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Update polyround.scad
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polyround.scad
403
polyround.scad
@@ -6,9 +6,8 @@
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// License: GPL 3
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//uncomment to see the examples
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//examples();
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module examples(){
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//Example of how a parametric part might be designed with this tool
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width=20; height=25;
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@@ -20,14 +19,12 @@ module examples(){
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[slotPosition+slotW,height-slotH,internalR],[slotPosition+slotW,height,minR],[width,height,minR],[width,0,farcornerR]];
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translate([-25,0,0])polygon(polyRound(points,5));
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%translate([-25,0,0.2])polygon(getpoints(points));//transparent copy of the polgon without rounding
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//Example of features 2
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// 1 2 3 4 5 6
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b=[[-4,0,1],[5,3,1.5],[0,7,0],[8,7,10],[20,20,1],[10,0,10]]; //points
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// polygon(polyRound(b,30));/*polycarious() will make the same shape but doesn't have radii conflict handling*/ //polygon(polycarious(b,30));
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%translate([0,0,0.2])polygon(getpoints(b));//transparent copy of the polgon without rounding
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b=[[-4,0,1],[5,3,1.5],[0,7,0.1],[8,7,10],[20,20,0.8],[10,0,10]]; //points
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polygon(polyRound(b,30));/*polycarious() will make the same shape but doesn't have radii conflict handling*/ //polygon(polycarious(b,30));
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%translate([0,0,0.3])polygon(getpoints(b));//transparent copy of the polgon without rounding
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//Example of features 3
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// 1 2 3 4 5 6
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p=[[0,0,1.2],[0,20,1],[15,15,1],[3,10,3],[15,0,1],[6,2,10]];//points
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@@ -39,20 +36,23 @@ module examples(){
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r1a=10; r1b=10;
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r2a=30; r2b=30;
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r3a=10; r3b=40;
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r4a=15; r4b=20;
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c1=[[0,0,0],[0,20,r1a],[20,20,r1b],[20,0,0]];//both radii fit and don't need to be changed
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translate([-25,-25,0])polygon(polyRound(c1,8));
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echo("c1 debug",polyRound(c1,8,debug=1));// [0,0,0,0] all zeros indicates none of the radii were reduced
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translate([-25,-30,0])polygon(polyRound(c1,8));
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echo(str("c1 debug= ",polyRound(c1,8,mode=1)," all zeros indicates none of the radii were reduced"));
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c2=[[0,0,0],[0,20,r2a],[20,20,r2b],[20,0,0]];//radii are too large and are reduced to fit
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translate([0,-25,0])polygon(polyRound(c2,8));
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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
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translate([0,-30,0])polygon(polyRound(c2,8));
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echo(str("c2 debug= ",polyRound(c2,8,mode=1)," 2nd and 3rd radii reduced by 20mm i.e. from 30 to 10mm radius"));
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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
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translate([25,-25,0])polygon(polyRound(c3,8));
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echo("c3 debug",polyRound(c3,8,debug=1));// [0,-6,-24,0] 2nd and 3rd radii reduced by 6 and 24mm respectively
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translate([25,-30,0])polygon(polyRound(c3,8));
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echo(str("c3 debug= ",polyRound(c3,8,mode=1)," 2nd and 3rd radii reduced by 6 and 24mm respectively"));
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//resulting in radii of 4 and 16mm,
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//notice the ratio from the orginal radii stays the same r3a/r3b = 10/40 = 4/16
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c4=[[0,0,0],[0,20,r4a],[20,20,r4b],[20,0,0]];//radii are too large again but not corrected this time
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translate([50,-30,0])polygon(polyRound(c4,8,mode=2));//mode 2 = no radii limiting
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//example of rounding random points, this has no current use but is a good demonstration
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random=[for(i=[0:20])[rnd(0,50),rnd(0,50),/*rnd(0,30)*/1000]];
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R =polyRound(random,7);
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@@ -80,92 +80,247 @@ module examples(){
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translate([tangentsNcen[2][0],tangentsNcen[2][1],-0.2])circle(r=radius,$fn=25);//draws the cirle
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%polygon(getpoints(radiipoints));//draws a polygon
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}
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//for(i=[0:len(b2)-1]) translate([b2[i].x,b2[i].y,2])#circle(0.2);
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ex=[[0,0,-1],[2,8,0],[5,4,3],[15,10,0.5],[10,2,1]];
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translate([15,-50,0]){
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ang=55;
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minR=0.2;
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rotate([0,0,ang+270])translate([0,-5,0])square([10,10],true);
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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]];
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a=RailCustomiser(ex,o1=0.5,minR=minR,a1=ang-90,a2=0,mode=2);
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b=revList(RailCustomiser(ex,o1=-0.5,minR=minR,a1=ang-90,a2=0,mode=2));
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points=concat(a,clipP,b);
