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// Library: round-anything
// Version: 1.0
// Author: IrevDev
// Contributors: TLC123
// Copyright: 2017
// License: GPL 3
//examples();
module examples(){
//Example of how a parametric part might be designed with this tool
width=20; height=25;
slotW=8; slotH=15;
slotPosition=8;
minR=1.5; farcornerR=6;
internalR=3;
points=[
[0, 0, farcornerR],
[0, height, minR],
[slotPosition, height, minR],
[slotPosition, height-slotH, internalR],
[slotPosition+slotW, height-slotH, internalR],
[slotPosition+slotW, height, minR],
[width, height, minR],
[width, 0, minR]
];
points2=[
[0, 0, farcornerR],
["l", height, minR],
[slotPosition, "l", minR],
["l", height-slotH, internalR],
[slotPosition+slotW, "l", internalR],
["l", height, minR],
[width, "l", minR],
["l", height*0.2, minR],
[45, 0, minR+5, "ayra"]
];//,["l",0,minR]];
echo(processRadiiPoints(points2));
translate([-25,0,0]){
polygon(polyRound(points,5));
}
%translate([-25,0,0.2]){
polygon(getpoints(points));//transparent copy of the polgon without rounding
}
translate([-50,0,0]){
polygon(polyRound(points2,5));
}
%translate([-50,0,0.2]){
polygon(getpoints(processRadiiPoints(points2)));//transparent copy of the polgon without rounding
}
//Example of features 2
// 1 2 3 4 5 6
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));
%translate([0,0,0.3])polygon(getpoints(b));//transparent copy of the polgon without rounding
//Example of features 3
// 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
a=polyRound(p,5);
translate([25,0,0]){
polygon(a);
}
%translate([25,0,0.2]){
polygon(getpoints(p));//transparent copy of the polgon without rounding
}
//example of radii conflict handling and debuging feature
r1a=10; r1b=10;
r2a=30; r2b=30;
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
translate([-25,-30,0]){
polygon(polyRound(c1,8));
}
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
translate([0,-30,0]){
polygon(polyRound(c2,8));
}
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
translate([25,-30,0]){
polygon(polyRound(c3,8));
}
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,
//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
random=[for(i=[0:20])[rnd(0,50),rnd(0,50),/*rnd(0,30)*/1000]];
R =polyRound(random,7);
translate([-25,25,0]){
polyline(R);
}
//example of different modes of the CentreN2PointsArc() function 0=shortest arc, 1=longest arc, 2=CW, 3=CCW
p1=[0,5];p2=[10,5];centre=[5,0];
translate([60,0,0]){
color("green"){
polygon(CentreN2PointsArc(p1,p2,centre,0,20));//draws the shortest arc
}
color("cyan"){
polygon(CentreN2PointsArc(p1,p2,centre,1,20));//draws the longest arc
}
}
translate([75,0,0]){
color("purple"){
polygon(CentreN2PointsArc(p1,p2,centre,2,20));//draws the arc CW (which happens to be the short arc)
}
color("red"){
polygon(CentreN2PointsArc(p2,p1,centre,2,20));//draws the arc CW but p1 and p2 swapped order resulting in the long arc being drawn
}
}
radius=6;
radiipoints=[[0,0,0],[10,20,radius],[20,0,0]];
tangentsNcen=round3points(radiipoints);
translate([100,0,0]){
for(i=[0:2]){
color("red")translate(getpoints(radiipoints)[i])circle(1);//plots the 3 input points
color("cyan")translate(tangentsNcen[i])circle(1);//plots the two tangent poins and the circle centre
}
translate([tangentsNcen[2][0],tangentsNcen[2][1],-0.2])circle(r=radius,$fn=25);//draws the cirle
%polygon(getpoints(radiipoints));//draws a polygon
}
//for(i=[0:len(b2)-1]) translate([b2[i].x,b2[i].y,2])#circle(0.2);
ex=[[0,0,-1],[2,8,0],[5,4,3],[15,10,0.5],[10,2,1]];
translate([15,-50,0]){
ang=55;
minR=0.2;
rotate([0,0,ang+270])translate([0,-5,0])square([10,10],true);
clipP=[[9,1,0],[9,0,0],[9.5,0,0],[9.5,1,0.2],[10.5,1,0.2],[10.5,0,0],[11,0,0],[11,1,0]];
a=RailCustomiser(ex,o1=0.5,minR=minR,a1=ang-90,a2=0,mode=2);
b=revList(RailCustomiser(ex,o1=-0.5,minR=minR,a1=ang-90,a2=0,mode=2));
points=concat(a,clipP,b);
points2=concat(ex,clipP,b);
polygon(polyRound(points,20));
//%polygon(polyRound(points2,20));
}
//the following exapmle shows how the offsets in RailCustomiser could be used to makes shells
translate([-20,-60,0]){
for(i=[-9:0.5:1])polygon(polyRound(RailCustomiser(ex,o1=i-0.4,o2=i,minR=0.1),20));
}
// This example shows how a list of points can be used multiple times in the same
nutW=5.5; nutH=3; boltR=1.6;
minT=2; minR=0.8;
nutCapture=[
[-boltR, 0, 0],
[-boltR, minT, 0],
[-nutW/2, minT, minR],
[-nutW/2, minT+nutH, minR],
[nutW/2, minT+nutH, minR],
[nutW/2, minT, minR],
[boltR, minT, 0],
[boltR, 0, 0],
];
aSquare=concat(
[[0,0,0]],
moveRadiiPoints(nutCapture,tran=[5,0],rot=0),
[[20,0,0]],
moveRadiiPoints(nutCapture,tran=[20,5],rot=90),
[[20,10,0]],
[[0,10,0]]
);
echo(aSquare);
translate([40,-60,0]){
polygon(polyRound(aSquare,20));
translate([10,12,0])polygon(polyRound(nutCapture,20));
}
translate([70,-52,0]){
a=mirrorPoints(ex,0,[1,0]);
polygon(polyRound(a,20));
}
translate([0,-90,0]){
r_extrude(3,0.5*$t,0.5*$t,100)polygon(polyRound(b,30));
#translate([7,4,3])r_extrude(3,-0.5,0.95,100)circle(1,$fn=30);
}
translate([-30,-90,0])
shell2d(-0.5,0,0)polygon(polyRound(b,30));
}
function polyRound(radiipoints,fn=5,mode=0)=
/*Takes a list of radii points of the format [x,y,radius] and rounds each point
with fn resolution
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
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)]
],
newrp2=processRadiiPoints(newrp),
temp=[
for(i=[0:len(newrp2)-1]) //for each point in the radii array
let(
thepoints=[for(j=[-getpoints:getpoints])newrp2[wrap(i+j,len(newrp2))]],//collect 5 radii points
temp2=mode==2?round3points(thepoints,fn):round5points(thepoints,fn,mode)
)
mode==1?temp2:newrp2[i][2]==0?
[[newrp2[i][0],newrp2[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 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
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]) abs(rp[i][2])],//get the centre 3 radii
//start by determining what the radius should be at point 3
//find angles at points 2 , 3 and 4
a2=cosineRuleAngle(p[0],p[1],p[2]),
a3=cosineRuleAngle(p[1],p[2],p[3]),
a4=cosineRuleAngle(p[2],p[3],p[4]),
//find the distance between points 2&3 and between points 3&4
d23=pointDist(p[1],p[2]),
d34=pointDist(p[2],p[3]),
//find the radius factors
F23=(d23*tan(a2/2)*tan(a3/2))/(r[0]*tan(a3/2)+r[1]*tan(a2/2)),
F34=(d34*tan(a3/2)*tan(a4/2))/(r[1]*tan(a4/2)+r[2]*tan(a3/2)),
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
tangD=newR/tan(a3/2),//distance to the tangent point from p3
circD=newR/sin(a3/2),//distance to the circle centre from p3
//find the angle from the p3
an23=getAngle(p[1],p[2]),//angle from point 3 to 2
an34=getAngle(p[3],p[2]),//angle from point 3 to 4
//find tangent points
t23=[p[2][0]-cos(an23)*tangD,p[2][1]-sin(an23)*tangD],//tangent point between points 2&3
t34=[p[2][0]-cos(an34)*tangD,p[2][1]-sin(an34)*tangD],//tangent point between points 3&4
//find circle centre
tmid=getMidpoint(t23,t34),//midpoint between the two tangent points
anCen=getAngle(tmid,p[2]),//angle from point 3 to circle centre
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
debug==1?//if debug in disabled return arc (default)
(newR-r[1]):
[t23,t34,cen];
function round3points(rp,fn)=
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
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
tangD=r/tan(ang/2),//distance to the tangent point 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
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
)
[t12,t23,cen];
function parallelFollow(rp,thick=4,minR=1,mode=1)=
//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.
the mode determines how the arc is plotted
mode==0, shortest arc possible
mode==1, longest arc possible
mode==2, plotted clockwise
mode==3, plotted counter clockwise
*/
let(
CWorCCW=CWorCCW([cen,p1,p2]),//determine the direction of rotation
//determine the arc angle depending on the mode
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)
,
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
];
module round2d(OR=3,IR=1){
offset(OR){
offset(-IR-OR){
offset(IR){
children();
}
}
}
}
module shell2d(o1,OR=0,IR=0,o2=0){
difference(){
round2d(OR,IR){
offset(max(o1,o2)){
children(0);//original 1st child forms the outside of the shell
}
}
round2d(IR,OR){
difference(){//round the inside cutout
offset(min(o1,o2)){
children(0);//shrink the 1st child to form the inside of the shell
}
if($children>1){
for(i=[1:$children-1]){
children(i);//second child and onwards is used to add material to inside of the shell
}
}
}
}
}
}
module internalSq(size,r,center=0){
tran=center==1?[0,0]:size/2;
translate(tran){
square(size,true);
offs=sin(45)*r;
for(i=[-1,1],j=[-1,1]){
translate([(size.x/2-offs)*i,(size.y/2-offs)*j])circle(r);
}
}
}
module r_extrude(ln,r1=0,r2=0,fn=30){
n1=sign(r1);n2=sign(r2);
r1=abs(r1);r2=abs(r2);
translate([0,0,r1]){
linear_extrude(ln-r1-r2){
children();
}
}
for(i=[0:1/fn:1]){
translate([0,0,i*r1]){
linear_extrude(r1/fn){
offset(n1*sqrt(sq(r1)-sq(r1-i*r1))-n1*r1){
children();
}
}
}
translate([0,0,ln-r2+i*r2]){
linear_extrude(r2/fn){
offset(n2*sqrt(sq(r2)-sq(i*r2))-n2*r2){
children();
}
}
}
}
}
function mirrorPoints(b,rot=0,atten=[0,0])= //mirrors a list of points about Y, ignoring the first and last points and returning them in reverse order for use with polygon or polyRound
let(
a=moveRadiiPoints(b,[0,0],-rot),
temp3=[for(i=[0+atten[0]:len(a)-1-atten[1]])
[a[i][0],-a[i][1],a[i][2]]
],
temp=moveRadiiPoints(temp3,[0,0],rot),
temp2=revList(temp3)
)
concat(b,temp2);
function processRadiiPoints(rp)=
[for(i=[0:len(rp)-1])
processRadiiPoints2(rp,i)
];
function processRadiiPoints2(list,end=0,idx=0,result=0)=
idx>=end+1?result:
processRadiiPoints2(list,end,idx+1,relationalRadiiPoints(result,list[idx]));
function cosineRuleBside(a,c,C)=c*cos(C)-sqrt(sq(a)+sq(c)+sq(cos(C))-sq(c));
function absArelR(po,pn)=
let(
th2=atan(po[1]/po[0]),
r2=sqrt(sq(po[0])+sq(po[1])),
r3=cosineRuleBside(r2,pn[1],th2-pn[0])
)
[cos(pn[0])*r3,sin(pn[0])*r3,pn[2]];
function relationalRadiiPoints(po,pi)=
let(
p0=pi[0],
p1=pi[1],
p2=pi[2],
pv0=pi[3][0],
pv1=pi[3][1],
pt0=pi[3][2],
pt1=pi[3][3],
pn=
(pv0=="y"&&pv1=="x")||(pv0=="r"&&pv1=="a")||(pv0=="y"&&pv1=="a")||(pv0=="x"&&pv1=="a")||(pv0=="y"&&pv1=="r")||(pv0=="x"&&pv1=="r")?
[p1,p0,p2,concat(pv1,pv0,pt1,pt0)]:
[p0,p1,p2,concat(pv0,pv1,pt0,pt1)],
n0=pn[0],
n1=pn[1],
n2=pn[2],
nv0=pn[3][0],
nv1=pn[3][1],
nt0=pn[3][2],
nt1=pn[3][3],
temp=
pn[0]=="l"?
