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Update polyround.scad

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Irev-Dev
2017-09-14 12:56:50 +00:00
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polyround.scad
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@@ -6,9 +6,8 @@
// License: GPL 3 // License: GPL 3
//uncomment to see the examples
//examples(); //examples();
module examples(){ module examples(){
//Example of how a parametric part might be designed with this tool //Example of how a parametric part might be designed with this tool
width=20; height=25; width=20; height=25;
@@ -20,14 +19,12 @@ module examples(){
[slotPosition+slotW,height-slotH,internalR],[slotPosition+slotW,height,minR],[width,height,minR],[width,0,farcornerR]]; [slotPosition+slotW,height-slotH,internalR],[slotPosition+slotW,height,minR],[width,height,minR],[width,0,farcornerR]];
translate([-25,0,0])polygon(polyRound(points,5)); translate([-25,0,0])polygon(polyRound(points,5));
%translate([-25,0,0.2])polygon(getpoints(points));//transparent copy of the polgon without rounding %translate([-25,0,0.2])polygon(getpoints(points));//transparent copy of the polgon without rounding
//Example of features 2 //Example of features 2
// 1 2 3 4 5 6 // 1 2 3 4 5 6
b=[[-4,0,1],[5,3,1.5],[0,7,0],[8,7,10],[20,20,1],[10,0,10]]; //points b=[[-4,0,1],[5,3,1.5],[0,7,0.1],[8,7,10],[20,20,0.8],[10,0,10]]; //points
// polygon(polyRound(b,30));/*polycarious() will make the same shape but doesn't have radii conflict handling*/ //polygon(polycarious(b,30)); polygon(polyRound(b,30));/*polycarious() will make the same shape but doesn't have radii conflict handling*/ //polygon(polycarious(b,30));
%translate([0,0,0.2])polygon(getpoints(b));//transparent copy of the polgon without rounding %translate([0,0,0.3])polygon(getpoints(b));//transparent copy of the polgon without rounding
//Example of features 3 //Example of features 3
// 1 2 3 4 5 6 // 1 2 3 4 5 6
p=[[0,0,1.2],[0,20,1],[15,15,1],[3,10,3],[15,0,1],[6,2,10]];//points p=[[0,0,1.2],[0,20,1],[15,15,1],[3,10,3],[15,0,1],[6,2,10]];//points
@@ -39,20 +36,23 @@ module examples(){
r1a=10; r1b=10; r1a=10; r1b=10;
r2a=30; r2b=30; r2a=30; r2b=30;
r3a=10; r3b=40; r3a=10; r3b=40;
r4a=15; r4b=20;
c1=[[0,0,0],[0,20,r1a],[20,20,r1b],[20,0,0]];//both radii fit and don't need to be changed c1=[[0,0,0],[0,20,r1a],[20,20,r1b],[20,0,0]];//both radii fit and don't need to be changed
translate([-25,-25,0])polygon(polyRound(c1,8)); translate([-25,-30,0])polygon(polyRound(c1,8));
echo("c1 debug",polyRound(c1,8,debug=1));// [0,0,0,0] all zeros indicates none of the radii were reduced echo(str("c1 debug= ",polyRound(c1,8,mode=1)," all zeros indicates none of the radii were reduced"));
c2=[[0,0,0],[0,20,r2a],[20,20,r2b],[20,0,0]];//radii are too large and are reduced to fit c2=[[0,0,0],[0,20,r2a],[20,20,r2b],[20,0,0]];//radii are too large and are reduced to fit
translate([0,-25,0])polygon(polyRound(c2,8)); translate([0,-30,0])polygon(polyRound(c2,8));
echo("c2 debug",polyRound(c2,8,debug=1));// [0,-20,-20,0] 2nd and 3rd radii reduced by 20mm i.e. from 30 to 10mm radius echo(str("c2 debug= ",polyRound(c2,8,mode=1)," 2nd and 3rd radii reduced by 20mm i.e. from 30 to 10mm radius"));
