use //for cheaper minwoski use use use use use use /*DES (Distorted Elliptical Saddle) Sculpted Profile Version 2: Eliptical Rectangle */ //NOTE: with sweep cuts, top surface may not be visible in review, it should be visible once rendered mirror([0,0,0])keycap( keyID = 4, //change profile refer to KeyParameters Struct cutLen = 0, //Don't change. for chopped caps Stem = true, //tusn on shell and stems Dish = true, //turn on dish cut Stab = 0, visualizeDish = false, // turn on debug visual of Dish crossSection = false, // center cut to check internal homeDot = false, //turn on homedots Legends = false ); //Parameters wallthickness = 1.5; topthickness = 3; // stepsize = 50; //resolution of Trajectory step = 2; //resolution of ellipes fn = 32; //resolution of Rounded Rectangles: 60 for output layers = 40; //resolution of vertical Sweep: 50 for output dotRadius = 1.25; //home dot size // roll for trajectories fr1 = 0; fr2 = 0; br1 = 0; br2 = 0; //---Stem param Tol = 0.10; //stem tolarance stemRot = 0; stemRad = 5.55; // stem outer radius stemLen = 5.55 ; stemCrossHeight = 4; extra_vertical = 0.6; StemBrimDep = 0.25; stemLayers = 50; //resolution of stem to cap top transition keyParameters = //keyParameters[KeyID][ParameterID] [ // BotWid, BotLen, TWDif, TLDif, keyh, WSft, LSft XSkew, YSkew, ZSkew, WEx, LEx, CapR0i, CapR0f, CapR1i, CapR1f, CapREx, StemEx //normie hipro v1 [17.16, 17.16, 6.5, 6.5, 11.5, 0, 0, -3, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 [35.46, 17.16, 6.5, 6.5, 11.0, 0, 0, -10, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 2u [17.16, 17.16, 6.5, 6.5, 9, 0, 0, 3, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R3 Home [17.16*2,17.16, 6.5, 6.5, 8.6, 0, 0, -8, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 2u low pro 3 //normie hi-sculpt 4 row system 17~23 [17.16, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 4 [22.26, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 1.25u [26.66, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 1.5u [31.06, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 1.75u [35.56, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 2.0u 8 [40.86, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 2.25u 8 [50.66, 17.16, 6.5, 6.5, 11.0, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 2.75u 8 //normie mild 4 row system [17.16, 17.16, 6.5, 6.5, 10.3, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 9 [22.26, 17.16, 6.5, 6.5, 10.3, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 10 [26.66, 17.16, 6.5, 6.5, 10.3, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 11 [31.06, 17.16, 6.5, 6.5, 10.3, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 12 [35.56, 17.16, 6.5, 6.5, 10.3, 0, 0, -9, 0, 0, 2, 2, 1, 5, 1, 3.5, 2, 2], //R5 13 //nueron R5s [35.46, 17.96, 6.5, 6.5, 10.5, 0, 0, -5, 0, 0, 2, 2, 1, 5, 1, 5, 2, 2], //R5 2u [26.66, 17.16, 6.5, 6.5, 10.5, 0, 0, -3, 0, 0, 2, 2, 1, 5, 1, 5, 2, 2], //R5 1.5u [40.66, 17.16, 6.5, 6.5, 10.5, 0, 0, -3, 0, 0, 2, 2, 1, 5, 1, 5, 2, 2], //R5 2.25u [49.86, 17.16, 6.5, 