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// Library: round-anything
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// Version: 1.0
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// Author: IrevDev
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// Contributors: TLC123
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// Copyright: 2020
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// License: MIT
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function addZcoord(points,displacement)=[for(i=[0:len(points)-1])[points[i].x,points[i].y, displacement]];
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function translate3Dcoords(points,tran=[0,0,0],mult=[1,1,1])=[for(i=[0:len(points)-1])[
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(points[i].x*mult.x)+tran.x,
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(points[i].y*mult.y)+tran.y,
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(points[i].z*mult.z)+tran.z
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]];
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function offsetPolygonPoints(points, offset=0)=
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// Work sthe same as the offset does, except for the fact that instead of a 2d shape
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// It works directly on polygon points
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// It returns the same number of points just offset into or, away from the original shape.
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// points= a series of x,y points[[x1,y1],[x2,y2],...]
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// offset= amount to offset by, negative numbers go inwards into the shape, positive numbers go out
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// return= a series of x,y points[[x1,y1],[x2,y2],...]
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let(
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isCWorCCW=sign(offset)*CWorCCW(points)*-1,
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lp=len(points)
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)
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[for(i=[0:lp-1]) parallelFollow([
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points[listWrap(i-1,lp)],
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points[i],
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points[listWrap(i+1,lp)],
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],thick=offset,mode=isCWorCCW)];
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function makeCurvedPartOfPolyHedron(radiiPoints,r,fn,minR=0.01)=
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// this is a private function that I'm not expecting library users to use directly
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// radiiPoints= serise of x, y, r points
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// r= radius of curve that will be put on the end of the extrusion
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// fn= amount of subdivisions
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// minR= if one of the points in radiiPoints is less than r, it's likely to converge and form a sharp edge,
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// the min radius on these converged edges can be controled with minR, though because of legacy reasons it can't be 0, but can be a very small number.
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// return= array of [polyhedronPoints, Polyhedronfaces, theLength of a singe layer in the curve]
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let(
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lp=len(radiiPoints),
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radii=[for(i=[0:lp-1])radiiPoints[i].z],
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isCWorCCWOverall=CWorCCW(radiiPoints),
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dir=sign(r),
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absR=abs(r),
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fractionOffLp=1-1/fn,
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allPoints=[for(fraction=[0:1/fn:1])
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let(
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iterationOffset=dir*sqrt(sq(absR)-sq(fraction*absR))-dir*absR,
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theOffsetPoints=offsetPolygonPoints(radiiPoints,iterationOffset),
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polyRoundOffsetPoints=[for(i=[0:lp-1])
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let(
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pointsAboutCurrent=[
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theOffsetPoints[listWrap(i-1,lp)],
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theOffsetPoints[i],
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theOffsetPoints[listWrap(i+1,lp)]
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],
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isCWorCCWLocal=CWorCCW(pointsAboutCurrent),
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isInternalRadius=(isCWorCCWLocal*isCWorCCWOverall)==-1,
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// the radius names are only true for positive r,
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// when are r is negative increasingRadius is actually decreasing and vice-vs
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// increasingRadiusWithPositiveR is just to verbose of a variable name for my liking
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increasingRadius=max(radii[i]-iterationOffset, minR),
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decreasingRadius=max(radii[i]+iterationOffset, minR)
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)
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[theOffsetPoints[i].x, theOffsetPoints[i].y, isInternalRadius? increasingRadius: decreasingRadius]
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],
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pointsForThisLayer=polyRound(polyRoundOffsetPoints,fn)
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)
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addZcoord(pointsForThisLayer,fraction*absR)
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],
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polyhedronPoints=flatternArray(allPoints),
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allLp=len(allPoints),
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layerLength=len(allPoints[0]),
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loopToSecondLastLayer=allLp-2,
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sideFaces=[for(layerIndex=[0:loopToSecondLastLayer])let(
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currentLayeroffset=layerIndex*layerLength,
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nextLayeroffset=(layerIndex+1)*layerLength,
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layerFaces=[for(subLayerIndex=[0:layerLength-1])
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[
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currentLayeroffset+subLayerIndex, currentLayeroffset + listWrap(subLayerIndex+1,layerLength), nextLayeroffset+listWrap(subLayerIndex+1,layerLength), nextLayeroffset+subLayerIndex]
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]