c3=[[0,0,0],[0,20,r3a],[20,20,r3b],[20,0,0]];//radii are too large again and are reduced to fit, but keep their ratios c3=[[0,0,0],[0,20,r3a],[20,20,r3b],[20,0,0]];//radii are too large again and are reduced to fit, but keep their ratios
translate([25,-25,0])polygon(polyRound(c3,8)); translate([25,-30,0])polygon(polyRound(c3,8));
echo("c3 debug",polyRound(c3,8,debug=1));// [0,-6,-24,0] 2nd and 3rd radii reduced by 6 and 24mm respectively echo(str("c3 debug= ",polyRound(c3,8,mode=1)," 2nd and 3rd radii reduced by 6 and 24mm respectively"));
//resulting in radii of 4 and 16mm, //resulting in radii of 4 and 16mm,
//notice the ratio from the orginal radii stays the same r3a/r3b = 10/40 = 4/16 //notice the ratio from the orginal radii stays the same r3a/r3b = 10/40 = 4/16
c4=[[0,0,0],[0,20,r4a],[20,20,r4b],[20,0,0]];//radii are too large again but not corrected this time
translate([50,-30,0])polygon(polyRound(c4,8,mode=2));//mode 2 = no radii limiting
//example of rounding random points, this has no current use but is a good demonstration //example of rounding random points, this has no current use but is a good demonstration
random=[for(i=[0:20])[rnd(0,50),rnd(0,50),/*rnd(0,30)*/1000]]; random=[for(i=[0:20])[rnd(0,50),rnd(0,50),/*rnd(0,30)*/1000]];
R =polyRound(random,7); R =polyRound(random,7);
@@ -80,92 +80,247 @@ module examples(){
translate([tangentsNcen[2][0],tangentsNcen[2][1],-0.2])circle(r=radius,$fn=25);//draws the cirle translate([tangentsNcen[2][0],tangentsNcen[2][1],-0.2])circle(r=radius,$fn=25);//draws the cirle
%polygon(getpoints(radiipoints));//draws a polygon %polygon(getpoints(radiipoints));//draws a polygon
} }
//for(i=[0:len(b2)-1]) translate([b2[i].x,b2[i].y,2])#circle(0.2);
ex=[[0,0,-1],[2,8,0],[5,4,3],[15,10,0.5],[10,2,1]];
translate([15,-50,0]){
ang=55;
minR=0.2;
rotate([0,0,ang+270])translate([0,-5,0])square([10,10],true);
clipP=[[9,1,0],[9,0,0],[9.5,0,0],[9.5,1,0.2],[10.5,1,0.2],[10.5,0,0],[11,0,0],[11,1,0]];
a=RailCustomiser(ex,o1=0.5,minR=minR,a1=ang-90,a2=0,mode=2);
b=revList(RailCustomiser(ex,o1=-0.5,minR=minR,a1=ang-90,a2=0,mode=2));
points=concat(a,clipP,b);
points2=concat(ex,clipP,b);
polygon(polyRound(points,20));
//%polygon(polyRound(points2,20));
}
//the following exapmle shows how the offsets in RailCustomiser could be used to makes shells
translate([-20,-60,0]){
for(i=[-9:0.5:1])polygon(polyRound(RailCustomiser(ex,o1=i-0.4,o2=i,minR=0.1),20));
}
// This example shows how a list of points can be used multiple times in the same
nutW=5.5; nutH=3; boltR=1.6;
minT=2; minR=0.8;
nutCapture=[
[-boltR, 0, 0],
[-boltR, minT, 0],
[-nutW/2, minT, minR],
[-nutW/2, minT+nutH, minR],
[nutW/2, minT+nutH, minR],
[nutW/2, minT, minR],
[boltR, minT, 0],
[boltR, 0, 0],
];
aSquare=concat(
[[0,0,0]],
moveRadiiPoints(nutCapture,tran=[5,0],rot=0),
[[20,0,0]],
moveRadiiPoints(nutCapture,tran=[20,5],rot=90),
[[20,10,0]],
[[0,10,0]]
);
echo(aSquare);
translate([40,-60,0]){
polygon(polyRound(aSquare,20));
translate([10,12,0])polygon(polyRound(nutCapture,20));
}
} }
{function polyRound(radiipoints,fn=5,mode=0)=
function polyRound(radiipoints,fn=5,debug=0)= /* Takes a list of radii points of the format [x,y,radius] and rounds each point
