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It's great to see all this straightedge and compass stuff turned into a game, and I absolutely applaud the developers for launching it. The above math, plus so
by delhanty 10y ago
It's great to see all this straightedge and compass stuff turned into a game, and I absolutely applaud the developers for launching it.
The above math, plus some graph theory (biconnected components etc.) is what drove D-Cubed's DCM 2D component dated, which powered the sketcher portion of many parametric MCAD systems after D-Cubed's launch by John Owen in 1989. See his paper "Algebraic Solution for Geometry from Dimensional Constraints" referenced on the Siemens PLM site:
https://www.plm.automation.siemens.com/en_us/products/open/d-cubed/references.shtml https://www.plm.automation.siemens.com/en_us/products/open/d...
The original parametric CAD system, PTC's Pro Engineer (now Creo) predates that (1987) and had it's own numeric (Newton-Raphson) solver. John Owen's innovation of using Galois Theory combined with Graph Theory to solve straightedge and compass configurations was a significant technical advance at the time, and the DCM 2D component ended up powering most sketchers in the industry.
Disclaimer: I worked at D-Cubed 1995-2000.
- fsloth 10y agoCool! I've never seen a practical example using Galois theory before. 10 years of computer graphics experience, but very little maths beyond my physics degree...