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points2=concat(ex,clipP,b);
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polygon(polyRound(points,20));
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//%polygon(polyRound(points2,20));
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}
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//the following exapmle shows how the offsets in RailCustomiser could be used to makes shells
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translate([-20,-60,0]){
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for(i=[-9:0.5:1])polygon(polyRound(RailCustomiser(ex,o1=i-0.4,o2=i,minR=0.1),20));
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}
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// This example shows how a list of points can be used multiple times in the same
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nutW=5.5; nutH=3; boltR=1.6;
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minT=2; minR=0.8;
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nutCapture=[
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[-boltR, 0, 0],
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[-boltR, minT, 0],
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[-nutW/2, minT, minR],
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[-nutW/2, minT+nutH, minR],
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[nutW/2, minT+nutH, minR],
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[nutW/2, minT, minR],
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[boltR, minT, 0],
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[boltR, 0, 0],
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];
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aSquare=concat(
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[[0,0,0]],
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moveRadiiPoints(nutCapture,tran=[5,0],rot=0),
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[[20,0,0]],
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moveRadiiPoints(nutCapture,tran=[20,5],rot=90),
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[[20,10,0]],
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[[0,10,0]]
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);
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echo(aSquare);
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translate([40,-60,0]){
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polygon(polyRound(aSquare,20));
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translate([10,12,0])polygon(polyRound(nutCapture,20));
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}
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}
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function polyRound(radiipoints,fn=5,debug=0)=
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let(p=getpoints(radiipoints)) //make list of coordinates without radii
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let(Lp=len(p))
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{function polyRound(radiipoints,fn=5,mode=0)=
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/* Takes a list of radii points of the format [x,y,radius] and rounds each point
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with fn resolution
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mode=0 - automatic radius limiting - DEFAULT
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mode=1 - Debug, output radius reduction for automatic radius limiting
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mode=2 - No radius limiting*/
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let(
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getpoints=mode==2?1:2,
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p=getpoints(radiipoints), //make list of coordinates without radii
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Lp=len(p),
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//remove the middle point of any three colinear points
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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)] ])
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let(temp=[for(i=[0:len(newrp)-1]) //for each point in the radii array
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let(the5points=[for(j=[-2:2])newrp[wrap(i+j,len(newrp))]])//collect 5 radii points
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let(temp2=round5points(the5points,fn,debug))
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debug>0?temp2:newrp[i][2]==0?[[newrp[i][0],newrp[i][1]]]: //return the original point if the radius is 0
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CentreN2PointsArc(temp2[0],temp2[1],temp2[2],0,fn) //return the arc if everything is normal
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])
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[for (a = temp) for (b = a) b];//flattern and return the array
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function round5points(rp,fn,debug=0)=
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rp[2][2]==0&&debug==0?[[rp[2][0],rp[2][1]]]://return the middle point if the radius is 0
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rp[2][2]==0&&debug==1?0://if debug is enabled and the radius is 0 return 0
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let(p=getpoints(rp)) //get list of points
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let(r=[for(i=[1:3]) rp[i][2]])//get the centre 3 radii
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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)] ],
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temp=[for(i=[0:len(newrp)-1]) //for each point in the radii array
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let(
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thepoints=[for(j=[-getpoints:getpoints])newrp[wrap(i+j,len(newrp))]],//collect 5 radii points
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temp2=mode==2?round3points(thepoints,fn):round5points(thepoints,fn,mode)
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)
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mode==1?temp2:newrp[i][2]==0?[[newrp[i][0],newrp[i][1]]]: //return the original point if the radius is 0
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CentreN2PointsArc(temp2[0],temp2[1],temp2[2],0,fn) //return the arc if everything is normal
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]
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)
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[for (a = temp) for (b = a) b];}//flattern and return the array
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{function round5points(rp,fn,debug=0)=
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rp[2][2]==0&&debug==0?[[rp[2][0],rp[2][1]]]://return the middle point if the radius is 0
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rp[2][2]==0&&debug==1?0://if debug is enabled and the radius is 0 return 0
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let(
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p=getpoints(rp), //get list of points
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r=[for(i=[1:3]) rp[i][2]],//get the centre 3 radii
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//start by determining what the radius should be at point 3
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//find angles at points 2 , 3 and 4
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let(a2=cosineRuleAngle(p[0],p[1],p[2]))
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let(a3=cosineRuleAngle(p[1],p[2],p[3]))
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let(a4=cosineRuleAngle(p[2],p[3],p[4]))
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a2=cosineRuleAngle(p[0],p[1],p[2]),
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a3=cosineRuleAngle(p[1],p[2],p[3]),
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a4=cosineRuleAngle(p[2],p[3],p[4]),
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//find the distance between points 2&3 and between points 3&4
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let(d23=pointDist(p[1],p[2]))
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let(d34=pointDist(p[2],p[3]))
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d23=pointDist(p[1],p[2]),
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d34=pointDist(p[2],p[3]),
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//find the radius factors
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let(F23=(d23*tan(a2/2)*tan(a3/2))/(r[0]*tan(a3/2)+r[1]*tan(a2/2)))
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let(F34=(d34*tan(a3/2)*tan(a4/2))/(r[1]*tan(a4/2)+r[2]*tan(a3/2)))
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let(newR=min(r[1],F23*r[1],F34*r[1]))//use the smallest radius
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//now that the radius has been determined, find tangent points and circle centre
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let(tangD=newR/tan(a3/2))//distance to the tangent point from p3
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let(circD=newR/sin(a3/2))//distance to the circle centre from p3
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//find the angle from the p3
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let(an23=getAngle(p[1],p[2]))//angle from point 3 to 2
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let(an34=getAngle(p[3],p[2]))//angle from point 3 to 4
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//find tangent points
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let(t23=[p[2][0]-cos(an23)*tangD,p[2][1]-sin(an23)*tangD])//tangent point between points 2&3
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let(t34=[p[2][0]-cos(an34)*tangD,p[2][1]-sin(an34)*tangD])//tangent point between points 3&4
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//find circle centre
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let(tmid=getMidpoint(t23,t34))//midpoint between the two tangent points
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let(anCen=getAngle(tmid,p[2]))//angle from point 3 to circle centre
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let(cen=[p[2][0]-cos(anCen)*circD,p[2][1]-sin(anCen)*circD])//circle center by offseting from point 3
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F23=(d23*tan(a2/2)*tan(a3/2))/(r[0]*tan(a3/2)+r[1]*tan(a2/2)),
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F34=(d34*tan(a3/2)*tan(a4/2))/(r[1]*tan(a4/2)+r[2]*tan(a3/2)),
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newR=min(r[1],F23*r[1],F34*r[1]),//use the smallest radius
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//now that the radius has been determined, find tangent points and circle centre
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tangD=newR/tan(a3/2),//distance to the tangent point from p3
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circD=newR/sin(a3/2),//distance to the circle centre from p3
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//find the angle from the p3
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an23=getAngle(p[1],p[2]),//angle from point 3 to 2
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an34=getAngle(p[3],p[2]),//angle from point 3 to 4
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//find tangent points
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t23=[p[2][0]-cos(an23)*tangD,p[2][1]-sin(an23)*tangD],//tangent point between points 2&3
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t34=[p[2][0]-cos(an34)*tangD,p[2][1]-sin(an34)*tangD],//tangent point between points 3&4
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//find circle centre
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tmid=getMidpoint(t23,t34),//midpoint between the two tangent points
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anCen=getAngle(tmid,p[2]),//angle from point 3 to circle centre
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cen=[p[2][0]-cos(anCen)*circD,p[2][1]-sin(anCen)*circD]
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)
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//circle center by offseting from point 3
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//determine the direction of rotation
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debug==0?//if debug in disabled return arc (default)
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[t23,t34,cen]
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:(newR-r[1]);
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function polycarious(radiipoints,fn=5)=
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let(p=getpoints(radiipoints))
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let(newrp=[for(i=[0:len(p)-1])
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let(the3points=[for(j=[-1:1]) p[wrap(i+j,len(p))]])
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if(isColinear(the3points[0],the3points[1],the3points[2])==0) radiipoints[wrap(i+0,len(p))]
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])
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let(temp=[for(i=[0:len(newrp)-1])
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let(the3points=[for(j=[-1:1]) newrp[wrap(i+j,len(newrp))]])//collect 3 points
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let(temp2=round3points(the3points,fn))
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newrp[i][2]==0?[[newrp[i][0],newrp[i][1]]]: //return the original point if the radius is 0
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CentreN2PointsArc(temp2[0],temp2[1],temp2[2],0,fn) //return the arc if everything is normal
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])
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[for (a = temp) for (b = a) b]; //flattern and return the array
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function round3points(rp,fn)=
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debug==1?//if debug in disabled return arc (default)
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(newR-r[1]):
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[t23,t34,cen];}
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{function round3points(rp,fn)=
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rp[1][2]==0?[[rp[1][0],rp[1][1]]]://return the middle point if the radius is 0
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let(p=getpoints(rp)) //get list of points
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let(r=rp[1][2])//get the centre 3 radii
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let(ang=cosineRuleAngle(p[0],p[1],p[2]))//angle between the lines
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let(
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p=getpoints(rp), //get list of points
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r=rp[1][2],//get the centre 3 radii
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ang=cosineRuleAngle(p[0],p[1],p[2]),//angle between the lines
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//now that the radius has been determined, find tangent points and circle centre
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let(tangD=r/tan(ang/2))//distance to the tangent point from p2
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let(circD=r/sin(ang/2))//distance to the circle centre from p2
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//find the angles from the p2 with respect to the postitive x axis
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let(a12=getAngle(p[0],p[1]))//angle from point 2 to 1
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let(a23=getAngle(p[2],p[1]))//angle from point 2 to 3
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//find tangent points
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let(t12=[p[1][0]-cos(a12)*tangD,p[1][1]-sin(a12)*tangD])//tangent point between points 1&2
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let(t23=[p[1][0]-cos(a23)*tangD,p[1][1]-sin(a23)*tangD])//tangent point between points 2&3
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tangD=r/tan(ang/2),//distance to the tangent point from p2
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circD=r/sin(ang/2),//distance to the circle centre from p2
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//find the angles from the p2 with respect to the postitive x axis
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a12=getAngle(p[0],p[1]),//angle from point 2 to 1
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a23=getAngle(p[2],p[1]),//angle from point 2 to 3
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//find tangent points
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t12=[p[1][0]-cos(a12)*tangD,p[1][1]-sin(a12)*tangD],//tangent point between points 1&2
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t23=[p[1][0]-cos(a23)*tangD,p[1][1]-sin(a23)*tangD],//tangent point between points 2&3
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//find circle centre
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let(tmid=getMidpoint(t12,t23))//midpoint between the two tangent points
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let(angCen=getAngle(tmid,p[1]))//angle from point 2 to circle centre
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let(cen=[p[1][0]-cos(angCen)*circD,p[1][1]-sin(angCen)*circD])//circle center by offseting from point 2
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[t12,t23,cen];
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//CentreN2PointsArc(t12,t23,cen,0,fn);
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function CentreN2PointsArc(p1,p2,cen,mode=0,fn)=
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tmid=getMidpoint(t12,t23),//midpoint between the two tangent points
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angCen=getAngle(tmid,p[1]),//angle from point 2 to circle centre
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cen=[p[1][0]-cos(angCen)*circD,p[1][1]-sin(angCen)*circD] //circle center by offseting from point 2
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)
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[t12,t23,cen];}
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{function parallelFollow(rp,thick=4,minR=1,mode=1)=
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//rp[1][2]==0?[rp[1][0],rp[1][1],0]://return the middle point if the radius is 0
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thick==0?[rp[1][0],rp[1][1],0]://return the middle point if the radius is 0
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let(
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p=getpoints(rp), //get list of points
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r=thick,//get the centre 3 radii
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ang=cosineRuleAngle(p[0],p[1],p[2]),//angle between the lines
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//now that the radius has been determined, find tangent points and circle centre
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tangD=r/tan(ang/2),//distance to the tangent point from p2
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sgn=CWorCCW(rp),//rotation of the three points cw or ccw?let(sgn=mode==0?1:-1)
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circD=mode*sgn*r/sin(ang/2),//distance to the circle centre from p2
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//find the angles from the p2 with respect to the postitive x axis
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a12=getAngle(p[0],p[1]),//angle from point 2 to 1
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a23=getAngle(p[2],p[1]),//angle from point 2 to 3
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//find tangent points
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t12=[p[1][0]-cos(a12)*tangD,p[1][1]-sin(a12)*tangD],//tangent point between points 1&2
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t23=[p[1][0]-cos(a23)*tangD,p[1][1]-sin(a23)*tangD],//tangent point between points 2&3
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//find circle centre
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tmid=getMidpoint(t12,t23),//midpoint between the two tangent points
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angCen=getAngle(tmid,p[1]),//angle from point 2 to circle centre
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cen=[p[1][0]-cos(angCen)*circD,p[1][1]-sin(angCen)*circD],//circle center by offseting from point 2
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||||
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.