let(p=getpoints(radiipoints)) //make list of coordinates without radii with fn resolution
let(Lp=len(p)) mode=0 - automatic radius limiting - DEFAULT
mode=1 - Debug, output radius reduction for automatic radius limiting
mode=2 - No radius limiting*/
let(
getpoints=mode==2?1:2,
p=getpoints(radiipoints), //make list of coordinates without radii
Lp=len(p),
//remove the middle point of any three colinear points //remove the middle point of any three colinear points
let(newrp=[for(i=[0:len(p)-1]) if(isColinear(p[wrap(i-1,Lp)],p[wrap(i+0,Lp)],p[wrap(i+1,Lp)])==0)radiipoints[wrap(i+0,Lp)] ]) newrp=[for(i=[0:len(p)-1]) if(isColinear(p[wrap(i-1,Lp)],p[wrap(i+0,Lp)],p[wrap(i+1,Lp)])==0||p[wrap(i+0,Lp)].z!=0)radiipoints[wrap(i+0,Lp)] ],
let(temp=[for(i=[0:len(newrp)-1]) //for each point in the radii array temp=[for(i=[0:len(newrp)-1]) //for each point in the radii array
let(the5points=[for(j=[-2:2])newrp[wrap(i+j,len(newrp))]])//collect 5 radii points let(
let(temp2=round5points(the5points,fn,debug)) thepoints=[for(j=[-getpoints:getpoints])newrp[wrap(i+j,len(newrp))]],//collect 5 radii points
debug>0?temp2:newrp[i][2]==0?[[newrp[i][0],newrp[i][1]]]: //return the original point if the radius is 0 temp2=mode==2?round3points(thepoints,fn):round5points(thepoints,fn,mode)
CentreN2PointsArc(temp2[0],temp2[1],temp2[2],0,fn) //return the arc if everything is normal )
]) mode==1?temp2:newrp[i][2]==0?[[newrp[i][0],newrp[i][1]]]: //return the original point if the radius is 0
[for (a = temp) for (b = a) b];//flattern and return the array CentreN2PointsArc(temp2[0],temp2[1],temp2[2],0,fn) //return the arc if everything is normal
]
function round5points(rp,fn,debug=0)= )
rp[2][2]==0&&debug==0?[[rp[2][0],rp[2][1]]]://return the middle point if the radius is 0 [for (a = temp) for (b = a) b];}//flattern and return the array
rp[2][2]==0&&debug==1?0://if debug is enabled and the radius is 0 return 0 {function round5points(rp,fn,debug=0)=
let(p=getpoints(rp)) //get list of points rp[2][2]==0&&debug==0?[[rp[2][0],rp[2][1]]]://return the middle point if the radius is 0
let(r=[for(i=[1:3]) rp[i][2]])//get the centre 3 radii rp[2][2]==0&&debug==1?0://if debug is enabled and the radius is 0 return 0
let(
p=getpoints(rp), //get list of points
r=[for(i=[1:3]) rp[i][2]],//get the centre 3 radii
//start by determining what the radius should be at point 3 //start by determining what the radius should be at point 3
//find angles at points 2 , 3 and 4 //find angles at points 2 , 3 and 4
let(a2=cosineRuleAngle(p[0],p[1],p[2])) a2=cosineRuleAngle(p[0],p[1],p[2]),
let(a3=cosineRuleAngle(p[1],p[2],p[3])) a3=cosineRuleAngle(p[1],p[2],p[3]),
let(a4=cosineRuleAngle(p[2],p[3],p[4])) a4=cosineRuleAngle(p[2],p[3],p[4]),
//find the distance between points 2&3 and between points 3&4 //find the distance between points 2&3 and between points 3&4
let(d23=pointDist(p[1],p[2])) d23=pointDist(p[1],p[2]),
let(d34=pointDist(p[2],p[3])) d34=pointDist(p[2],p[3]),
//find the radius factors //find the radius factors
let(F23=(d23*tan(a2/2)*tan(a3/2))/(r[0]*tan(a3/2)+r[1]*tan(a2/2))) F23=(d23*tan(a2/2)*tan(a3/2))/(r[0]*tan(a3/2)+r[1]*tan(a2/2)),
let(F34=(d34*tan(a3/2)*tan(a4/2))/(r[1]*tan(a4/2)+r[2]*tan(a3/2))) F34=(d34*tan(a3/2)*tan(a4/2))/(r[1]*tan(a4/2)+r[2]*tan(a3/2)),
let(newR=min(r[1],F23*r[1],F34*r[1]))//use the smallest radius newR=min(r[1],F23*r[1],F34*r[1]),//use the smallest radius
//now that the radius has been determined, find tangent points and circle centre //now that the radius has been determined, find tangent points and circle centre
let(tangD=newR/tan(a3/2))//distance to the tangent point from p3 tangD=newR/tan(a3/2),//distance to the tangent point from p3
let(circD=newR/sin(a3/2))//distance to the circle centre from p3 circD=newR/sin(a3/2),//distance to the circle centre from p3
//find the angle from the p3 //find the angle from the p3
let(an23=getAngle(p[1],p[2]))//angle from point 3 to 2 an23=getAngle(p[1],p[2]),//angle from point 3 to 2
let(an34=getAngle(p[3],p[2]))//angle from point 3 to 4 an34=getAngle(p[3],p[2]),//angle from point 3 to 4
//find tangent points //find tangent points
let(t23=[p[2][0]-cos(an23)*tangD,p[2][1]-sin(an23)*tangD])//tangent point between points 2&3 t23=[p[2][0]-cos(an23)*tangD,p[2][1]-sin(an23)*tangD],//tangent point between points 2&3
let(t34=[p[2][0]-cos(an34)*tangD,p[2][1]-sin(an34)*tangD])//tangent point between points 3&4 t34=[p[2][0]-cos(an34)*tangD,p[2][1]-sin(an34)*tangD],//tangent point between points 3&4
//find circle centre //find circle centre
let(tmid=getMidpoint(t23,t34))//midpoint between the two tangent points tmid=getMidpoint(t23,t34),//midpoint between the two tangent points
let(anCen=getAngle(tmid,p[2]))//angle from point 3 to circle centre anCen=getAngle(tmid,p[2]),//angle from point 3 to circle centre
let(cen=[p[2][0]-cos(anCen)*circD,p[2][1]-sin(anCen)*circD])//circle center by offseting from point 3 cen=[p[2][0]-cos(anCen)*circD,p[2][1]-sin(anCen)*circD]
)
//circle center by offseting from point 3
//determine the direction of rotation //determine the direction of rotation
debug==0?//if debug in disabled return arc (default) debug==1?//if debug in disabled return arc (default)
[t23,t34,cen] (newR-r[1]):
:(newR-r[1]); [t23,t34,cen];}
{function round3points(rp,fn)=
function polycarious(radiipoints,fn=5)=
let(p=getpoints(radiipoints))
let(newrp=[for(i=[0:len(p)-1])
let(the3points=[for(j=[-1:1]) p[wrap(i+j,len(p))]])
if(isColinear(the3points[0],the3points[1],the3points[2])==0) radiipoints[wrap(i+0,len(p))]
])
let(temp=[for(i=[0:len(newrp)-1])
let(the3points=[for(j=[-1:1]) newrp[wrap(i+j,len(newrp))]])//collect 3 points
let(temp2=round3points(the3points,fn))
newrp[i][2]==0?[[newrp[i][0],newrp[i][1]]]: //return the original point if the radius is 0
CentreN2PointsArc(temp2[0],temp2[1],temp2[2],0,fn) //return the arc if everything is normal
])
[for (a = temp) for (b = a) b]; //flattern and return the array
function round3points(rp,fn)=
rp[1][2]==0?[[rp[1][0],rp[1][1]]]://return the middle point if the radius is 0 rp[1][2]==0?[[rp[1][0],rp[1][1]]]://return the middle point if the radius is 0
let(p=getpoints(rp)) //get list of points let(
let(r=rp[1][2])//get the centre 3 radii p=getpoints(rp), //get list of points
let(ang=cosineRuleAngle(p[0],p[1],p[2]))//angle between the lines r=rp[1][2],//get the centre 3 radii
ang=cosineRuleAngle(p[0],p[1],p[2]),//angle between the lines
//now that the radius has been determined, find tangent points and circle centre //now that the radius has been determined, find tangent points and circle centre
let(tangD=r/tan(ang/2))//distance to the tangent point from p2 tangD=r/tan(ang/2),//distance to the tangent point from p2
let(circD=r/sin(ang/2))//distance to the circle centre from p2 circD=r/sin(ang/2),//distance to the circle centre from p2
//find the angles from the p2 with respect to the postitive x axis //find the angles from the p2 with respect to the postitive x axis
let(a12=getAngle(p[0],p[1]))//angle from point 2 to 1 a12=getAngle(p[0],p[1]),//angle from point 2 to 1
let(a23=getAngle(p[2],p[1]))//angle from point 2 to 3 a23=getAngle(p[2],p[1]),//angle from point 2 to 3
//find tangent points //find tangent points
let(t12=[p[1][0]-cos(a12)*tangD,p[1][1]-sin(a12)*tangD])//tangent point between points 1&2 t12=[p[1][0]-cos(a12)*tangD,p[1][1]-sin(a12)*tangD],//tangent point between points 1&2
let(t23=[p[1][0]-cos(a23)*tangD,p[1][1]-sin(a23)*tangD])//tangent point between points 2&3 t23=[p[1][0]-cos(a23)*tangD,p[1][1]-sin(a23)*tangD],//tangent point between points 2&3
//find circle centre //find circle centre
let(tmid=getMidpoint(t12,t23))//midpoint between the two tangent points tmid=getMidpoint(t12,t23),//midpoint between the two tangent points
let(angCen=getAngle(tmid,p[1]))//angle from point 2 to circle centre angCen=getAngle(tmid,p[1]),//angle from point 2 to circle centre
let(cen=[p[1][0]-cos(angCen)*circD,p[1][1]-sin(angCen)*circD])//circle center by offseting from point 2 cen=[p[1][0]-cos(angCen)*circD,p[1][1]-sin(angCen)*circD] //circle center by offseting from point 2
[t12,t23,cen]; )
//CentreN2PointsArc(t12,t23,cen,0,fn); [t12,t23,cen];}
{function parallelFollow(rp,thick=4,minR=1,mode=1)=
function CentreN2PointsArc(p1,p2,cen,mode=0,fn)= //rp[1][2]==0?[rp[1][0],rp[1][1],0]://return the middle point if the radius is 0
thick==0?[rp[1][0],rp[1][1],0]://return the middle point if the radius is 0
let(
p=getpoints(rp), //get list of points
r=thick,//get the centre 3 radii
ang=cosineRuleAngle(p[0],p[1],p[2]),//angle between the lines
//now that the radius has been determined, find tangent points and circle centre
tangD=r/tan(ang/2),//distance to the tangent point from p2
sgn=CWorCCW(rp),//rotation of the three points cw or ccw?let(sgn=mode==0?1:-1)
circD=mode*sgn*r/sin(ang/2),//distance to the circle centre from p2
//find the angles from the p2 with respect to the postitive x axis
a12=getAngle(p[0],p[1]),//angle from point 2 to 1
a23=getAngle(p[2],p[1]),//angle from point 2 to 3
//find tangent points
t12=[p[1][0]-cos(a12)*tangD,p[1][1]-sin(a12)*tangD],//tangent point between points 1&2
t23=[p[1][0]-cos(a23)*tangD,p[1][1]-sin(a23)*tangD],//tangent point between points 2&3
//find circle centre
tmid=getMidpoint(t12,t23),//midpoint between the two tangent points
angCen=getAngle(tmid,p[1]),//angle from point 2 to circle centre
cen=[p[1][0]-cos(angCen)*circD,p[1][1]-sin(angCen)*circD],//circle center by offseting from point 2
outR=max(minR,rp[1][2]-thick*sgn*mode) //ensures radii are never too small.