[po[0],pn[1],pn[2]]
:pn[1]=="l"?
[pn[0],po[1],pn[2]]
:nv0==undef?
[pn[0],pn[1],pn[2]]//abs x, abs y as default when undefined
:nv0=="a"?
nv1=="r"?
nt0=="a"?
nt1=="a"||nt1==undef?
[cos(n0)*n1,sin(n0)*n1,n2]//abs angle, abs radius
:absArelR(po,pn)//abs angle rel radius
:nt1=="r"||nt1==undef?
[po[0]+cos(pn[0])*pn[1],po[1]+sin(pn[0])*pn[1],pn[2]]//rel angle, rel radius
:[pn[0],pn[1],pn[2]]//rel angle, abs radius
:nv1=="x"?
nt0=="a"?
nt1=="a"||nt1==undef?
[pn[1],pn[1]*tan(pn[0]),pn[2]]//abs angle, abs x
:[po[0]+pn[1],(po[0]+pn[1])*tan(pn[0]),pn[2]]//abs angle rel x
:nt1=="r"||nt1==undef?
[po[0]+pn[1],po[1]+pn[1]*tan(pn[0]),pn[2]]//rel angle, rel x
:[pn[1],po[1]+(pn[1]-po[0])*tan(pn[0]),pn[2]]//rel angle, abs x
:nt0=="a"?
nt1=="a"||nt1==undef?
[pn[1]/tan(pn[0]),pn[1],pn[2]]//abs angle, abs y
:[(po[1]+pn[1])/tan(pn[0]),po[1]+pn[1],pn[2]]//abs angle rel y
:nt1=="r"||nt1==undef?
[po[0]+(pn[1]-po[0])/tan(90-pn[0]),po[1]+pn[1],pn[2]]//rel angle, rel y
:[po[0]+(pn[1]-po[1])/tan(pn[0]),pn[1],pn[2]]//rel angle, abs y
:nv0=="r"?
nv1=="x"?
nt0=="a"?
nt1=="a"||nt1==undef?
[pn[1],sign(pn[0])*sqrt(sq(pn[0])-sq(pn[1])),pn[2]]//abs radius, abs x
:[po[0]+pn[1],sign(pn[0])*sqrt(sq(pn[0])-sq(po[0]+pn[1])),pn[2]]//abs radius rel x
:nt1=="r"||nt1==undef?
[po[0]+pn[1],po[1]+sign(pn[0])*sqrt(sq(pn[0])-sq(pn[1])),pn[2]]//rel radius, rel x
:[pn[1],po[1]+sign(pn[0])*sqrt(sq(pn[0])-sq(pn[1]-po[0])),pn[2]]//rel radius, abs x
:nt0=="a"?
nt1=="a"||nt1==undef?
[sign(pn[0])*sqrt(sq(pn[0])-sq(pn[1])),pn[1],pn[2]]//abs radius, abs y
:[sign(pn[0])*sqrt(sq(pn[0])-sq(po[1]+pn[1])),po[1]+pn[1],pn[2]]//abs radius rel y
:nt1=="r"||nt1==undef?
[po[0]+sign(pn[0])*sqrt(sq(pn[0])-sq(pn[1])),po[1]+pn[1],pn[2]]//rel radius, rel y
:[po[0]+sign(pn[0])*sqrt(sq(pn[0])-sq(pn[1]-po[1])),pn[1],pn[2]]//rel radius, abs y
:nt0=="a"?
nt1=="a"||nt1==undef?
[pn[0],pn[1],pn[2]]//abs x, abs y
:[pn[0],po[1]+pn[1],pn[2]]//abs x rel y
:nt1=="r"||nt1==undef?
[po[0]+pn[0],po[1]+pn[1],pn[2]]//rel x, rel y
:[po[0]+pn[0],pn[1],pn[2]]//rel x, abs y
)
temp;
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)),
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.y-p1.y)/(p2.x-p1.x);
function getAngle(p1,p2)=p1==p2?0: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
hull() {
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 = []) =
s == [] ?
(rands(min(a, b), max( a, b), 1)[0]):(rands(min(a, b), max(a, b), 1, s)[0]); // nice rands wrapper
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