Re: [math-fun] (NFI) XGP/TeX dreams
Some ideas for high school math (these are pretty obvious & lame): * 3D plots, so students can actually feel the shapes. Yes, you can produce 3D color plots & manipulate them with 3D glasses using current high-end PC's, but sometimes kids like to see physical objects. * experiment with reflective properties of different shapes -- e.g., lenses, reflective mirrors (need to be polished), etc. * experiment with center of gravity, etc., of different shapes * experiment with brachistochrone-type curves * experiment with curves of constant width * experiment with interlocking gears of different shapes * experiment with boat/submarine hulls of different shapes being pulled through the water etc. Perhaps Mike's point also needing a laser scanner is quite important. But the XGP appeared before any decent digital cameras! If I were a kid who had to get a CAT scan, I'd love to "print out" a copy of one of my own bones. That would be very cool! --- I haven't studied CAD/CAM languages recently, but the ones from 10+ years ago were pretty uninspiring. Perhaps an artist/mathematician _without any "computer language" skills_ will show us how to do it better. We need some "direct manipulation" ideas for how to describe objects which are very different from the traditional computer language ideas. At 03:57 PM 8/18/2011, Fred lunnon wrote:
The phrase "3-D printer" is catchy, but misleading: printing in the sense of reproduction of text is essentially two-dimensional.
Even in 2-D, pictorial reproduction and creation is technically more complex, involving skills lying completely outside the domain of DTP; its 3-D equivalent --- sculpture --- captures better what these devices do.
One obvious area of application (for which they are apparently already regularly used) is simply rapid prototyping of CAD/CAM designs, for which appropriate solid-modelling languages are already highly developed, having been utilised for many years to build virtual models for viewing on-screen, or (imposing crucial limitations) solid milling.
Looking beyond old-hat industrial plotting, there seems to be no obvious reason why --- for example --- PostScript cannot be immediately generalised to 3-D, and used to drive a laser sintering prototyper.
The technology is anyway still in its infancy: just around the corner are surely devices which will mix materials (cf. colour printing vs. black-and-white) and apply surface finishes, as well as improving resolution.
It will have arrived when some bright postgrad programs one of these engines to reproduce itself. Now there's a prospect providing food for thought ... [Though if Mike's 3-D photocopier hits the streets first, maybe even the postgrad will be redundant.]
Fred Lunnon
On 8/18/11, Henry Baker <hbaker1@pipeline.com> wrote:
I don't recall the exact date that the XGP showed up at MIT's Project Mac, but I think it was the very early 1970's. The XGP was the first bitmapped XeroGraphic Printer, and it changed the course of printing history, including leading inevitably to the Apple Macintosh/desktop publishing industry and the now ubiquitous "multifunction printer/scanner/fax" that probably all of you have in your homes.
The coolest thing about the XGP is that it was available to (nearly) anyone at 545 Tech Square, and it immediately became a huge hit. Once the appropriate page layout languages and fonts became available, people twiddled with them incessantly, until their theses looked like ransom notes!
One of the important steps along the way was the development of Knuth's TeX, which subsequently became the standard for mathematical publishing -- where it remains today.
---
Fast forward to 2011. 3D printers exist, but don't appear to have generated the same excitement as the original XGP. I'm not sure quite why, because a 3D printer is sooo much cooler than the XGP ever was. Maybe these printers are too expensive; maybe they're too slow; maybe they're too hard to access.
What is missing that would make the 3D printer today as exciting as the XGP was in the early 1970's ?
Does Knuth (or a Knuth-wannabe) have to come up with 3D TeX ?
What do mathematicians want from a 3D printer, anyway ?
What would be the effect of putting a free 3D printer into 100 universities ? 1,000 universities ? 5,000 high schools ? 10,000 grade schools ? 50,000 libraries ?
(I have no connection with any 3D printer company, but think that it is a major revolution.)
On Aug 18, 2011, at 7:24 PM, Henry Baker wrote:
Perhaps Mike's point also needing a laser scanner is quite important. But the XGP appeared before any decent digital cameras!
Oh, but don't forget that we had Xerox COPIERS 10 years before the XGP. Where is my 3-D scanner/printer to make the copy of my sculpture. Or gear. Or face. And, although we had no decent digital cameras, we did have very high performance film readers and printers. When I first arrived at Project MAC, the Xerox copier was one of the most amazing things.
If I were a kid who had to get a CAT scan, I'd love to "print out" a copy of one of my own bones. That would be very cool!
--- I haven't studied CAD/CAM languages recently, but the ones from 10+ years ago were pretty uninspiring. Perhaps an artist/mathematician _without any "computer language" skills_ will show us how to do it better. We need some "direct manipulation" ideas for how to describe objects which are very different from the traditional computer language ideas.
