Book written by Roger Burrows; reviewed by Ralph Grabowski


We are saturated in CAD, and so the close link between geometry and design is obvious to us. You can't have one without the other. Computeraided designing is based on vectors, and vector math is unabashedly geometric  even when we do not see vectors at work.
Vectors are mathematical constructs that define the distance and direction at the same time. Think of an arrow: its length specifies a value like a distance (two feet long); its direction specifies the angle (15 degrees, say). In CAD, all lines are vectors that start at A and point to B. A and B are each 3D coordinates, and doing the appropriate math on the coordinates will generate the length and angle of the line  information you typically see displayed by the CAD program's Properties palette.
But math involving vectors is hard. It involves manipulating 3x3 or 4x4 or even larger matrices. (See figure 1.) While matrices are handy for dealing with 3D entities, they are something we humans struggle to calculate by hand, primarily because it is tedious  I know: I just managed to pass vector math in first year of university. If you're wondering what it's like, think back to doing long division in elementary school.
Figure 1: A set of standard of 3x3 transformation matrices; 3D transformations need 4x4 matrices (image source alanzucconi.com)
Nearly no handheld calculator handles matrices, because they take up too much room in the limited memory (although I did at one time own a TI58 that boasted it).
Computers, on the other hand, excel at matrix manipulations, because they are perfect at any task that is repetitive. Furthermore, matrices provide a trivial solution in dealing with 3D environments, and even ones with more than three dimensions. When we rotate an entire 3D model or change the surface topology, an unimaginable number of matrix transformation calculations take place in the time of an eyeblink, as detailed by Nikolay Golovanov (see figure 2).
Figure 2: Matrices used to define surfaces for a CAD geometric kernel
(Nikolay Golovanov's Geometric Modeling contains everything you need to write your own geometric modeler: amazon.com/GeometricModelingmathematicsNikolayGolovanov/dp/1497473195)
Starting Somewhere
Before we arrived at the math of matrices, we needed to start somewhere else. The earliest geometric shapes involved no math, because math had not yet been discovered. Spiral shapes were carved into a rock in Ireland, perhaps in 3,200BC. In South Africa, intersecting lines that delineated diamond shapes are thought to have been carved in 70,000BC. We don't know why someone carved them, but anthropologists are always standing by with a "the lines marked the changing seasons, or were some form of commerce" explanation. I figure they are the result of a bored kid who in today's would have become an industrial designer.
Math did not automatically involve geometry. The cumbersome Roman number system of I, V, X, L, C, and M (but no 0) could barely do arithmetic, never mind trigonometry. Try, for example subtracting today's year from another year: MMXIX  MCMLVI  LXIII
The reason it's hard is because the Romans never figured out placeholders; their math is strung together like words. Placeholders are what indicate ones (at the right end), tens, hundreds, and so on in neat columns. 2019  1956  63
Geometry without Math
Those of us who practiced drafting  before computers  became proficient in geometry without math. We practiced what I imagine the Greeks did in ancient times, using compasses, Tsquares, and triangles (see figure 3). Ships hulls and aircraft skins sculpted by hand on massive sheets of paper using ducks to hold lofting curves in place.
Figure 3: Manual drafting techniques (image source 'Technical Drawing')
It is remarkable what is possible to design without computations. Even critical structures like bolts holding together aircraft frames were designed without calculations: structural engineers looked up strength tables. Sure, someone had calculated (by hand) all those strength parameters, but once calculated they never needed to be calculated ever again. I still have my engineering texts for pavement design, hydraulics, and structural steel.
Figure 4: Strength tables (image source 'Limit State Design')
And so we go back to ancient Celtic times when the bored teenage scratched spirals into a flat rock, or an architect from the middle ages who spent decades on making a neogothic church look just right  all without computers
3D Thinking in Design and Architecture
Roger Burrows records millennia of designs in his book from last year, 3D Thinking in Architecture: From Antiquity to the Future. This is not a book you sit down to read. It is a reference book, even one suitable for the coffee table.
Figure 5: Spread from the book
His meticulous sketches (very impressive!) and photography records designs since 70,000BC, with a tip of the hat to the spiral designs displayed by galaxies. (See figure 5.) Although there is "3D" in the title, the subject does not come up until half way through, in Chapter 8, The Renaissance. Most of the book concerns itself with how patterns were developed  by hand, without computers. And not just in Western lands, but also of the Inca, Arabs, and Egyptians. By the last chapter, "The Future of Geometry," we start to see ugly designs made possible by algorithms, as well as impossible ones.
I feel that the best use of this book is for inspiration.
3D Thinking in Architecture: From Antiquity to the Future by Roger Burrows $60 328 pages; hardcover Published by Thames & Hudson, 2018 ISBN13 9780500519547 

  
Bricsys 24/7 Common Data Environment (CDE) and @BricsCAD BIM has been accepted for use by the Hong Kong Development Bureau.
  
Nemetschek Group's Solibri division launches a new product family  Anywhere, Site, Office and Enterprise  for viewing, checking, classification, quantity take off, procurement, project management. "A complete workflow solution to ensures that you build correctly first time, every time."
  
