diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..7372184 --- /dev/null +++ b/LICENSE @@ -0,0 +1,7 @@ +Copyright 2020 Kurt Hutten + +Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/MinkowskiRound.scad b/MinkowskiRound.scad index 8ad2127..35e6900 100644 --- a/MinkowskiRound.scad +++ b/MinkowskiRound.scad @@ -1,8 +1,8 @@ // Library: MinkowskiRound.scad // Version: 1.0 // Author: IrevDev -// Copyright: 2017 -// License: GPL 3 +// Copyright: 2020 +// License: MIT /* ---Modules @@ -38,71 +38,75 @@ Both this modules do the same thing as minkowskiRound() but focus on either insi //}//--I rendered this out with a $fn=25 and it took more than 12 hours on my computer - - module round2d(OR=3,IR=1){ - offset(OR)offset(-IR-OR)offset(IR)children(); + offset(OR){ + offset(-IR-OR){ + offset(IR){ + children(); + } + } + } } module minkowskiRound(OR=1,IR=1,enable=1,cubeSize=[500,500,500]){ - if(enable==0){//do nothing if not enabled - children(); - } else { - minkowski(){//expand the now positive shape back out - difference(){//make the negative shape positive again - cube(cubeSize-[0.1,0.1,0.1],center=true); - minkowski(){//expand the negative shape inwards - difference(){//create a negative of the children - cube(cubeSize,center=true); - minkowski(){//expand the children - children(); - sphere(IR); - } - } - sphere(OR+IR); - } + if(enable==0){//do nothing if not enabled + children(); + } else { + minkowski(){//expand the now positive shape back out + difference(){//make the negative shape positive again + cube(cubeSize-[0.1,0.1,0.1],center=true); + minkowski(){//expand the negative shape inwards + difference(){//create a negative of the children + cube(cubeSize,center=true); + minkowski(){//expand the children + children(); + sphere(IR); } - sphere(OR); + } + sphere(OR+IR); } + } + sphere(OR); } + } } module minkowskiOutsideRound(r=1,enable=1,cubeSize=[500,500,500]){ - if(enable==0){//do nothing if not enabled - children(); - } else { - minkowski(){//expand the now positive shape - difference(){//make the negative positive - cube(cubeSize-[0.1,0.1,0.1],center=true); - minkowski(){//expand the negative inwards - difference(){//create a negative of the children - cube(cubeSize,center=true); - children(); - } - sphere(r); - } - } - sphere(r); + if(enable==0){//do nothing if not enabled + children(); + } else { + minkowski(){//expand the now positive shape + difference(){//make the negative positive + cube(cubeSize-[0.1,0.1,0.1],center=true); + minkowski(){//expand the negative inwards + difference(){//create a negative of the children + cube(cubeSize,center=true); + children(); + } + sphere(r); } + } + sphere(r); } + } } module minkowskiInsideRound(r=1,enable=1,cubeSize=[500,500,500]){ - if(enable==0){//do nothing if not enabled - children(); - } else { - difference(){//make the negative positive again - cube(cubeSize-[0.1,0.1,0.1],center=true); - minkowski(){//expand the negative shape inwards - difference(){//make the expanded children a negative shape - cube(cubeSize,center=true); - minkowski(){//expand the children - children(); - sphere(r); - } - } - sphere(r); - } + if(enable==0){//do nothing if not enabled + children(); + } else { + difference(){//make the negative positive again + cube(cubeSize-[0.1,0.1,0.1],center=true); + minkowski(){//expand the negative shape inwards + difference(){//make the expanded children a negative shape + cube(cubeSize,center=true); + minkowski(){//expand the children + children(); + sphere(r); + } } + sphere(r); + } } -} + } +} \ No newline at end of file diff --git a/polyround.scad b/polyround.scad index d043e15..126df1e 100644 --- a/polyround.scad +++ b/polyround.scad @@ -2,176 +2,227 @@ // Version: 1.0 // Author: IrevDev // Contributors: TLC123 -// Copyright: 2017 -// License: GPL 3 +// Copyright: 2020 +// License: MIT //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 + //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 } - 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 + color("cyan"){ + polygon(CentreN2PointsArc(p1,p2,centre,1,20));//draws the longest arc } - - 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)); + } + translate([75,0,0]){ + color("purple"){ + polygon(CentreN2PointsArc(p1,p2,centre,2,20));//draws the arc CW (which happens to be the short arc) } - - //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)); + 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 } - - // 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( + } + + 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,$fn=25);//draws the cirle + %polygon(getpoints(radiipoints));//draws a polygon + } + + //for(i=[0:len(b2)-1]) translate([b2[i].x,b2[i].y,2])#circle(0.2); + ex=[[0,0,-1],[2,8,0],[5,4,3],[15,10,0.5],[10,2,1]]; + translate([15,-50,0]){ + ang=55; + minR=0.2; + rotate([0,0,ang+270])translate([0,-5,0])square([10,10],true); + clipP=[[9,1,0],[9,0,0],[9.5,0,0],[9.5,1,0.2],[10.5,1,0.2],[10.5,0,0],[11,0,0],[11,1,0]]; + a=RailCustomiser(ex,o1=0.5,minR=minR,a1=ang-90,a2=0,mode=2); + b=revList(RailCustomiser(ex,o1=-0.5,minR=minR,a1=ang-90,a2=0,mode=2)); + points=concat(a,clipP,b); + points2=concat(ex,clipP,b); + polygon(polyRound(points,20)); + //%polygon(polyRound(points2,20)); + } + + //the following exapmle shows how the offsets in RailCustomiser could be used to makes shells + translate([-20,-60,0]){ + for(i=[-9:0.5:1])polygon(polyRound(RailCustomiser(ex,o1=i-0.4,o2=i,minR=0.1),20)); + } + + // This example shows how a list of points can be used multiple times in the same + nutW=5.5; nutH=3; boltR=1.6; + minT=2; minR=0.8; + nutCapture=[ + [-boltR, 0, 0], + [-boltR, minT, 0], + [-nutW/2, minT, minR], + [-nutW/2, minT+nutH, minR], + [nutW/2, minT+nutH, minR], + [nutW/2, minT, minR], + [boltR, minT, 0], + [boltR, 0, 0], + ]; + aSquare=concat( [[0,0,0]], moveRadiiPoints(nutCapture,tran=[5,0],rot=0), [[20,0,0]], moveRadiiPoints(nutCapture,tran=[20,5],rot=90), [[20,10,0]], [[0,10,0]] - ); - echo(aSquare); - translate([40,-60,0]){ - polygon(polyRound(aSquare,20)); - translate([10,12,0])polygon(polyRound(nutCapture,20)); - } - - translate([70,-52,0]){ - a=mirrorPoints(ex,0,[1,0]); - polygon(polyRound(a,20)); - } + ); + echo(aSquare); + translate([40,-60,0]){ + polygon(polyRound(aSquare,20)); + translate([10,12,0])polygon(polyRound(nutCapture,20)); + } + + translate([70,-52,0]){ + a=mirrorPoints(ex,0,[1,0]); + polygon(polyRound(a,20)); + } - - translate([0,-90,0]){ - r_extrude(3,0.5*$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([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)); - + 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 + +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)= + 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( @@ -189,348 +240,424 @@ module examples(){ 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] - ) + //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 + [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 + 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 + 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 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)= + 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 + 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) + 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 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, + 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 + +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)); - 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)= +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 - */ + 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) + 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)= + 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 - ) + 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(); + 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:$children-1])children(i);//second child and onwards is used to add material to inside of the shell + round2d(OR,IR){ + offset(max(o1,o2)){ + children(0);//original 1st child forms the outside of the shell + } + } + round2d(IR,OR){ + difference(){//round the inside cutout + offset(min(o1,o2)){ + children(0);//shrink the 1st child to form the inside of the shell + } + if($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(); + 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); + } } } -{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);} +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)]; + [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])); + 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]]; + 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 + 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[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( + [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]);} + ) + 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) )]); +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); + 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 = []) = +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 \ No newline at end of file + (rands(min(a, b), max( a, b), 1)[0]):(rands(min(a, b), max(a, b), 1, s)[0]); // nice rands wrapper \ No newline at end of file