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
his comes in the form of an HTML page with links to every component, so you will need to view it in your web browser. (I use Chrome and it doesn't seem to be working correctly, but when opened in IE its fine.)
2) Included in each help topic for each component is the Inputs and Outputs descriptions and data types.
3) You supply the data. What you supply and how you supply it is for you to decide. There are umpteen different ways. Are you asking for a list of those ways for each input?
4) Points can either be Rhino objects or 3D co-ordinates. To create a point you can use any of these methods, but it mostly comes down to user preference. I like using Panels as this displays outside of the component.
5) Because of the nature of vectors they represent magnitude and direction but they don't have an independent location, so there is a component that will display vectors in Rhino.
6) The user.
7) There is a Primer on the front page. Here you find the Basics, but because GH is ever evolving in its current beta state you might find things that aren't relevant any more or simply don't work the same. And here is the reason why nobody is writing an update because it could be soon out of date.
8) Importing images by either dragging them from explorer onto the canvas or right click context menu Image...
9) Single line = Single Item of Data. Double line = Multiple items of data on the same Branch. Dashed Double Line = Multiple Data on Multiple Branches.
10) User preference
11) Toolbar management is probably the bane of David's life. Most things are logically placed. For example the Curve Tab, Primitives are any simple curve types that you are creating from scratch. Similarly Splines is for more complex curve types created from scratch. Analysis is where you find components that are finding answers supplied by curves, control points, curvature, parameters, end points etc. Division is a subset of this category but has a group of its own. And Utilities is where you find curve related actions that you want to perform, offsetting, rebuilding projecting, exploding etc.
12) I would image it would have been the Point On Curve component in Curve>Analysis. Why that group? You are not putting a point on a curve you are analysing a curve for the location of a point based on some parameters that you are supplying. For example "what is the mid point?"
I hope this goes some way towards answering you questions. No doubt this will have generated more so don't be afraid to ask, it took me several releases of Explicit History (aka Grasshopper) before I realised what the egg did, it never occurred to me that I could put my objects into Rhino when I was finished. Or the fact that I could use panels to 'see' data outputs.
Al the best,
Danny…
Added by Danny Boyes at 3:48am on December 9, 2010
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.
…
he "return" is comment out as shown below?
After restarting Rhino and Grasshopper, I opened the outdoors_airflow demo file, and the first step of creating the case file is ok:
Then the blockMesh component gives the following error: seems I have to manually start OF first..
so, as the error message suggested, I open OF by Start_OF.bat:
Then come back to the blockMesh component, now it can be executed while the OF command line window is also openning:
... and the blockMesh finished successfully:
... so I proceeded to run snappyHexMesh, checkMesh and update fvScheme:
... up to the simpleFoam component, I got the error again:
The warning message is:
1. Solution exception: --> OpenFOAM command Failed!#0 Foam::error::printStack(Foam::Ostream&) in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #1 Foam::sigFpe::sigHandler(int) in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #2 ? in "/lib64/libc.so.6" #3 double Foam::sumProd<double>(Foam::UList<double> const&, Foam::UList<double> const&) in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #4 Foam::PCG::solve(Foam::Field<double>&, Foam::Field<double> const&, unsigned char) const in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #5 Foam::GAMGSolver::solveCoarsestLevel(Foam::Field<double>&, Foam::Field<double> const&) const in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #6 Foam::GAMGSolver::Vcycle(Foam::PtrList<Foam::lduMatrix::smoother> const&, Foam::Field<double>&, Foam::Field<double> const&, Foam::Field<double>&, Foam::Field<double>&, Foam::Field<double>&, Foam::Field<double>&, Foam::Field<double>&, Foam::PtrList<Foam::Field<double> >&, Foam::PtrList<Foam::Field<double> >&, unsigned char) const in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #7 Foam::GAMGSolver::solve(Foam::Field<double>&, Foam::Field<double> const&, unsigned char) const in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libOpenFOAM.so" #8 Foam::fvMatrix<double>::solveSegregated(Foam::dictionary const&) in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/lib/libfiniteVolume.so" #9 Foam::fvMatrix<double>::solve(Foam::dictionary const&) in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/bin/simpleFoam" #10 Foam::fvMatrix<double>::solve() in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/bin/simpleFoam" #11 ? in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/bin/simpleFoam" #12 __libc_start_main in "/lib64/libc.so.6" #13 ? in "/opt/OpenFOAM/OpenFOAM-v1606+/platforms/linux64GccDPInt32Opt/bin/simpleFoam"
... and the command lines in the readMe! output are pretty long and it is saved in the text file attached here.
So, my questions are:
1. why I have to manually start OF first before I can use the blockMesh component? Should butterfly automatically start OF?
2. what might be the cause of the unsuccessful run of simpleFoam in the end?
Hope you can kindly advise! Thank you!
- Ji
…
your fully glazed building). Once a person looks away from the glazed building, they no longer experience glare. If you know the view that someone will have looking at your building, Honeybee has a large number of tools that will give you real and reliable numbers for glare.
I know that you are planning to use a different method here but I point out the above just to be clear that you are not necessarily sure that people will experience glare if you are just looking at the times of the year when direct sun will be bouncing off of the glass building onto another building. However, I can see this as a good starting point to assess the hours where there is a risk of glare in the building where light is being bounced to.
With that preamble out of the way, I can say that you are using a version of Ladybug that is 6 months old and I have updated your file for you. To update your components and to be sure that the file below works correctly, you should re-download the user objects from the main Ladybug page and drag them onto your canvas.
If you want to look at sunrays for a whole year, I would keep your number of test points low by increasing your grid size (I think 5 should suit your purposes). Also, you should only set the number of bounces to 1 as you are only really concerned about the one bounce off of the glass building. With these two things done, you can then hook up an analysis period and have it do bounces for every sun-up hour of the period an not take for ever to calculate on your machine. Perhaps an easier way to do this would be to take a sun-up hour for every month instead of a full analysis period, as I have done in your attached file.
Finally, you need to make the last bounce length long enough to intersect the neighboring building (I increased it to 15 meters). Then you can use the native grasshopper components to count the number of intersections.
You can see this all in this file:
https://www.dropbox.com/s/poe7i1zwut2fjg6/Glarescript19sept_CWM.gh?dl=0…