|
||||
the mode determines how the arc is plotted
|
||||
mode==0, shortest arc possible
|
||||
@@ -173,58 +328,62 @@ function CentreN2PointsArc(p1,p2,cen,mode=0,fn)=
|
||||
mode==2, plotted clockwise
|
||||
mode==3, plotted counter clockwise
|
||||
*/
|
||||
//determine the direction of rotation
|
||||
let(e1=(cen[0]-p1[0])*(cen[1]+p1[1]))//edge 1
|
||||
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?
|
||||
let(
|
||||
CWorCCW=CWorCCW([cen,p1,p2]),//determine the direction of rotation
|
||||
//determine the arc angle depending on the mode
|
||||
let(p1p2Angle=cosineRuleAngle(p2,cen,p1))
|
||||
let(arcAngle=
|
||||
p1p2Angle=cosineRuleAngle(p2,cen,p1),
|
||||
arcAngle=
|
||||
mode==0?p1p2Angle:
|
||||
mode==1?p1p2Angle-360:
|
||||
mode==2&&CWorCCW==-1?p1p2Angle:
|
||||
mode==2&&CWorCCW== 1?p1p2Angle-360:
|
||||
mode==3&&CWorCCW== 1?p1p2Angle:
|
||||
mode==3&&CWorCCW==-1?p1p2Angle-360:
|
||||
cosineRuleAngle(p2,cen,p1))
|
||||
let(r=pointDist(p1,cen))//determine the radius
|
||||
let(p1Angle=getAngle(cen,p1))//angle of line 1
|
||||
[for(i=[0:fn]) [cos(p1Angle+(arcAngle/fn)*i*CWorCCW)*r+cen[0],sin(p1Angle+(arcAngle/fn)*i*CWorCCW)*r+cen[1]]];
|
||||
|
||||
function invtan(run,rise)=
|
||||
cosineRuleAngle(p2,cen,p1)
|
||||
,
|
||||
r=pointDist(p1,cen),//determine the radius
|
||||
p1Angle=getAngle(cen,p1) //angle of line 1
|
||||
)
|
||||
[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)))
|
||||
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)=
|
||||
let(p12=abs(pointDist(p1,p2)))
|
||||
let(p13=abs(pointDist(p1,p3)))
|
||||
let(p23=abs(pointDist(p2,p3)))
|
||||
acos((sq(p23)+sq(p12)-sq(p13))/(2*p23*p12));
|
||||
|
||||
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)=
|
||||
let(
|
||||
p12=abs(pointDist(p1,p2)),
|
||||
p13=abs(pointDist(p1,p3)),
|
||||
p23=abs(pointDist(p2,p3))
|
||||
)
|
||||
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 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 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 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) )]);
|
||||
} // polyline plotter
|
||||
|
||||
module line(p1, p2 ,width=0.3)
|
||||
{ // single line plotter
|
||||
module line(p1, p2 ,width=0.3) { // single line plotter
|
||||
hull() {
|
||||
translate(p1) sphere(width);
|
||||
translate(p2) sphere(width);
|
||||
translate(p1) circle(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 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 == [] ?
|
||||
(rands(min(a, b), max( a, b), 1)[0])
|
||||
:
|
||||
(rands(min(a, b), max(a, b), 1, s)[0])
|
||||
; // nice rands wrapper
|
||||
;} // nice rands wrapper
|
||||
|
||||
Reference in New Issue
Block a user