# A Primer On Computational Geometry – Part Two

Oscar Gordon

A Navy Turbine Tech who learned to spin wrenches on old cars, Oscar has since been trained as an Engineer & Software Developer & now writes tools for other engineers. When not in his shop or at work, he can be found spending time with his family, gardening, hiking, kayaking, gaming, or whatever strikes his fancy & fits in the budget.

### 16 Responses

1. Road Scholar says:

I sorta hate to do this for your first comment here, but…

What is a square except two right triangles with a common hypotenuse? Or four equilateral triangles with points and edges in common?

That second sentence is wrong. You can’t build a square out of equilateral triangles. You can build a regular hexagon out of six of them. You can build a square out of either 2 or 4 right triangles.

Now that I’ve satisfied my inner pedant please carry on. I’m finding this series interesting.Report

• Oscar Gordon in reply to Road Scholar says:

Crap, you are right. You can build a square from 4 isosceles triangles.Report

2. Freeman says:

Fascinating stuff! I regularly do a fair amount of computational geometry in my metrology work, mostly based on the geometry of circles to compute phase angles, etc., but it’s been a long time since I’ve done anything with 3-D graphic visualizations. It’s great to see the techniques broken down into their simplest components like this. On the whole it would seem to be a huge and mind-bendingly complex task to model something like your spiral example, but you’ve shown how in reality it’s just a large collection of very simple tasks glued together with simple rules!Report

• Oscar Gordon in reply to Freeman says:

Just wait, this all goes out the window when you things get curvy.Report

3. Kolohe says:

(the 0.02 extra is rounding error).

And if you build another program that gathers all those rounding errors together….Report

4. Mike Schilling says:

punched onto computer cards and hand fed, one by one, into a computer

More pedantry. Even in the bad old days, a card reader could read a stack of cards from its hopper.Report

• Oscar Gordon in reply to Mike Schilling says:

According to my dynamics prof, when he was an intern at NASA, they were hand fed.

Granted, he also walked to NASA, barefoot, through the snow, uphill, both ways, but that’s the story he told and I’m sticking to it!Report

• Leaving aside the possibility of a one-off DIY sort of thing, I’m with Schilling. Hollerith invented a practical mechanical feeder in the 1890s; all of the interesting things done with cards, certainly from the 1920s on, were interesting because of fast auto feeding; all of the early UNIVAC and IBM computers came with high speed card readers.

People do card-at-a-time readers these days, typically for the purpose of recovering data from some sort of antique card deck. The usual approach is to put the cards on a contrasting background one at a time, take a picture of it, warp the picture into a standard shape, then read off the position of the punched holes.Report

• Oscar Gordon in reply to Mike Schilling says:

@mike-schilling

PS I was hoping you’d be reading this series.Report

5. George Turner says:

If triangles were important we’d have a standard English word for them, something akin to “ball”, “cube”, “star”, “block”, “point”, “line”, “square”. But we don’t – because triangles aren’t important. We could get along just fine using half rectangles for all our triangular needs.Report

• Mike Schilling in reply to George Turner says:

No when it was important to be acute. Or obtuse.Report

• Oscar Gordon in reply to George Turner says:

Wedge, pyramid, delta

ETA: The importance is even more profound once you factor in trig functions. If you don’t have a protractor and you need to know the angle formed by two straight lines, you’d better understand triangles.

Also, 3 of the 4 ‘squares’ I have in my tool box at home are triangles.Report

6. Kimmi says:

Be interested to know what operations GPUs are optimized around. (When you get to it…)Report