hermann on Mon, 11 Dec 2023 22:37:30 +0100 |
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Re: norml2() with variables in vector? | GP->OpenSCAD |
On 2023-12-08 17:43, Bill Allombert wrote:
Ah yes, qfminim only return the solution with positive first coordinates.If you want the others, just negate the result: M=v~*v;S=[x|x<-Vec(qfminim(M,101)[3]),qfeval(M,x)==101]; concat(S,-S) Cheers, Bill.
Thanks, good to know that just negation gives the others. I wanted to visualize the 3-dimensional coordinates, and remembered that I did that often with OpenSCAD in the past. While "a picture says more than 1000 words", for 3D being able to translate, rotate and zoom is the equivalent. Below openscad_demo.gp adds to the short code sofar. In order to enable a view without installing openscad, I did screen recording with peek. With sos=0 the vectors before mapping with matrix v are displayed. All points are on a plane, the blue dots are with qfeval=101, the other dots with qfeval<101. Interesting structure: https://stamm-wilbrandt.de/images/Peek_2023-12-11_22-24.gif With sos=1 (sum of squares) the sum of 3 squares are displayed, which are on sphere with radius 101: https://stamm-wilbrandt.de/images/Peek_2023-12-11_22-21.gif pi@raspberrypi5:~ $ cat openscad_demo.gp \\ PARI/GP->openscad demo \\ sos=1 displays sum of 3 squares sphere, sos=0 the pre mapping plane \\ \\ Try: sos=1 gp -q < openscad_demo.gp > gp.scad \\ sph(coord)=print("translate(",coord,") sphere(0.4);"); col(name)=print("color(\"",name,"\",1.0)"); v=[-102, -107, 93; 22, 23, -20; 1, 1, -1]~; M=v~*v; S=[x|x<-Vec(qfminim(M,101)[3]),qfeval(M,x)==101]; S2=[x|x<-Vec(qfminim(M,101)[3]),qfeval(M,x)<101]; { print("$fn=20;"); if(!eval(getenv("sos")), foreach(S,s,col("blue");sph(s~)); foreach(S2,s,sph(s~)) , foreach(S,s, if(vecsearch(abs(s),4),col("black")); sph((v*s)~))) } pi@raspberrypi5:~ $ Regards, Hermann.