The hyperboloid of one sheet is a fascinating shape that turns up in many places. It was therefore a great example to take for a test of thearender which I recently purchased. This shows off its double ruled nature:
CAMel
September 29, 2011CAMel is a project to develop Rhino Grasshopper components for CAM (Computer Aided Manufacturing). Hence the silly name. It is very much work in progress, but if you are brave enough, here is a first release. All images and the video on this page are of a machine running GCode generated by CAMel.
Download CAMel 0.12
Download Rhino file (only needed if you want to see the example setup).
At present the components are just clusters with scripted components written within Grasshopper. The next major step will be to convert this into a proper grasshopper plug-in. This release has a grasshopper component with some documentation (there is a little more inside the clusters). All the code is CC-BY-SA licensed, and of course it should be noted that this is very much “use at your own risk”! My belief is that Grasshopper provides a natural environment to experiment with creating your own toolpaths. The purpose of CAMel is to make this process as easy as possible by giving the tools to convert simple toolpath ideas into usable paths and then exporting the GCode that will drive a machine.
The main components are as follows:
- GCode Writer: Converts lists of points, vectors and feed rates into GCode for the machine.
- GCode Checker: Reads GCode and checks and optimises it. For example a 5-axis machine can usually obtain any tool angle in two different ways. This selects the better angle. It will also give warnings of undesirable behavior in the GCode.
- Surfacing: Creates a toolpath to cut an arbitrary surface (very rough version, designed to test others)
- Swarf cutting: Creates toolpath from information about the movement of the tip of the tool and the point in which the tool enters the surface. For a 5-axis machine these paths can be quite different.
The code is currently set up for a single machine, I am happy to try to help adapt it to other machines (other commitments allowing) so get in touch if you are interested.
These components and code were developed with Santiago R Perez 21st Century Chair of Integrated Practice at the Fay Jones School of Architecture, University of Arkansas. I work in the Mathematics Department at the same university.
How to write machines
November 18, 2009(If you are coming from Zeilberger’s opinions, the appropriate article is here)
Last weekend I was in Gothenburg at the incredibly inspiring Free Society conference FSCONS. Of course I was talking about mathematics, specifically how to get people learning it through fun, rather than “because it is useful”. My talk was called “Street Maths” (click for slides).
In discussions with many including Smári McCarthy and Marcin Jacubowski the idea developed further and one result is this (highly opinionated
manifesto for literacy.
In 1964 Paulo Freire was arrested and exiled from Brazil for teaching peasants to read. Both sides recognised the power of literacy, as a threat to oppression and a path towards a better life for individuals.
Today in the developed world we take it as an essential. Those who cannot read are not merely marginalised but kept out of society. Yet new skills are becoming necessary. Our formal interactions are now almost more likely to be through a computer than a pen. This change is sweeping through so fast that it can be hard to keep up. We have all joked that the kids teach the adults how to use the latest device.
Lets give the education system its due. The schools curriculum in the UK recognises that for Information and Computer technology (ICT):
…creative and productive use of ICT an essential skill for life.
How do they suggest we try to achieve this?
The study of ICT should include:
- use of a range of information, with different characteristics, structures and purposes, and evaluation of how it matches requirements and its fitness for purpose
- use of a variety of information sources, including large data sets, in a range of contexts
- use and review of the effectiveness of different ICT tools, including a range of software applications, in terms of meeting user needs and solving problems
- developing an understanding of the need to:
* employ safe working practices in order to minimise physical stress
* keep information secure
* manage information organisation, storage and access to secure content and enable efficient retrieval- the impact of ICT on individuals, communities and society, including the social, economic, legal and ethical implications of access to, and use of, ICT.
Think about these for a second as we consider the skill of literacy. It has two parts. Reading is of course important, but teaching people to read only allows one way communication. We also teach to write. We are taught to use written content, but also to create it. Think about this as you again read the list above. It only talks about learning to “use” ICT.
We need the skills to write and create as well as simply use. Firstly, for some a bright idea will result in a new use for computers. Just as for some the ability to write leads to a published book. For others some simple creations will help their lives or those close by them, just as some write diaries. Finally there are many who do not write much at all. Yet learning to write writing still helps us develop our reading. The same is true for technology, but it is even more essential. Reading is a fixed skill. A language develops too slowly for reading skills to need much change. This is not the case with computers. The skills to use a particular piece of software can change with a single upgrade, even when we are not forced to change to a more advanced competitor. The usage skills therefore can easily go out of date. The more fundamental skills teach not just the skills to create but the ability to learn; to adapt to rapid changes.
So what skills are needed to create technology? Programming is obviously first. There is, however, a lot more to technology than computers. There are a vast number of ways that gadgets can be used, and will be used. Should we leave people waiting for someone else to make something close enough to what they need? What about adding the basic skills to make things?
Unlike literacy and use of computers these are not new skills. They are in fact ancient. Not a very long time ago if you wanted something you either had to make it yourself, or go to someone who could make it for you. Then we had the industrial revolution. The economy of scale. We came to rely on factories. This now goes so deep we hardly think of making something ourselves. For truly mass items like a hammer or a car, we are probably right. What about a more specialised device though, like say a tractor? Or a 3d printing machine? Here plans are freely available that require some skill, but not expertise, to build. Including money for building time the product can be made for a fraction of the cost (in many cases 1/10 or less). Even better, with such open design comes a powerful new option. Take the generic solution and adapt it to your own situation. With time the design improves as individuals using it make refinements and add options. To do this takes a certain mindset and some basic skills. A literacy of making.
The natural response to this is that, on top of the skills, tools are required and those tools are themselves prohibitively expensive. Though this is true right now, it is changing. Movements such as FabLabs and Hacker spaces have the tools and make them available for free, or at a small cost. Even better, the machines can be part of the change. One of the machines above is a 3d printer, this is not just cheap to produce, it is capable of making itself. The development of other machines has begun, with the ambitious goal of creating a RepLab a multipurpose factory that can create itself at a cost of less than $10000. Even commercially the machines only cost about $100000. Things are changing. Fast. The question is can we get the people in place with the creativity and skills to take full advantage of them?
WoW 6: Gorgeous 4d graphics
May 6, 2009At some point I should write something about 4d polytopes. They are an incredible work of the human imagination. There are a few places you can find good information on them, just google them. Or go to the wikipedia page. If you do the latter you will find some wonderful images. You might wonder how they were made. I did, and was very happy for it. Some of them come from an open source application: jenn3d
The still images it produces are beautiful out of the box:

Bi-truncated 8-cell

Truncated 24-cell
The great thing is it is open source so you can go in and hack at it to make your own images, it also has a slightly unclear command line format to specify models.

Tetrahedra from truncated 120-cell
Maxwell Demon: Website of the week
I am handing out awards, the imaginatively titled “Maxwell’s Demon” website of the week:
There is even a prize, £50. Though I am lazy so the conditions of this are that the winner:
1) Realises they have won.
2) Contacts me.
3) Puts the logo on their site.
Of course 3 is hard to enforce so you could probably take the money and remove the graphical mess. I will therefore claim that 3 is to ensure that you are indeed the winner.

Posted by gelada 