Ok, perhaps a Microsoft Kinect/Xbox with the right software could make a passable model for a student's face (or hand, or ...), which could then be "printed" out on the printer. That would be a pretty cool start at getting the student excited. Then utilize existing "morphing" SW to make combination faces of 2 or more kids, or make monster masks for Halloween? At 04:40 PM 8/18/2011, Thomas Knight wrote:
On Aug 18, 2011, at 7:24 PM, Henry Baker wrote:
Perhaps Mike's point also needing a laser scanner is quite important. But the XGP appeared before any decent digital cameras!
Oh, but don't forget that we had Xerox COPIERS 10 years before the XGP. Where is my 3-D scanner/printer to make the copy of my sculpture. Or gear. Or face. And, although we had no decent digital cameras, we did have very high performance film readers and printers.
When I first arrived at Project MAC, the Xerox copier was one of the most amazing things.
If I were a kid who had to get a CAT scan, I'd love to "print out" a copy of one of my own bones. That would be very cool!
--- I haven't studied CAD/CAM languages recently, but the ones from 10+ years ago were pretty uninspiring. Perhaps an artist/mathematician _without any "computer language" skills_ will show us how to do it better. We need some "direct manipulation" ideas for how to describe objects which are very different from the traditional computer language ideas.
On 08/18/2011 07:51 PM, Henry Baker wrote:
Ok, perhaps a Microsoft Kinect/Xbox with the right software could make a passable model for a student's face (or hand, or ...), which could then be "printed" out on the printer. That would be a pretty cool start at getting the student excited. Then utilize existing "morphing" SW to make combination faces of 2 or more kids, or make monster masks for Halloween? http://boingboing.net/2011/06/09/mash-me-the-head-of.html
This reminds me of something I meant to mention earlier. In my early teens, I returned often to the Science Museum in South Kensington (London), where tucked away in an obscure gallery on an upper floor were a collection of decrepit plaster models of Archimedean polyhedra, their edges almost completely eroded by age and moisture. I eventually began painstakingly to design and build my own collection from cartridge paper, which with hindsight was a major step towards becoming a mathematician. The point of this is that there is --- in sufficiently geeky individuals at any rate --- a powerful intrinsic emotional response engendered by solid manifestations of symmetry --- and similar mechanisms --- which greatly exceeds that of flat representations, particularly where children are involved. Fred Lunnon [PS --- Henry, your reply address is malfunctioning again: when I hit "reply" this time (tho' not last time), my post was about to return only to you, rather than to math-fun!] On 8/19/11, Henry Baker <hbaker1@pipeline.com> wrote:
Some ideas for high school math (these are pretty obvious & lame):
* 3D plots, so students can actually feel the shapes. Yes, you can produce 3D color plots & manipulate them with 3D glasses using current high-end PC's, but sometimes kids like to see physical objects.
* experiment with reflective properties of different shapes -- e.g., lenses, reflective mirrors (need to be polished), etc.
* experiment with center of gravity, etc., of different shapes
* experiment with brachistochrone-type curves
* experiment with curves of constant width
* experiment with interlocking gears of different shapes
* experiment with boat/submarine hulls of different shapes being pulled through the water
etc.
Perhaps Mike's point also needing a laser scanner is quite important. But the XGP appeared before any decent digital cameras!
If I were a kid who had to get a CAT scan, I'd love to "print out" a copy of one of my own bones. That would be very cool!
--- I haven't studied CAD/CAM languages recently, but the ones from 10+ years ago were pretty uninspiring. Perhaps an artist/mathematician _without any "computer language" skills_ will show us how to do it better. We need some "direct manipulation" ideas for how to describe objects which are very different from the traditional computer language ideas.
At 03:57 PM 8/18/2011, Fred lunnon wrote:
The phrase "3-D printer" is catchy, but misleading: printing in the sense of reproduction of text is essentially two-dimensional.
Even in 2-D, pictorial reproduction and creation is technically more complex, involving skills lying completely outside the domain of DTP; its 3-D equivalent --- sculpture --- captures better what these devices do.
One obvious area of application (for which they are apparently already regularly used) is simply rapid prototyping of CAD/CAM designs, for which appropriate solid-modelling languages are already highly developed, having been utilised for many years to build virtual models for viewing on-screen, or (imposing crucial limitations) solid milling.
Looking beyond old-hat industrial plotting, there seems to be no obvious reason why --- for example --- PostScript cannot be immediately generalised to 3-D, and used to drive a laser sintering prototyper.
The technology is anyway still in its infancy: just around the corner are surely devices which will mix materials (cf. colour printing vs. black-and-white) and apply surface finishes, as well as improving resolution.
It will have arrived when some bright postgrad programs one of these engines to reproduce itself. Now there's a prospect providing food for thought ... [Though if Mike's 3-D photocopier hits the streets first, maybe even the postgrad will be redundant.]
Fred Lunnon
On 8/18/11, Henry Baker <hbaker1@pipeline.com> wrote:
I don't recall the exact date that the XGP showed up at MIT's Project Mac, but I think it was the very early 1970's. The XGP was the first bitmapped XeroGraphic Printer, and it changed the course of printing history, including leading inevitably to the Apple Macintosh/desktop publishing industry and the now ubiquitous "multifunction printer/scanner/fax" that probably all of you have in your homes.
The coolest thing about the XGP is that it was available to (nearly) anyone at 545 Tech Square, and it immediately became a huge hit. Once the appropriate page layout languages and fonts became available, people twiddled with them incessantly, until their theses looked like ransom notes!
One of the important steps along the way was the development of Knuth's TeX, which subsequently became the standard for mathematical publishing -- where it remains today.
---
Fast forward to 2011. 3D printers exist, but don't appear to have generated the same excitement as the original XGP. I'm not sure quite why, because a 3D printer is sooo much cooler than the XGP ever was. Maybe these printers are too expensive; maybe they're too slow; maybe they're too hard to access.
What is missing that would make the 3D printer today as exciting as the XGP was in the early 1970's ?
Does Knuth (or a Knuth-wannabe) have to come up with 3D TeX ?
What do mathematicians want from a 3D printer, anyway ?
What would be the effect of putting a free 3D printer into 100 universities ? 1,000 universities ? 5,000 high schools ? 10,000 grade schools ? 50,000 libraries ?
(I have no connection with any 3D printer company, but think that it is a major revolution.)
Just thought I'd mention that at the cheap end a "3D printer" in Kit form is now available for around £600 but it's only 3 colour (RGB plastic) and the res. is only 0.4mm. At the higher end of the scale check out Z-Corporation's Z650 (from a UK quote), "feature" res. 0.1mm: ********************* 1. New! ZPrinter 650® Colour 3D Printer £ 54,990 Superior colour and resolution, large format Includes. Delivery and Staff Training. 2. New! zp150 Consumable Starter Kit inc. 3.ZEdit Pro f.o.c. Spec: Machine specifications: Build volume (largest part size): approximately 10” x 15” x 8” (254mm x 381mm x 203mm) Equipment dimensions: approximately 74” W x 57” H x 29” (188 cm x 145 cm x 74 cm) Equipment weight (empty): 750 lbs. (340 kg) Control panel: 5 Lines / 20 Character LCD Display, Single control knob (move up, move down, select) High resolution! 600x540 dpi, for enhanced crispness of detail and surface finish. Print Heads: 5 Hewlett Packard c4810a (HP11) 10/100 Base T Ethernet Supported Recommended operating conditions: Temperature Maximum Range: 50°F to 85°F (10°C to 29°C) Recommended Range: 55°F to 80°F (13°C to 27°C) Humidity Maximum Range: 15% to 70% RH, non-condensing Recommended Range: 20% to 60% RH, non-condensing (may experience sub-optimal performance at extremes) Power Requirements at Site of Installation: ZPrinter 650: 200 – 240 VAC / 7.5 Amps / 50 Hz – 60 Hz ZPrint, ZEdit, and ZEdit Pro System Software Specifications: (One (1) seat included in base system) Z Corporation system software package provides interface between customer's CAD system and the ZPrinter 650 3D Printer. Software accepts solid models in a variety of file formats including STL, VRML, PLY, and 3DS. ZEdit Pro – Advanced File Preparation Software ($2500 value/seat) ********************* If going for accuracy/resolution rather than colour there was one (I think for over £200,000) being shown off at the Gadget Show event in Birmingham earlier this year - that was considerably higher in terms of "solid" resolution and could print a single object in varying colours but at the moment is restricted to around 10 grey-shades from black to white, plus transparent and a translucent yellow/amber. Of course the slight issue for general use of the Z650 is the following from the same quote as above: *************** ZScanner 700PX Hand Held 3D Laser Scanner, £ p.o.a. New! ZScanner 700CX Hand Held 3D Colour Laser Scanner, £ p.o.a. ZScanner 800 Hi-Res Hand Held 3D Laser Scanner, £ p.o.a. ****************
On 08/18/2011 07:24 PM, Henry Baker wrote:
... I haven't studied CAD/CAM languages recently, but the ones from 10+ years ago were pretty uninspiring. Perhaps an artist/mathematician _without any "computer language" skills_ will show us how to do it better. We need some "direct manipulation" ideas for how to describe objects which are very different from the traditional computer language ideas. It's worth making a strong distinction between CAD and CAM.
CAD languages based on Constructive Solid Geometry _do_ describe the shape of an object in fairly rigorous, tractable ways. But they say absolutely nothing about how to make the object. CAM languages such as G-code (http://en.wikipedia.org/wiki/G-code) describe how to make the object by moving a (subtractive) tool through space occupied by raw material. It's basically connect-the-dots, but with an eraser. Going from one to the other is roughly like compilation.
* experiment with center of gravity, etc., of different shapes
...
Most of these could be done with fairly low-resolution printers. The exception would be: * experiment with mono-monostatic solids, such as the Gömböc. It has a shape tolerance < 0.1 mm, so even the high-end commercially available printers are inadequate. Sincerely, Adam P. Goucher
participants (6)
-
Adam P. Goucher -
David Makin -
Fred lunnon -
Henry Baker -
John Aspinall -
Thomas Knight