Hi all together I believe, that openscad can YET already rotate an object around an arbitrary axis! for(angle=[0,120,240]) { rotate(v=[1,1,1],a=angle) cylinder(r=1,h=10); } this turns an cylinder showing up into 3 different directions showing up, front, and right. i can imagine this like rotating an object around a cube's corner [image: image.png] code for that is already present in src/core/Transform.cc On Fri, Mar 24, 2023 at 10:24 PM Kevin Toppenberg <kdtop3@gmail.com> wrote: > The math is too dense for me to pick apart, but it seems that when I > worked on this in a different engine, that the math involves quaternions. > > Does this solution use quaternions? > > Kevin > > On Wed, Mar 22, 2023 at 10:45 PM Sanjeev Prabhakar < > sprabhakar2006@gmail.com> wrote: > >> I would propose if a module can be developed to rotate an object around >> an axis. >> >> e.g. for any sequence of rotations an equivalent axis and angle can be >> found from the functions written below >> >> function cvar(a)= >> let( >> text=a[0], >> >> b=search("-",a)!=[]&&search(".",a)!=[]?[for(i=[2:len(a)-1])if(a[i]!=".")a[i]]: >> search("-",a)!=[]&&search(".",a)==[]?[for(i=[2:len(a)-1])a[i]]: >> >> search("-",a)==[]&&search(".",a)!=[]?[for(i=[1:len(a)-1])if(a[i]!=".")a[i]]:[for(i=[1:len(a)-1])a[i]], >> n=[["0"],["1"],["2"],["3"],["4"],["5"],["6"],["7"],["8"],["9"]], >> l=len(b), >> c=[for(i=[0:l-1])each search(b[i],n)], >> d=[for(i=[0:len(c)-1])10^(l-i-1)], >> e=c*d, >> >> f=search(".",a)!=[]&&search("-",a)!=[]?e*10^-(l-(search(".",a)[0]-2)):search(".",a)!=[]&&search("-",a)==[]?e*10^-(l-(search(".",a)[0]-1)):e, >> g=search("-",a)!=[]?f*-1:f >> )[text,g]; >> >> //function to rotate a point around a vector(axis) with angle theta >> >> function q(vector=[1,0,0],point=[0,5,0],theta=0)= >> >> let(t=theta, >> v=vector/norm(vector), >> p=[cos(t/2),v*sin(t/2)], >> p1=[p.x,-p.y], >> q=[0,len(point)==2?[point.x,point.y,0]:point], >> pq=[p.x*q.x-p.y*q.y,p.x*q.y+p.y*q.x+cross(p.y,q.y)], >> pqp1=[pq.x*p1.x-pq.y*p1.y,pq.x*p1.y+pq.y*p1.x+cross(pq.y,p1.y)], >> transformation=pqp1.y >> ) >> >> transformation >> ; >> // function is input to another function q_rot >> function qmr1(s,r,pl,n=0)= n==len(s)?pl: >> qmr1(s,r, >> let( >> v1=s[n]=="x"?[1,0,0]:s[n]=="y"?[0,1,0]:[0,0,1], >> r1=r[n]==undef?0:r[n]) >> [for(p=pl)q(v1,p,r1)],n+1); >> //function is input to another function q_rot >> function qmr2(s,r,pl,n=0)= n==len(s)?pl:qmr2(s,r,let( >> v1=s[n]=="x"?[1,0,0]:s[n]=="y"?[0,1,0]:[0,0,1], >> r1=r[n]==undef?0:r[n]) >> [for(i=[0:len(pl)-1])[for(p=pl[i])q(v1,p,r1)]],n+1); >> >> //function to rotate a group of points "pl" around a series of axis with >> defined angles e.g q_rot(s=["z20","x40","y80"],pl=[[2,0],[10,2]])=> will >> rotate the line first around z axis by 20 deg then around x axis by 40 >> degrees and then around y axis by 80 degrees. >> function q_rot(s,pl)= >> is_num(pl[0][0])?qmr1([for(p=s)cvar(p)[0]],[for(p=s)cvar(p)[1]],pl):qmr2([for(p=s)cvar(p)[0]],[for(p=s)cvar(p)[1]],pl); >> >> // sequence of rotation defined by r1 >> r1=["x30","y40","z100"]; >> vz=[0,0,1]; >> v1=q_rot(r1,[vz])[0]; >> >> v2=cross(vz,v1); >> theta=acos(vz*v1/norm(v1)); >> >> // equivalent rotation axis and angle of rotation w.r.t vector vz >> echo(v2,theta); >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Wow! I have been using OpenSCAD for a few years now, and didn't realize this other way using Rotate. Here is some documentation for it: https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Transformations#rotate Thanks all! KT On Sun, Mar 26, 2023 at 7:59 AM