4 ms·

A lot of the engineering math associated with splines (NURBs) and surface approximations came from Citroen, Peugeot and Renault, the car makers, in the mid-20th

A lot of the engineering math associated with splines (NURBs) and surface approximations came from Citroen, Peugeot and Renault, the car makers, in the mid-20th century. I read a great book on this back in the 80's and can't remember the name. It was about the early days of CAD and its origins. Like, the control points on splines were called "ducks", which were weights attached to spring steel suspended from the ceiling of the studio, which caused the steel to bend into particular shapes computed mathematically beforehand by the design engineers. These curves were used to guide model making. It was a fascinating book.

nwatson 5y ago
Gerald Farin has written many books, articles, publications on Computer-Aided Geometric Design (CAGD) stretching back a long way, here's a sample of books on Amazon: https://www.amazon.com/Books-Gerald-Farin/s?rh=n%3A283155%2Cp_27%3AGerald+Farin https://www.amazon.com/Books-Gerald-Farin/s?rh=n%3A283155%2C... ... had a stint at Mercedes-Benz (edit: Mercedes-Benz)
jacobolus 5y ago
The use of such splines comes earlier from boat building. The process looks like: https://www.youtube.com/watch?v=oKJagvumvCI https://www.youtube.com/watch?v=oKJagvumvCI
- SavantIdiot 5y ago
  I didn't know that; that's a great video, thanks! I'm crazy jealous of his workshop.
  - jorts 5y ago
    The whole series is great and he releases videos every two weeks. The shop in that video he was able to use thanks to a nice couple who own it. He's since had to move the boat as a neighbor complained about him and he's in the Port Townsend shipyard.
- dan-robertson 5y ago
  Historic boat-building has little to do with nurbs or Bézier curves. It is true that a boat is a curved shape (as were cars or aeroplanes before the mathematical models were devised) but the construction is quite different. To state the obvious, there are no control points. Instead you get some cross-sections for various different planes, then scale it up and manually try to achieve G2 continuity by comparing the points described in multiple places in the plan (ie in different cross sections from different but intersecting planes), adjusting them, and springing batons to create curved lines. You get different shapes depending on how thick/springy your baton is. Once more of the boat is built, the process continues with adjustments and baton-springing to try to ensure that curvature is continuous and it’s derivative is not too large. But these plans would traditionally be produced by starting with a scale model for half the boat (often this model would be scaled up straight into the boat without plans in between). And traditional boat building (say 100 years ago) would often not be particularly true to the plans anyway, treating them much more as a guide (a case where this matters more is some of the traditional steel shipbuilding in Scotland where the yards were too small so boats were built in two halves then perfectly joined together at the end). Now compare this to the OP which is about various mathematical models for curves and surfaces, and the comments above which talk about the history of those models. I think the automaker usage described above was about the problem of going from the computer-described curves to the real world and I guess CNC at the time couldn’t do it properly (you surely aren’t going to CNC-mill a car model out of a massive block of metal) hence transforming a computer description into something suitable for a physical model—fixed lengths of spring steel plus weights. Spring steel sounds a bit like springing batons but I think that is where the connection ends and I think this connection has little to do with the rest of this reply chain. Though to be honest I’m not particularly sad that you posted it.
  - jacobolus 5y ago
    Traditional boat builders obviously did not employ piecewise-rational parametric curves with off-curve control points. But they did use physical splines to draw smooth curves long before car/airplane designers.
    - yetihehe 5y ago
bmitc 5y ago
If you can remember the name of that book, I'd love to know it!
- nigel_bree 5y ago
  Not sure about the specific text the parent had in mind but "Principles of Interactive Computer Graphics" by Newman and Sproull (1979, but I bought it in '81 in the student edition and it influenced me a lot in my youth) made a bit of the connection with Renault in the chapter on Bezier Curves - many of its other examples of advanced graphics (at the time) were on flight simulators and such built by Evans and Sutherland, where the "Evans" was one of Alan Kay's mentors at the University of Utah.
  - Naracion 5y ago
    And "Sutherland" was Ivan Sutherland, who created Sketchpad in 1963, and is credited to have pioneered the field of CAD, 3D graphics in general, immersive media and the modern GUI.
agumonkey 5y ago
People should watch the UNISURF system used in those days https://www.youtube.com/watch?v=c0_a6r2JaWQ https://www.youtube.com/watch?v=c0_a6r2JaWQ they'd be surprised
twelvechairs 5y ago
To be specific on the history Paul De Casteljau worked it our first in 1959 while working at Citroen. Not long after in the early 60s Pierre Bézier worked out the same thing at Renault independently and Bézier curves are named in his honor. In computer software, bezier curves have always been common in 2d desktop publishing (fonts, adobe illustrator and its predecessors etc.) but 3d software had an ambivalent relationship where animation software (3DS-max etc.) always used them but games avoided them due to higher computation time than straight meshes, hence lower framerates. Of course this is changing now.
yig 5y ago
‪Paul de Casteljau described Bézier curves before Pierre Bézier, and in the modern form (a cage of control points). Bézier defined them later, as a point and offset vectors. de Casteljau's algorithm is still used. Bézier is dead. de Casteljau lives. He was recently granted a Bézier Award.‬ ‪Sources:‬ http://mae.engr.ucdavis.edu/~farouki/bernstein.pdf http://mae.engr.ucdavis.edu/~farouki/bernstein.pdf ‪Wikipedia‬