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)layerFaces],
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polyhedronFaces=flatternArray(sideFaces)
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)
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[polyhedronPoints, polyhedronFaces, layerLength];
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function flatternRecursion(array, init=[], currentIndex)=
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// this is a private function, init and currentIndex are for the function's use
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// only for when it's calling itself, which is why there is a simplified version flatternArray that just calls this one
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// array= array to flattern by one level of nesting
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// init= the array used to cancat with the next call, only for when the function calls itself
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// currentIndex= so the function can keep track of how far it's progressed through the array, only for when it's calling itself
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// returns= flatterned array, by one level of nesting
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let(
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shouldKickOffRecursion=currentIndex==undef?1:0,
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isLastIndex=currentIndex+1==len(array)?1:0,
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flatArray=shouldKickOffRecursion?flatternRecursion(array,[],0):
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isLastIndex?concat(init,array[currentIndex]):
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flatternRecursion(array,concat(init,array[currentIndex]),currentIndex+1)
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)
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flatArray;
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function flatternArray(array)=
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// public version of flatternRecursion, has simplified params to avoid confusion
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// array= array to be flatterned
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// return= array that been flatterend by one level of nesting
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flatternRecursion(array);
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function offsetAllFacesBy(array,offset)=[
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// polyhedron faces are simply a list of indices to points, if your concat points together than you probably need to offset
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// your faces array to points to the right place in the new list
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// array= array of point indicies
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// offset= number to offset all indecies by
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// return= array of point indices (i.e. faces) with offset applied
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for(faceIndex=[0:len(array)-1])[
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for(pointIndex=[0:len(array[faceIndex])-1])array[faceIndex][pointIndex]+offset
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]
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];
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function extrudePolygonWithRadius(radiiPoints,h=5,r1=1,r2=1,fn=4)=
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// this basically calls makeCurvedPartOfPolyHedron twice to get the curved section of the final polyhedron
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// and then goes about assmbling them, as the side faces and the top and bottom face caps are missing
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// radiiPoints= series of [x,y,r] points,
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// h= height of the extrude (total including radius sections)
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// r1,r2= define the radius at the top and bottom of the extrud respectively, negative number flange out the extrude
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// fn= number of subdivisions
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// returns= [polyhedronPoints, polyhedronFaces]
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let(
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// top is the top curved part of the extrude
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top=makeCurvedPartOfPolyHedron(radiiPoints,r1,fn),
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topRadiusPoints=translate3Dcoords(top[0],[0,0,h-r1]),
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singeLayerLength=top[2],
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topRadiusFaces=top[1],
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radiusPointsLength=len(topRadiusPoints), // is the same length as bottomRadiusPoints
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// bottom is the bottom curved part of the extrude
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bottom=makeCurvedPartOfPolyHedron(radiiPoints,r2,fn),
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// Z axis needs to be multiplied by -1 to flip it so the radius is going in the right direction [1,1,-1]
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bottomRadiusPoints=translate3Dcoords(bottom[0],[0,0,abs(r2)],[1,1,-1]),
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// becaues the points will be all concatenated into the same array, and the bottom points come second, than
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// the original indices the faces are points towards are wrong and need to have an offset applied to them
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bottomRadiusFaces=offsetAllFacesBy(bottom[1],radiusPointsLength),
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// all of the side panel of the extrusion, connecting points from the inner layers of each
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// of the curved sections
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sideFaces=[for(i=[0:singeLayerLength-1])[
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i,
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listWrap(i+1,singeLayerLength),
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radiusPointsLength + listWrap(i+1,singeLayerLength),
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radiusPointsLength + i
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]],
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// both of these caps are simple every point from the last layer of the radius points
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topCapFace=[for(i=[0:singeLayerLength-1])radiusPointsLength-singeLayerLength+i],
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bottomCapFace=[for(i=[0:singeLayerLength-1])radiusPointsLength*2-singeLayerLength+i],
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finalPolyhedronPoints=concat(topRadiusPoints,bottomRadiusPoints),
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finalPolyhedronFaces=concat(topRadiusFaces,bottomRadiusFaces, sideFaces, [topCapFace], [bottomCapFace])
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)