Guenther Sohler <guenther.sohler@gmail.com> wrote: > Hi all together > > I believe, that openscad can YET already rotate an object around an > arbitrary axis! > > for(angle=[0,120,240]) > { > rotate(v=[1,1,1],a=angle) > cylinder(r=1,h=10); > } > > this turns an cylinder showing up into 3 different directions showing up, > front, and right. > i can imagine this like rotating an object around a cube's corner > > [image: image.png] > > > code for that is already present in src/core/Transform.cc > > > > > > On Fri, Mar 24, 2023 at 10:24 PM Kevin Toppenberg <kdtop3@gmail.com> > wrote: > >> The math is too dense for me to pick apart, but it seems that when I >> worked on this in a different engine, that the math involves quaternions. >> >> Does this solution use quaternions? >> >> Kevin >> >> On Wed, Mar 22, 2023 at 10:45 PM Sanjeev Prabhakar < >> sprabhakar2006@gmail.com> wrote: >> >>> I would propose if a module can be developed to rotate an object around >>> an axis. >>> >>> e.g. for any sequence of rotations an equivalent axis and angle can be >>> found from the functions written below >>> >>> function cvar(a)= >>> let( >>> text=a[0], >>> >>> b=search("-",a)!=[]&&search(".",a)!=[]?[for(i=[2:len(a)-1])if(a[i]!=".")a[i]]: >>> search("-",a)!=[]&&search(".",a)==[]?[for(i=[2:len(a)-1])a[i]]: >>> >>> search("-",a)==[]&&search(".",a)!=[]?[for(i=[1:len(a)-1])if(a[i]!=".")a[i]]:[for(i=[1:len(a)-1])a[i]], >>> n=[["0"],["1"],["2"],["3"],["4"],["5"],["6"],["7"],["8"],["9"]], >>> l=len(b), >>> c=[for(i=[0:l-1])each search(b[i],n)], >>> d=[for(i=[0:len(c)-1])10^(l-i-1)], >>> e=c*d, >>> >>> f=search(".",a)!=[]&&search("-",a)!=[]?e*10^-(l-(search(".",a)[0]-2)):search(".",a)!=[]&&search("-",a)==[]?e*10^-(l-(search(".",a)[0]-1)):e, >>> g=search("-",a)!=[]?f*-1:f >>> )[text,g]; >>> >>> //function to rotate a point around a vector(axis) with angle theta >>> >>> function q(vector=[1,0,0],point=[0,5,0],theta=0)= >>> >>> let(t=theta, >>> v=vector/norm(vector), >>> p=[cos(t/2),v*sin(t/2)], >>> p1=[p.x,-p.y], >>> q=[0,len(point)==2?[point.x,point.y,0]:point], >>> pq=[p.x*q.x-p.y*q.y,p.x*q.y+p.y*q.x+cross(p.y,q.y)], >>> pqp1=[pq.x*p1.x-pq.y*p1.y,pq.x*p1.y+pq.y*p1.x+cross(pq.y,p1.y)], >>> transformation=pqp1.y >>> ) >>> >>> transformation >>> ; >>> // function is input to another function q_rot >>> function qmr1(s,r,pl,n=0)= n==len(s)?pl: >>> qmr1(s,r, >>> let( >>> v1=s[n]=="x"?[1,0,0]:s[n]=="y"?[0,1,0]:[0,0,1], >>> r1=r[n]==undef?0:r[n]) >>> [for(p=pl)q(v1,p,r1)],n+1); >>> //function is input to another function q_rot >>> function qmr2(s,r,pl,n=0)= n==len(s)?pl:qmr2(s,r,let( >>> v1=s[n]=="x"?[1,0,0]:s[n]=="y"?[0,1,0]:[0,0,1], >>> r1=r[n]==undef?0:r[n]) >>> [for(i=[0:len(pl)-1])[for(p=pl[i])q(v1,p,r1)]],n+1); >>> >>> //function to rotate a group of points "pl" around a series of axis with >>> defined angles e.g q_rot(s=["z20","x40","y80"],pl=[[2,0],[10,2]])=> will >>> rotate the line first around z axis by 20 deg then around x axis by 40 >>> degrees and then around y axis by 80 degrees. >>> function q_rot(s,pl)= >>> is_num(pl[0][0])?qmr1([for(p=s)cvar(p)[0]],[for(p=s)cvar(p)[1]],pl):qmr2([for(p=s)cvar(p)[0]],[for(p=s)cvar(p)[1]],pl); >>> >>> // sequence of rotation defined by r1 >>> r1=["x30","y40","z100"]; >>> vz=[0,0,1]; >>> v1=q_rot(r1,[vz])[0]; >>> >>> v2=cross(vz,v1); >>> theta=acos(vz*v1/norm(v1)); >>> >>> // equivalent rotation axis and angle of rotation w.r.t vector vz >>> echo(v2,theta); >>> _______________________________________________ >>> OpenSCAD mailing list >>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >