the construcction method and extracting the necesary information to consider fabricating the project.
I´m having conceptual challengings on the methodology for this simulation, so I will post a small overview of what I`ve done.
1.- Understanding the Geometry.
This is a sclupture by the Venezuelan/Hungarian/German artist Zoltan Kunckel (KuZo).
The shape is achieved bending a pre water cut square sheet of stainless steel. After bended manually, the different lashes are pulled on the opposite direction. New curvatures are produced after all is deployed.
2.- Reproducing the Shape digitally.
Using Karamba I built a definition to reproduce the produced by physical stress. This model served to find deformations that occur when a set of loads are applied to a mesh. Following this process will allow us to find a coherent and more natural cross section so then we could re-shape simulating the bending process of a piece of ductile material.
3.- Discretizing curve
Reducing the model to its simplest element is a key aspect of finite nonlinear analysis. Once our shape is already defined we can divide its principal characteristic of its principal given curve.
At this point I have already found the desired curve.
I Think the better strategy to simulate bending the steel sheet into this shape, is rationalize the curve and divide it finding the tangents one of the curve that compose this sort of parabola. bur i don`t know how to parametrize that in GH.
Please. If someone have a better Idea about this process I`ll glad to read sugestions.
Tomás Mena
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