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[
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finalPolyhedronPoints,
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finalPolyhedronFaces
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];
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module polyRoundExtrude(radiiPoints,length=5,r1=1,r2=1,fn=10,convexity=10) {
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polyhedronPointsNFaces=extrudePolygonWithRadius(radiiPoints,length,r1,r2,fn);
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polyhedron(points=polyhedronPointsNFaces[0], faces=polyhedronPointsNFaces[1], convexity=convexity);
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}
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// testingInternals();
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module testingInternals(){
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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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translate([-25,25,0]){
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polyline(R);
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}
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//example of different modes of the CentreN2PointsArc() function 0=shortest arc, 1=longest arc, 2=CW, 3=CCW
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p1=[0,5];p2=[10,5];centre=[5,0];
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translate([60,0,0]){
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color("green"){
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polygon(CentreN2PointsArc(p1,p2,centre,0,20));//draws the shortest arc
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}
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color("cyan"){
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polygon(CentreN2PointsArc(p1,p2,centre,1,20));//draws the longest arc
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}
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}
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translate([75,0,0]){
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color("purple"){
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polygon(CentreN2PointsArc(p1,p2,centre,2,20));//draws the arc CW (which happens to be the short arc)
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}
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color("red"){
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polygon(CentreN2PointsArc(p2,p1,centre,2,20));//draws the arc CW but p1 and p2 swapped order resulting in the long arc being drawn
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}
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}
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radius=6;
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radiipoints=[[0,0,0],[10,20,radius],[20,0,0]];
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tangentsNcen=round3points(radiipoints);
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translate([10,0,0]){
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for(i=[0:2]){
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color("red")translate(getpoints(radiipoints)[i])circle(1);//plots the 3 input points
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color("cyan")translate(tangentsNcen[i])circle(1);//plots the two tangent poins and the circle centre
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}
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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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}
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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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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, otherwise adding a radius to the middle of a straigh line causes problems
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radiiPointsWithoutTrippleColinear=[
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for(i=[0:len(p)-1]) if(
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// keep point if it isn't colinear or if the radius is 0
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!isColinear(
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p[listWrap(i-1,Lp)],
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p[listWrap(i+0,Lp)],
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p[listWrap(i+1,Lp)]
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p[listWrap(i+0,Lp)].z!=0
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) radiipoints[listWrap(i+0,Lp)]
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],
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newrp2=processRadiiPoints(radiiPointsWithoutTrippleColinear),
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plusMinusPointRange=mode==2?1:2,
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temp=[
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for(i=[0:len(newrp2)-1]) //for each point in the radii array
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let(
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thepoints=[for(j=[-plusMinusPointRange:plusMinusPointRange])newrp2[listWrap(i+j,len(newrp2))]],//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:newrp2[i][2]==0?
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[[newrp2[i][0],newrp2[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]) abs(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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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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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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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
|
|
|
|
|
//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
|
|
|
|
|
angleFromPoint1ToPoint2=getAngle(p[0],p[1]),
|
|
|
|
|
angleFromPoint2ToPoint3=getAngle(p[2],p[1]),
|
|
|
|
|
//find tangent points
|
|
|
|
|
t12=[p[1][0]-cos(angleFromPoint1ToPoint2)*tangD,p[1][1]-sin(angleFromPoint1ToPoint2)*tangD],//tangent point between points 1&2
|
|
|
|
|
t23=[p[1][0]-cos(angleFromPoint2ToPoint3)*tangD,p[1][1]-sin(angleFromPoint2ToPoint3)*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
|
|
|
|
|
angleFromPoint1ToPoint2=getAngle(p[0],p[1]),
|
|
|
|
|
angleFromPoint2ToPoint3=getAngle(p[2],p[1]),
|
|
|
|
|
//find tangent points
|
|
|
|
|
t12=[p[1][0]-cos(angleFromPoint1ToPoint2)*tangD,p[1][1]-sin(angleFromPoint1ToPoint2)*tangD],//tangent point between points 1&2
|
|
|
|
|
t23=[p[1][0]-cos(angleFromPoint2ToPoint3)*tangD,p[1][1]-sin(angleFromPoint2ToPoint3)*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 beamChain(radiiPoints,offset1=0,offset2,mode=0,minR=0,startAngle,endAngle)=
|
|
|
|
|
/*This function takes a series of radii points and plots points to run along side at a consistant distance, think of it as offset but for line instead of a polygon
|
|
|
|
|
radiiPoints=radii points,
|
|
|
|
|
offset1 & offset2= The two offsets that give the beam it's thickness. When using with mode=2 only offset1 is needed as there is no return path for the polygon
|
|
|
|
|
minR=min radius, if all of your radii are set properly within the radii points this value can be ignored
|
|
|
|
|
startAngle & endAngle= Angle at each end of the beam, different mode determine if this angle is relative to the ending legs of the beam or absolute.