)
concat(cen,outR);}
{function findPoint(ang1,refpoint1,ang2,refpoint2,r=0)=
let(
m1=tan(ang1),c1=refpoint1.y-m1*refpoint1.x,
m2=tan(ang2),c2=refpoint2.y-m2*refpoint2.x,
outputX=(c2-c1)/(m1-m2),
outputY=m1*outputX+c1
)
[outputX,outputY,r];
}
{function RailCustomiser(rp,o1=0,o2,mode=0,minR=0,a1,a2)=
/*This function takes a series of radii points and plots points to run along side at a constanit distance, think of it as offset but for line instead of a polygon
rp=radii points, o1&o2=offset 1&2,minR=min radius, a1&2=angle 1&2
mode=1 - include endpoints a1&2 are relative to the angle of the last two points and equal 90deg if not defined
mode=2 - endpoints not included
mode=3 - include endpoints a1&2 are absolute from the x axis and are 0 if not defined
negative radiuses only allowed for the first and last radii points
As it stands this function could probably be tidied a lot, but it works, I'll tidy later*/
let(
o2undef=o2==undef?1:0,
o2=o2undef==1?0:o2,
CWorCCW1=sign(o1)*CWorCCW(rp),
CWorCCW2=sign(o2)*CWorCCW(rp),
o1=abs(o1),
o2b=abs(o2),
Lrp3=len(rp)-3,
Lrp=len(rp),
a1=mode==0&&a1==undef?
getAngle(rp[0],rp[1])+90:
mode==2&&a1==undef?
0:
mode==0?
getAngle(rp[0],rp[1])+a1:
a1,
a2=mode==0&&a2==undef?
getAngle(rp[Lrp-1],rp[Lrp-2])+90:
mode==2&&a2==undef?
0:
mode==0?
getAngle(rp[Lrp-1],rp[Lrp-2])+a2:
a2,
OffLn1=[for(i=[0:Lrp3]) o1==0?rp[i+1]:parallelFollow([rp[i],rp[i+1],rp[i+2]],o1,minR,mode=CWorCCW1)],
OffLn2=[for(i=[0:Lrp3]) o2==0?rp[i+1]:parallelFollow([rp[i],rp[i+1],rp[i+2]],o2b,minR,mode=CWorCCW2)],
Rp1=abs(rp[0].z),
Rp2=abs(rp[Lrp-1].z),
endP1a=findPoint(getAngle(rp[0],rp[1]),OffLn1[0],a1,rp[0],Rp1),
endP1b=findPoint(getAngle(rp[Lrp-1],rp[Lrp-2]),OffLn1[len(OffLn1)-1],a2,rp[Lrp-1],Rp2),
endP2a=findPoint(getAngle(rp[0],rp[1]),OffLn2[0],a1,rp[0],Rp1),
endP2b=findPoint(getAngle(rp[Lrp-1],rp[Lrp-2]),OffLn2[len(OffLn1)-1],a2,rp[Lrp-1],Rp2),
absEnda=getAngle(endP1a,endP2a),
absEndb=getAngle(endP1b,endP2b),
negRP1a=[cos(absEnda)*rp[0].z*10+endP1a.x,sin(absEnda)*rp[0].z*10+endP1a.y,0.0],
negRP2a=[cos(absEnda)*-rp[0].z*10+endP2a.x,sin(absEnda)*-rp[0].z*10+endP2a.y,0.0],
negRP1b=[cos(absEndb)*rp[Lrp-1].z*10+endP1b.x,sin(absEndb)*rp[Lrp-1].z*10+endP1b.y,0.0],
negRP2b=[cos(absEndb)*-rp[Lrp-1].z*10+endP2b.x,sin(absEndb)*-rp[Lrp-1].z*10+endP2b.y,0.0],
OffLn1b=(mode==0||mode==2)&&rp[0].z<0&&rp[Lrp-1].z<0?
concat([negRP1a],[endP1a],OffLn1,[endP1b],[negRP1b])
:(mode==0||mode==2)&&rp[0].z<0?
concat([negRP1a],[endP1a],OffLn1,[endP1b])
:(mode==0||mode==2)&&rp[Lrp-1].z<0?
concat([endP1a],OffLn1,[endP1b],[negRP1b])
:mode==0||mode==2?
concat([endP1a],OffLn1,[endP1b])
:
OffLn1
,
OffLn2b=(mode==0||mode==2)&&rp[0].z<0&&rp[Lrp-1].z<0?
concat([negRP2a],[endP2a],OffLn2,[endP2b],[negRP2b])
:(mode==0||mode==2)&&rp[0].z<0?
concat([negRP2a],[endP2a],OffLn2,[endP2b])
:(mode==0||mode==2)&&rp[Lrp-1].z<0?
concat([endP2a],OffLn2,[endP2b],[negRP2b])
:mode==0||mode==2?
concat([endP2a],OffLn2,[endP2b])
:
OffLn2
)//end of let()
o2undef==1?OffLn1b:concat(OffLn2b,revList(OffLn1b));}
{function revList(list)=//reverse list
let(Llist=len(list)-1)
[for(i=[0:Llist]) list[Llist-i]];
}
{function CWorCCW(p)=
let(
Lp=len(p),
e=[for(i=[0:Lp-1]) (p[wrap(i+0,Lp)].x-p[wrap(i+1,Lp)].x)*(p[wrap(i+0,Lp)].y+p[wrap(i+1,Lp)].y)]
)
sign(sum(e));}
{function CentreN2PointsArc(p1,p2,cen,mode=0,fn)=
/* This function plots an arc from p1 to p2 with fn increments using the cen as the centre of the arc. /* This function plots an arc from p1 to p2 with fn increments using the cen as the centre of the arc.
the mode determines how the arc is plotted the mode determines how the arc is plotted
mode==0, shortest arc possible mode==0, shortest arc possible
@@ -173,58 +328,62 @@ function CentreN2PointsArc(p1,p2,cen,mode=0,fn)=
mode==2, plotted clockwise mode==2, plotted clockwise
mode==3, plotted counter clockwise mode==3, plotted counter clockwise
*/ */
//determine the direction of rotation let(
let(e1=(cen[0]-p1[0])*(cen[1]+p1[1]))//edge 1 CWorCCW=CWorCCW([cen,p1,p2]),//determine the direction of rotation
let(e2=(p2[0]-cen[0])*(p2[1]+cen[1]))//edge 2
let(e3=(p1[0]-p2[0])*(p1[1]+p2[1]))//edge 3
let(CWorCCW=(e1+e2+e3)/abs(e1+e2+e3))//rotation of the three points cw or ccw?
//determine the arc angle depending on the mode //determine the arc angle depending on the mode
let(p1p2Angle=cosineRuleAngle(p2,cen,p1)) p1p2Angle=cosineRuleAngle(p2,cen,p1),
let(arcAngle= arcAngle=
mode==0?p1p2Angle: mode==0?p1p2Angle:
mode==1?p1p2Angle-360: mode==1?p1p2Angle-360:
mode==2&&CWorCCW==-1?p1p2Angle: mode==2&&CWorCCW==-1?p1p2Angle:
mode==2&&CWorCCW== 1?p1p2Angle-360: mode==2&&CWorCCW== 1?p1p2Angle-360:
mode==3&&CWorCCW== 1?p1p2Angle: mode==3&&CWorCCW== 1?p1p2Angle:
mode==3&&CWorCCW==-1?p1p2Angle-360: mode==3&&CWorCCW==-1?p1p2Angle-360:
cosineRuleAngle(p2,cen,p1)) cosineRuleAngle(p2,cen,p1)
let(r=pointDist(p1,cen))//determine the radius ,
let(p1Angle=getAngle(cen,p1))//angle of line 1 r=pointDist(p1,cen),//determine the radius
[for(i=[0:fn]) [cos(p1Angle+(arcAngle/fn)*i*CWorCCW)*r+cen[0],sin(p1Angle+(arcAngle/fn)*i*CWorCCW)*r+cen[1]]]; p1Angle=getAngle(cen,p1) //angle of line 1
)
function invtan(run,rise)= [for(i=[0:fn]) [cos(p1Angle+(arcAngle/fn)*i*CWorCCW)*r+cen[0],sin(p1Angle+(arcAngle/fn)*i*CWorCCW)*r+cen[1]]];}
{function moveRadiiPoints(rp,tran=[0,0],rot=0)=
[for(i=rp)
let(
a=getAngle([0,0],[i.x,i.y]),//get the angle of the this point
h=pointDist([0,0],[i.x,i.y]) //get the hypotenuse/radius
)
[h*cos(a+rot)+tran.x,h*sin(a+rot)+tran.y,i.z]//calculate the point's new position
];}
{function invtan(run,rise)=
let(a=abs(atan(rise/run))) let(a=abs(atan(rise/run)))
rise==0&&run>0?0:rise>0&&run>0?a:rise>0&&run==0?90:rise>0&&run<0?180-a:rise==0&&run<0?180:rise<0&&run<0?a+180:rise<0&&run==0?270:rise<0&&run>0?360-a:"error"; rise==0&&run>0?0:rise>0&&run>0?a:rise>0&&run==0?90:rise>0&&run<0?180-a:rise==0&&run<0?180:rise<0&&run<0?a+180:rise<0&&run==0?270:rise<0&&run>0?360-a:"error";}
{function cosineRuleAngle(p1,p2,p3)=
function cosineRuleAngle(p1,p2,p3)= let(
let(p12=abs(pointDist(p1,p2))) p12=abs(pointDist(p1,p2)),
let(p13=abs(pointDist(p1,p3))) p13=abs(pointDist(p1,p3)),
let(p23=abs(pointDist(p2,p3))) p23=abs(pointDist(p2,p3))
acos((sq(p23)+sq(p12)-sq(p13))/(2*p23*p12)); )
acos((sq(p23)+sq(p12)-sq(p13))/(2*p23*p12));}
{function sum(list, idx = 0, result = 0) =
idx >= len(list) ? result : sum(list, idx + 1, result + list[idx]);}
function sq(x)=x*x; function sq(x)=x*x;
function getGradient(p1,p2)=(p2[1]-p1[1])/(p2[0]-p1[0]); function getGradient(p1,p2)=(p2.y-p1.y)/(p2.x-p1.x);
function getAngle(p1,p2)=invtan(p2[0]-p1[0],p2[1]-p1[1]); function getAngle(p1,p2)=invtan(p2[0]-p1[0],p2[1]-p1[1]);
function getMidpoint(p1,p2)=[(p1[0]+p2[0])/2,(p1[1]+p2[1])/2]; //returns the midpoint of two points function getMidpoint(p1,p2)=[(p1[0]+p2[0])/2,(p1[1]+p2[1])/2]; //returns the midpoint of two points
function pointDist(p1,p2)=sqrt(abs(sq(p1[0]-p2[0])+sq(p1[1]-p2[1]))); //returns the distance between two points function pointDist(p1,p2)=sqrt(abs(sq(p1[0]-p2[0])+sq(p1[1]-p2[1]))); //returns the distance between two points
function isColinear(p1,p2,p3)=getGradient(p1,p2)==getGradient(p2,p3)?1:0;//return 1 if 3 points are colinear function isColinear(p1,p2,p3)=getGradient(p1,p2)==getGradient(p2,p3)?1:0;//return 1 if 3 points are colinear
module polyline(p) {for(i=[0:max(0,len(p)-1)])line(p[i],p[wrap(i+1,len(p) )]); module polyline(p) {for(i=[0:max(0,len(p)-1)])line(p[i],p[wrap(i+1,len(p) )]);
} // polyline plotter } // polyline plotter
module line(p1, p2 ,width=0.3) { // single line plotter
module line(p1, p2 ,width=0.3)
{ // single line plotter
hull() { hull() {
translate(p1) sphere(width); translate(p1) circle(width);
translate(p2) sphere(width); translate(p2) circle(width);
} }
} }
function getpoints(p)=[for(i=[0:len(p)-1])[p[i].x,p[i].y]];// gets [x,y]list of[x,y,r]list function getpoints(p)=[for(i=[0:len(p)-1])[p[i].x,p[i].y]];// gets [x,y]list of[x,y,r]list
function wrap(x,x_max=1,x_min=0) = (((x - x_min) % (x_max - x_min)) + (x_max - x_min)) % (x_max - x_min) + x_min; // wraps numbers inside boundaries function wrap(x,x_max=1,x_min=0) = (((x - x_min) % (x_max - x_min)) + (x_max - x_min)) % (x_max - x_min) + x_min; // wraps numbers inside boundaries
function rnd(a = 1, b = 0, s = []) = {function rnd(a = 1, b = 0, s = []) =
s == [] ? s == [] ?
(rands(min(a, b), max( a, b), 1)[0]) (rands(min(a, b), max( a, b), 1)[0])
: :
(rands(min(a, b), max(a, b), 1, s)[0]) (rands(min(a, b), max(a, b), 1, s)[0])
; // nice rands wrapper ;} // nice rands wrapper