  
Siemens Q2 revenues are up 2% to $23.4 billion YoY [year over year]. but their net profit was down 5%. Last year, Siemens spun off its medical technology business, Healthineers, and the next spinoff will be the Gas & Power division, representing 1/3 of its revenues. The company has 380,000 employees.
  
Hexagon is benefiting from exchange rates, as its net sales increased 10% to e916.5 (US$1 billion) in Q1 from a year ago. (Without the exchange rate boost, sales would have gone up 4%.) The Hexagon PPM division, which includes Intergraph and Bricsys, recorded 7% organic growth, excluding the exchange rate benefit. ("Organic growth" means a revenue increase excluding acquisitions.) The Safety & Infrastructure division dragged down results, with sales falling 17%.investors.hexagon.com/en/financialinformation/reportsandpresentations?page=/en/interimreportq12019
  
MachineWorks expands Polygonica's 3D polygon modeling with a new Anisotropic Offsetting function: offset solids in different directions. See how it works at youtube.com/watch?v=MQi7UJVl63A
  


The ITC was awarded the money judgment it asked for by a United States Federal Court. The audit still needs to be conducted, so the legal dispute remains active.  Shawn Lindsay Harris Berne Christensen LLP
Ah, yes, to receive my monthly copy of Computer Graphics World and flip to my favorite column, "Ask Mr. Protocol." I also remember moving offices back around Y2K and taking the pleasure of sifting through the decadelong accumulation of CAD related journals.
I especially liked the crystal ball prognostications...one in particular was the coming obsolescence of monitors on our computers. Instead, we were to have 3D holograms of our CAD models floating above our desktops, as if malleable by hand. That was to happen five years from the date of publication. Sadly, the article is now ten years old.
I'll not even share what I spent to piece together my first PC, let alone continuously update or replace it. This thought always amuses me: For years people would remark that they haven't used one for years, but to this day, the Floppy Disk icon is a universal "Save" symbol even now to a generation who has never even seen one. How does that work?
Thanks for the memories.  Sam Hochberg (via WorldCAD Access)
The editor replies:
Re: Readers Respond: Dassault vs Solidworks
So, what are the odds that you will get invited back to Solidworks World next year?  Bill Fane
The editor replies: Solidworks hasn't invited me there since 2011. I wonder it was something that I said?
  
There seems to be a lot of confusion about what Dassault Systèmes has planned for SOLIDWORKS. Let’s try and clear things up a little. 3DEXPERIENCE and the renaming of SOLIDWORKS World to 3DEXPERIENCE World has nothing to do with trying to replace SOLIDWORKS with CATIA or other 3DEPERIENCE products. Dassault Systems is looking for ways to offer SOLIDWORKS users additional tools and technology that compliment SOLIDWORKS, not replace it.
The new 3DEXPERIENCE products are an attempt to bridge the gap between powerful Dassault Systèmes products like CATIA and SIMULIA, which run on the CGM kernel, and the more mainstream SOLIDWORKS products running on the Parasolid kernel. Dassault Systèmes is attempting to find a way to take these powerful 3DEXPERIENCE technologies and provide the same easeofuse that SOLIDWORKS is well known for. This is perhaps best exemplified by the new SIMULIA Structural Simulation Engineer software. This cloudbased FEA software was created to extend the capabilities of SOLIDWORKS Simulation, not replace SOLIDWORKS Simulation.  Sam Scholes, senior account manager SOLIDWORKS solutions GoEngineer
  
If AutoCAD costs $2,500 (in Canada) per year to rent and money is worth 2.5%, then this represents a perpetuity value of $2500/0.025 = $100,000. Is the software really worth this? And, that's AutoCAD without training, too.  Dik Coates
The editor replies: It's a lot of money for not much in return each year from Autodesk. I am glad I do not depend on AutoCAD for my livelihood; if I did, I would be finding an alternative.
  
You wrote, "I also wonder about subscription churn, where gains from new subscribers are offset by losses from unsubscribers."
Perhaps the more accurate question is how low must architect/developer/coder costs be so that subscriptionchurn concerns are minimal?
 In 1914, if you could fix a horseless carriage, you were a god!
 By 1948, you were a greasemonkey.
 Greg Hruby
The editor replies: And now, back to god. My male neighbours watch in amazement as I do basic repairs on cars that I and my kids own; it ain't that hard!
  
Just noted that you've reached 1,000 ezine issues. Congratulations! I never missed your emails since 2016 when I initially subscribed. I consider your resource as one of the main sources of CAD related news. Thank you for your work and have a nice day!  Ramil Gasanov, senior technical marketing engineer cadexchanger.com, Russia
  
Just so you know, yours is probably the only newsletter I would ever pay for, even though half the time it just makes me angry the way the MCAD software companies treat the end users.
I used a couple of your books back in the old days to learn MicroStation and AutoCAD. This is way back in the old days, like the 80s. Keep that great information coming.  Christopher R. Emerson, senior standards specialist NiSource, USA 

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"Everything we do has a moral dimension, and we need to accept and engage with it. It's hard in security, because every tool we build has a dual use, and can do bad things in the wrong hands. We aren't responsible for every single use, but we are responsible for the world we create with our technologies."  Bruce Schneier theregister.co.uk/2019/03/07/policy_technology_schneier/ 



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