|
|
|
|
|
mode=1 - include endpoints startAngle&2 are relative to the angle of the last two points and equal 90deg if not defined
|
|
|
|
|
mode=2 - Only the forward path is defined, useful for combining the beam with other radii points, see examples for a use-case.
|
|
|
|
|
mode=3 - include endpoints startAngle&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(
|
|
|
|
|
offset2undef=offset2==undef?1:0,
|
|
|
|
|
offset2=offset2undef==1?0:offset2,
|
|
|
|
|
CWorCCW1=sign(offset1)*CWorCCW(radiiPoints),
|
|
|
|
|
CWorCCW2=sign(offset2)*CWorCCW(radiiPoints),
|
|
|
|
|
offset1=abs(offset1),
|
|
|
|
|
offset2b=abs(offset2),
|
|
|
|
|
Lrp3=len(radiiPoints)-3,
|
|
|
|
|
Lrp=len(radiiPoints),
|
|
|
|
|
startAngle=mode==0&&startAngle==undef?
|
|
|
|
|
getAngle(radiiPoints[0],radiiPoints[1])+90:
|
|
|
|
|
mode==2&&startAngle==undef?
|
|
|
|
|
0:
|
|
|
|
|
mode==0?
|
|
|
|
|
getAngle(radiiPoints[0],radiiPoints[1])+startAngle:
|
|
|
|
|
startAngle,
|
|
|
|
|
endAngle=mode==0&&endAngle==undef?
|
|
|
|
|
getAngle(radiiPoints[Lrp-1],radiiPoints[Lrp-2])+90:
|
|
|
|
|
mode==2&&endAngle==undef?
|
|
|
|
|
0:
|
|
|
|
|
mode==0?
|
|
|
|
|
getAngle(radiiPoints[Lrp-1],radiiPoints[Lrp-2])+endAngle:
|
|
|
|
|
endAngle,
|
|
|
|
|
OffLn1=[for(i=[0:Lrp3]) offset1==0?radiiPoints[i+1]:parallelFollow([radiiPoints[i],radiiPoints[i+1],radiiPoints[i+2]],offset1,minR,mode=CWorCCW1)],
|
|
|
|
|
OffLn2=[for(i=[0:Lrp3]) offset2==0?radiiPoints[i+1]:parallelFollow([radiiPoints[i],radiiPoints[i+1],radiiPoints[i+2]],offset2b,minR,mode=CWorCCW2)],
|
|
|
|
|
Rp1=abs(radiiPoints[0].z),
|
|
|
|
|
Rp2=abs(radiiPoints[Lrp-1].z),
|
|
|
|
|
endP1a=findPoint(getAngle(radiiPoints[0],radiiPoints[1]), OffLn1[0], startAngle,radiiPoints[0], Rp1),
|
|
|
|
|
endP1b=findPoint(getAngle(radiiPoints[Lrp-1],radiiPoints[Lrp-2]), OffLn1[len(OffLn1)-1], endAngle,radiiPoints[Lrp-1], Rp2),
|
|
|
|
|
endP2a=findPoint(getAngle(radiiPoints[0],radiiPoints[1]), OffLn2[0], startAngle,radiiPoints[0], Rp1),
|
|
|
|
|
endP2b=findPoint(getAngle(radiiPoints[Lrp-1],radiiPoints[Lrp-2]), OffLn2[len(OffLn1)-1], endAngle,radiiPoints[Lrp-1], Rp2),
|
|
|
|
|
absEnda=getAngle(endP1a,endP2a),
|
|
|
|
|
absEndb=getAngle(endP1b,endP2b),
|
|
|
|
|
negRP1a=[cos(absEnda)*radiiPoints[0].z*10+endP1a.x, sin(absEnda)*radiiPoints[0].z*10+endP1a.y, 0.0],
|
|
|
|
|
negRP2a=[cos(absEnda)*-radiiPoints[0].z*10+endP2a.x, sin(absEnda)*-radiiPoints[0].z*10+endP2a.y, 0.0],
|
|
|
|
|
negRP1b=[cos(absEndb)*radiiPoints[Lrp-1].z*10+endP1b.x, sin(absEndb)*radiiPoints[Lrp-1].z*10+endP1b.y, 0.0],
|
|
|
|
|
negRP2b=[cos(absEndb)*-radiiPoints[Lrp-1].z*10+endP2b.x, sin(absEndb)*-radiiPoints[Lrp-1].z*10+endP2b.y, 0.0],
|
|
|
|
|
OffLn1b=(mode==0||mode==2)&&radiiPoints[0].z<0&&radiiPoints[Lrp-1].z<0?
|
|
|
|
|
concat([negRP1a],[endP1a],OffLn1,[endP1b],[negRP1b])
|
|
|
|
|
:(mode==0||mode==2)&&radiiPoints[0].z<0?
|
|
|
|
|
concat([negRP1a],[endP1a],OffLn1,[endP1b])
|
|
|
|
|
:(mode==0||mode==2)&&radiiPoints[Lrp-1].z<0?
|
|
|
|
|
concat([endP1a],OffLn1,[endP1b],[negRP1b])
|
|
|
|
|
:mode==0||mode==2?
|
|
|
|
|
concat([endP1a],OffLn1,[endP1b])
|
|
|
|
|
:
|
|
|
|
|
OffLn1,
|
|
|
|
|
OffLn2b=(mode==0||mode==2)&&radiiPoints[0].z<0&&radiiPoints[Lrp-1].z<0?
|
|
|
|
|
concat([negRP2a],[endP2a],OffLn2,[endP2b],[negRP2b])
|
|
|
|
|
:(mode==0||mode==2)&&radiiPoints[0].z<0?
|
|
|
|
|
concat([negRP2a],[endP2a],OffLn2,[endP2b])
|
|
|
|
|
:(mode==0||mode==2)&&radiiPoints[Lrp-1].z<0?
|
|
|
|
|
concat([endP2a],OffLn2,[endP2b],[negRP2b])
|
|
|
|
|
:mode==0||mode==2?
|
|
|
|
|
concat([endP2a],OffLn2,[endP2b])
|
|
|
|
|
:
|
|
|
|
|
OffLn2
|
|
|
|
|
)//end of let()
|
|
|
|
|
offset2undef==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[listWrap(i+0,Lp)].x-p[listWrap(i+1,Lp)].x)*(p[listWrap(i+0,Lp)].y+p[listWrap(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(
|
|
|
|
|
isCWorCCW=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&&isCWorCCW==-1?p1p2Angle:
|
|
|
|
|
mode==2&&isCWorCCW== 1?p1p2Angle-360:
|
|
|
|
|
mode==3&&isCWorCCW== 1?p1p2Angle:
|
|
|
|
|
mode==3&&isCWorCCW==-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])
|
|
|
|
|
let(angleIncrement=(arcAngle/fn)*i*isCWorCCW)
|
|
|
|
|
[cos(p1Angle+angleIncrement)*r+cen.x,sin(p1Angle+angleIncrement)*r+cen.y]];
|
|
|
|
|
|
|
|
|
|
function translateRadiiPoints(radiiPoints,tran=[0,0],rot=0)=
|
|
|
|
|
[for(i=radiiPoints)
|
|
|
|
|
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,$fn=100){
|
|
|
|
|
offset(-IR-OR,$fn=100){
|
|
|
|
|
offset(IR,$fn=100){
|
|
|
|
|
children();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
module shell2d(offset1,offset2=0,minOR=0,minIR=0){
|
|
|
|
|
difference(){
|
|
|
|
|
round2d(minOR,minIR){
|
|
|
|
|
offset(max(offset1,offset2)){
|
|
|
|
|
children(0);//original 1st child forms the outside of the shell
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
round2d(minIR,minOR){
|
|
|
|
|
difference(){//round the inside cutout
|
|
|
|
|
offset(min(offset1,offset2)){
|
|
|
|
|
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 extrudeWithRadius(length,r1=0,r2=0,fn=30){
|
|
|
|
|
n1=sign(r1);n2=sign(r2);
|
|
|
|
|
r1=abs(r1);r2=abs(r2);
|
|
|
|
|
translate([0,0,r1]){
|
|
|
|
|
linear_extrude(length-r1-r2){
|
|
|
|
|
children();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
for(i=[0:fn-1]){
|
|
|
|
|
translate([0,0,i/fn*r1]){
|
|
|
|
|
linear_extrude(r1/fn+0.01){
|
|
|
|
|
offset(n1*sqrt(sq(r1)-sq(r1-i/fn*r1))-n1*r1){
|
|
|
|
|
children();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
translate([0,0,length-r2+i/fn*r2]){
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linear_extrude(r2/fn+0.01){
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offset(n2*sqrt(sq(r2)-sq(i/fn*r2))-n2*r2){
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children();
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}
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}
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}
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}
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}
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function mirrorPoints(radiiPoints,rot=0,endAttenuation=[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
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let(
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a=translateRadiiPoints(radiiPoints,[0,0],-rot),
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temp3=[for(i=[0+endAttenuation[0]:len(a)-1-endAttenuation[1]])
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[a[i][0],-a[i][1],a[i][2]]
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],
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temp=translateRadiiPoints(temp3,[0,0],rot),
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temp2=revList(temp3)
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)
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concat(radiiPoints,temp2);
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function processRadiiPoints(rp)=
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[for(i=[0:len(rp)-1])
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processRadiiPoints2(rp,i)
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];
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function processRadiiPoints2(list,end=0,idx=0,result=0)=
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idx>=end+1?result:
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processRadiiPoints2(list,end,idx+1,relationalRadiiPoints(result,list[idx]));
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function cosineRuleBside(a,c,C)=c*cos(C)-sqrt(sq(a)+sq(c)+sq(cos(C))-sq(c));
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function absArelR(po,pn)=
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let(
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th2=atan(po[1]/po[0]),
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r2=sqrt(sq(po[0])+sq(po[1])),
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r3=cosineRuleBside(r2,pn[1],th2-pn[0])
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)
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[cos(pn[0])*r3,sin(pn[0])*r3,pn[2]];
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function relationalRadiiPoints(po,pi)=
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let(
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p0=pi[0],
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p1=pi[1],
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p2=pi[2],
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pv0=pi[3][0],
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pv1=pi[3][1],
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pt0=pi[3][2],
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pt1=pi[3][3],
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pn=
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(pv0=="y"&&pv1=="x")||(pv0=="r"&&pv1=="a")||(pv0=="y"&&pv1=="a")||(pv0=="x"&&pv1=="a")||(pv0=="y"&&pv1=="r")||(pv0=="x"&&pv1=="r")?
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[p1,p0,p2,concat(pv1,pv0,pt1,pt0)]:
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[p0,p1,p2,concat(pv0,pv1,pt0,pt1)],
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n0=pn[0],
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n1=pn[1],
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n2=pn[2],
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nv0=pn[3][0],
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nv1=pn[3][1],
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nt0=pn[3][2],
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|
|
nt1=pn[3][3],
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|
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temp=
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pn[0]=="l"?
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[po[0],pn[1],pn[2]]
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:pn[1]=="l"?
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[pn[0],po[1],pn[2]]
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|
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:nv0==undef?
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[pn[0],pn[1],pn[2]]//abs x, abs y as default when undefined
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|
:nv0=="a"?
|
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|
nv1=="r"?
|
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|
nt0=="a"?
|
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|
nt1=="a"||nt1==undef?
|
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[cos(n0)*n1,sin(n0)*n1,n2]//abs angle, abs radius
|
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|
|
|
:absArelR(po,pn)//abs angle rel radius
|
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|
|
|
:nt1=="r"||nt1==undef?
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|
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[po[0]+cos(pn[0])*pn[1],po[1]+sin(pn[0])*pn[1],pn[2]]//rel angle, rel radius
|
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|
|
:[pn[0],pn[1],pn[2]]//rel angle, abs radius
|
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|
:nv1=="x"?
|
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|
|
nt0=="a"?
|
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|
|
|
nt1=="a"||nt1==undef?
|
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|
[pn[1],pn[1]*tan(pn[0]),pn[2]]//abs angle, abs x
|
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|
|
|
:[po[0]+pn[1],(po[0]+pn[1])*tan(pn[0]),pn[2]]//abs angle rel x
|
|
|
|
|
:nt1=="r"||nt1==undef?
|
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|
|
|
[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, width=0.3) {
|
|
|
|
|
for(i=[0:max(0,len(p)-1)]){
|
|
|
|
|
color([i*1/len(p),1-i*1/len(p),0,0.5])line(p[i],p[listWrap(i+1,len(p) )],width);
|
|
|
|
|
}
|
|
|
|
|
} // 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 listWrap(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
|
Bob