nwatson 5y ago

Gerald Farin has written many books, articles, publications on Computer-Aided Geometric Design (CAGD) stretching back a long way, here's a sample of books on Amazon: https://www.amazon.com/Books-Gerald-Farin/s?rh=n%3A283155%2Cp_27%3AGerald+Farin https://www.amazon.com/Books-Gerald-Farin/s?rh=n%3A283155%2C... ... had a stint at Mercedes-Benz (edit: Mercedes-Benz)

jacobolus 5y ago

The use of such splines comes earlier from boat building. The process looks like: https://www.youtube.com/watch?v=oKJagvumvCI https://www.youtube.com/watch?v=oKJagvumvCI

SavantIdiot 5y ago
I didn't know that; that's a great video, thanks! I'm crazy jealous of his workshop.
- jorts 5y ago
  The whole series is great and he releases videos every two weeks. The shop in that video he was able to use thanks to a nice couple who own it. He's since had to move the boat as a neighbor complained about him and he's in the Port Townsend shipyard.
dan-robertson 5y ago
Historic boat-building has little to do with nurbs or Bézier curves. It is true that a boat is a curved shape (as were cars or aeroplanes before the mathematical models were devised) but the construction is quite different. To state the obvious, there are no control points. Instead you get some cross-sections for various different planes, then scale it up and manually try to achieve G2 continuity by comparing the points described in multiple places in the plan (ie in different cross sections from different but intersecting planes), adjusting them, and springing batons to create curved lines. You get different shapes depending on how thick/springy your baton is. Once more of the boat is built, the process continues with adjustments and baton-springing to try to ensure that curvature is continuous and it’s derivative is not too large. But these plans would traditionally be produced by starting with a scale model for half the boat (often this model would be scaled up straight into the boat without plans in between). And traditional boat building (say 100 years ago) would often not be particularly true to the plans anyway, treating them much more as a guide (a case where this matters more is some of the traditional steel shipbuilding in Scotland where the yards were too small so boats were built in two halves then perfectly joined together at the end). Now compare this to the OP which is about various mathematical models for curves and surfaces, and the comments above which talk about the history of those models. I think the automaker usage described above was about the problem of going from the computer-described curves to the real world and I guess CNC at the time couldn’t do it properly (you surely aren’t going to CNC-mill a car model out of a massive block of metal) hence transforming a computer description into something suitable for a physical model—fixed lengths of spring steel plus weights. Spring steel sounds a bit like springing batons but I think that is where the connection ends and I think this connection has little to do with the rest of this reply chain. Though to be honest I’m not particularly sad that you posted it.
- jacobolus 5y ago
  Traditional boat builders obviously did not employ piecewise-rational parametric curves with off-curve control points. But they did use physical splines to draw smooth curves long before car/airplane designers.
  - yetihehe 5y ago

bmitc 5y ago

If you can remember the name of that book, I'd love to know it!

nigel_bree 5y ago
Not sure about the specific text the parent had in mind but "Principles of Interactive Computer Graphics" by Newman and Sproull (1979, but I bought it in '81 in the student edition and it influenced me a lot in my youth) made a bit of the connection with Renault in the chapter on Bezier Curves - many of its other examples of advanced graphics (at the time) were on flight simulators and such built by Evans and Sutherland, where the "Evans" was one of Alan Kay's mentors at the University of Utah.
- Naracion 5y ago
  And "Sutherland" was Ivan Sutherland, who created Sketchpad in 1963, and is credited to have pioneered the field of CAD, 3D graphics in general, immersive media and the modern GUI.

agumonkey 5y ago

People should watch the UNISURF system used in those days https://www.youtube.com/watch?v=c0_a6r2JaWQ https://www.youtube.com/watch?v=c0_a6r2JaWQ they'd be surprised

twelvechairs 5y ago

To be specific on the history Paul De Casteljau worked it our first in 1959 while working at Citroen. Not long after in the early 60s Pierre Bézier worked out the same thing at Renault independently and Bézier curves are named in his honor. In computer software, bezier curves have always been common in 2d desktop publishing (fonts, adobe illustrator and its predecessors etc.) but 3d software had an ambivalent relationship where animation software (3DS-max etc.) always used them but games avoided them due to higher computation time than straight meshes, hence lower framerates. Of course this is changing now.

yig 5y ago

‪Paul de Casteljau described Bézier curves before Pierre Bézier, and in the modern form (a cage of control points). Bézier defined them later, as a point and offset vectors. de Casteljau's algorithm is still used. Bézier is dead. de Casteljau lives. He was recently granted a Bézier Award.‬ ‪Sources:‬ http://mae.engr.ucdavis.edu/~farouki/bernstein.pdf http://mae.engr.ucdavis.edu/~farouki/bernstein.pdf ‪Wikipedia‬