6.5, 10.5, 0, 0, -3, 0, 0, 2, 2, 1, 5, 1, 5, 2, 2], //R5 2.75u ]; dishParameters = //dishParameter[keyID][ParameterID] [ //FFwd1 FFwd2 FPit1 FPit2 DshDepi DishDepf,DshHDif FArcIn FArcFn FArcEx BFwd1 BFwd2 BPit1 BPit2 BArcIn BArcFn BArcEx [ 4, 4, -10, -20, 3, 7, 8.2, 9, 2, 4, 9, 3, 15, 8.2, 9, 2], //R5 [ 4, 3.5, -13, -50, 2, 4.5, 18.2, 17.5, 2, 4.5, 2.5, -5, -50, 18.2, 17, 2], //R5 2u [ 3, 3, -10, -50, 3, 7, 8.8, 9, 2, 4, 3, -5, -30, 8.8, 9, 2], //R3 [ 3, 3.25, -10, -45, 2, 4.3, 18.2, 21, 2, 5, 3, -10, -30, 18.2, 21, 2], //R4 //normie hi-sculpt 4 row system 17~23 [ 4, 3, -10, -20, 1.5, 4, 8.2, 9, 2, 4, 3, -10, -30, 8.2, 9, 2], //R5 [ 4, 3, -10, -20, 1.5, 4, 10.2, 11, 2, 4, 3, -10, -30, 10.2, 11, 2],//R5 1.25u [ 4, 3, -10, -20, 1.5, 4, 12.4, 13, 2, 4, 3, -10, -30, 12.4, 13, 2], //R5 1.5u [ 4, 3, -10, -20, 1.5, 4, 14.6, 15, 2, 4, 3, -10, -30, 14.6, 15, 2], //R5 1.75u [ 4, 3, -10, -20, 1.5, 4, 16.8, 17, 2, 4, 3, -10, -30, 16.8, 17, 2], //R5 2.0u [ 4, 3, -10, -20, 1.5, 4, 19.5, 20, 2, 4, 3, -10, -30, 19.5, 20, 2], //R5 2.25u [ 4, 3, -10, -20, 1.5, 4, 24.5, 24.5, 2, 4, 3, -10, -30, 24.5, 24.5, 2], //R5 2.75u //normie hi-sculpt 4 row system 17~23 [ 4, 3, -10, -20, 1.5, 4, 8.2, 9, 2, 4, 3, -10, -30, 8.2, 9, 2], //R5 [ 4, 3, -10, -20, 1.5, 4, 10.2, 11, 2, 4, 3, -10, -30, 10.2, 11, 2],//R5 1.25u [ 4, 3, -10, -20, 1.5, 4, 12.4, 13, 2, 4, 3, -10, -30, 12.4, 13, 2], //R5 1.5u [ 4, 3, -10, -20, 1.5, 4, 14.6, 15, 2, 4, 3, -10, -30, 14.6, 15, 2], //R5 1.75u [ 4, 3, -10, -20, 1.5, 4, 16.8, 17, 2, 4, 3, -10, -30, 16.8, 17, 2], //R5 2.0u // [ 4, 3, -10, -20, 1.8, 4.5, 17.5, 19, 2, 4, 10, 3, 15, 17.5, 19, 2], //R5 [ 4, 3, -10, -20, 1.5, 4, 11.8, 12, 2, 4, 3, -10, -30, 11.8, 12, 2], //R5 1.5u [ 4, 3, -10, -20, 1.5, 4, 18.8, 18.8, 2, 4, 3, -10, -30, 18.8, 18.8, 2], //R5 2.25u [ 4, 3, -10, -20, 1.5, 4, 23.5, 24, 2, 4, 3, -10, -30, 23.5, 24, 2], //R5 2.75u ]; function FrontForward1(keyID) = dishParameters[keyID][0]; // function FrontForward2(keyID) = dishParameters[keyID][1]; // function FrontPitch1(keyID) = dishParameters[keyID][2]; // function FrontPitch2(keyID) = dishParameters[keyID][3]; // function DishDepth(keyID) = dishParameters[keyID][4]; // function DishHeightDif(keyID) = dishParameters[keyID][5]; // function FrontInitArc(keyID) = dishParameters[keyID][6]; function FrontFinArc(keyID) = dishParameters[keyID][7]; function FrontArcExpo(keyID) = dishParameters[keyID][8]; function BackForward1(keyID) = dishParameters[keyID][9]; // function BackForward2(keyID) = dishParameters[keyID][10]; // function BackPitch1(keyID) = dishParameters[keyID][11]; // function BackPitch2(keyID) = dishParameters[keyID][12]; // function BackInitArc(keyID) = dishParameters[keyID][13]; function BackFinArc(keyID) = dishParameters[keyID][14]; function BackArcExpo(keyID) = dishParameters[keyID][15]; function BottomWidth(keyID) = keyParameters[keyID][0]; // function BottomLength(keyID) = keyParameters[keyID][1]; // function TopWidthDiff(keyID) = keyParameters[keyID][2]; // function TopLenDiff(keyID) = keyParameters[keyID][3]; // function KeyHeight(keyID) = keyParameters[keyID][4]; // function TopWidShift(keyID) = keyParameters[keyID][5]; function TopLenShift(keyID) = keyParameters[keyID][6]; function XAngleSkew(keyID) = keyParameters[keyID][7]; function YAngleSkew(keyID) = keyParameters[keyID][8]; function ZAngleSkew(keyID) = keyParameters[keyID][9]; function WidExponent(keyID) = keyParameters[keyID][10]; function LenExponent(keyID) = keyParameters[keyID][11]; function CapRound0i(keyID) = keyParameters[keyID][12]; function CapRound0f(keyID) = keyParameters[keyID][13]; function CapRound1i(keyID) = keyParameters[keyID][14]; function CapRound1f(keyID) = keyParameters[keyID][15]; function ChamExponent(keyID) = keyParameters[keyID][16]; function StemExponent(keyID) = keyParameters[keyID][17]; function FrontTrajectory(keyID) = [ trajectory(forward = FrontForward1(keyID), pitch = FrontPitch1(keyID), roll = fr1), //more param available: yaw, roll, scale trajectory(forward = FrontForward2(keyID), pitch = FrontPitch2(keyID), roll = fr2) //You can add more traj if you wish ]; function BackTrajectory (keyID) = [ trajectory(forward = BackForward1(keyID), pitch = BackPitch1(keyID), roll = br1), trajectory(forward = BackForward2(keyID), pitch = BackPitch2(keyID), roll = br2), ]; //------- function defining Dish Shapes function ellipse(a, b, d = 0, rot1 = 0, rot2 = 360) = [for (t = [rot1:step:rot2]) [a*cos(t)+a, b*sin(t)*(1+d*cos(t))]]; //Centered at a apex to avoid inverted face function DishShape (a,b,c,d) = concat( [[c+a,-b]], ellipse(a, b, d = 0,rot1 = 270, rot2 =450), [[c+a,b]] ); function oval_path(theta, phi, a, b, c, deform = 0) = [ a*cos(theta)*cos(phi), //x c*sin(theta)*(1+deform*cos(theta)) , // b*sin(phi), ]; path_trans2 = [for (t=[0:step:180]) translation(oval_path(t,0,10,15,2,0))*rotation([0,90,0])]; //--------------Function definng Cap function CapTranslation(t, keyID) = [ ((1-t)/layers*TopWidShift(keyID)), //X shift ((1-t)/layers*TopLenShift(keyID)), //Y shift (t/layers*KeyHeight(keyID)) //Z shift ]; function InnerTranslation(t, keyID) = [ ((1-t)/layers*TopWidShift(keyID)), //X shift ((1-t)/layers*TopLenShift(keyID)), //Y shift (t/layers*(KeyHeight(keyID)-topthickness)) //Z shift ]; function CapRotation(t, keyID) = [ ((1-t)/layers*XAngleSkew(keyID)), //X shift ((1-t)/layers*YAngleSkew(keyID)), //Y shift ((1-t)/layers*ZAngleSkew(keyID)) //Z shift ]; function CapTransform(t, keyID) = [ pow(t/layers, WidExponent(keyID))*(BottomWidth(keyID) -TopWidthDiff(keyID)) + (1-pow(t/layers, WidExponent(keyID)))*BottomWidth(keyID) , pow(t/layers, LenExponent(keyID))*(BottomLength(keyID)-TopLenDiff(keyID)) + (1-pow(t/layers, LenExponent(keyID)))*BottomLength(keyID) ]; function CapRoundness(t, keyID) = [ pow(t/layers, ChamExponent(keyID))*(CapRound0f(keyID)) + (1-pow(t/layers, ChamExponent(keyID)))*CapRound0i(keyID), pow(t/layers, ChamExponent(keyID))*(CapRound1f(keyID)) + (1-pow(t/layers, ChamExponent(keyID)))*CapRound1i(keyID) ]; function CapRadius(t, keyID) = pow(t/layers, ChamExponent(keyID))*ChamfFinRad(keyID) + (1-pow(t/layers, ChamExponent(keyID)))*ChamfInitRad(keyID); function InnerTransform(t, keyID) = [ pow(t/layers, WidExponent(keyID))*(BottomWidth(keyID) -TopLenDiff(keyID)-wallthickness*2) + (1-pow(t/layers, WidExponent(keyID)))*(BottomWidth(keyID) -wallthickness*2), pow(t/layers, LenExponent(keyID))*(BottomLength(keyID)-TopLenDiff(keyID)-wallthickness*2) + (1-pow(t/layers, LenExponent(keyID)))*(BottomLength(keyID)-wallthickness*2) ]; function StemTranslation(t, keyID) = [ ((1-t)/stemLayers*TopWidShift(keyID)), //X shift ((1-t)/stemLayers*TopLenShift(keyID)), //Y shift stemCrossHeight+.1+StemBrimDep + (t/stemLayers*(KeyHeight(keyID)- topthickness - stemCrossHeight-.1 -StemBrimDep)) //Z shift ]; function StemRotation(t, keyID) = [ ((1-t)/stemLayers*XAngleSkew(keyID)), //X shift ((1-t)/stemLayers*YAngleSkew(keyID)), //Y shift ((1-t)/stemLayers*ZAngleSkew(keyID)) //Z shift ]; function StemTransform(t, keyID) = [ pow(t/stemLayers, StemExponent(keyID))*(BottomWidth(keyID) -TopLenDiff(keyID)-wallthickness) + (1-pow(t/stemLayers, StemExponent(keyID)))*(stemWid - 2*slop), pow(t/stemLayers, StemExponent(keyID))*(BottomLength(keyID)-TopLenDiff(keyID)-wallthickness) + (1-pow(t/stemLayers, StemExponent(keyID)))*(stemLen - 2*slop) ]; function StemRadius(t, keyID) = pow(t/stemLayers,3)*3 + (1-pow(t/stemLayers, 3))*1; //Stem Exponent ///----- KEY Builder Module module keycap(keyID = 0, cutLen = 0, visualizeDish = false, rossSection = false, Dish = true, Stem = false, homeDot = false, Stab = 0) { //Set Parameters for dish shape FrontPath = quantize_trajectories(FrontTrajectory(keyID), steps = stepsize, loop=false, start_position= $t*4); BackPath = quantize_trajectories(BackTrajectory(keyID), steps = stepsize, loop=false, start_position= $t*4); //Scaling initial and final dim tranformation by exponents function FrontDishArc(t) = pow((t)/(len(FrontPath)),FrontArcExpo(keyID))*FrontFinArc(keyID) + (1-pow(t/(len(FrontPath)),FrontArcExpo(keyID)))*FrontInitArc(keyID); function BackDishArc(t) = pow((t)/(len(FrontPath)),BackArcExpo(keyID))*BackFinArc(keyID) + (1-pow(t/(len(FrontPath)),BackArcExpo(keyID)))*BackInitArc(keyID); FrontCurve = [ for(i=[0:len(FrontPath)-1]) transform(FrontPath[i], DishShape(DishDepth(keyID), FrontDishArc(i), DishDepth(keyID)+2.5, d = 0)) ]; BackCurve = [ for(i=[0:len(BackPath)-1]) transform(BackPath[i], DishShape(DishDepth(keyID), BackDishArc(i), DishDepth(keyID)+2.5, d = 0)) ]; //builds difference(){ union(){ difference(){ skin([for (i=[0:layers-1]) transform(translation(CapTranslation(i, keyID)) * rotation(CapRotation(i, keyID)), elliptical_rectangle(CapTransform(i, keyID), b = CapRoundness(i,keyID),fn=fn))]); //outer shell //Cut inner shell if(Stem == true){ translate([0,0,-.001])skin([for (i=[0:layers-1]) transform(translation(InnerTranslation(i, keyID)) * rotation(CapRotation(i, keyID)), elliptical_rectangle(InnerTransform(i, keyID), b = CapRoundness(i,keyID),fn=fn))]); } } if(Stem == true){ translate([0,0,StemBrimDep])rotate(stemRot)difference(){ //cylinderical Stem body cylinder(d =5.5,KeyHeight(keyID)-StemBrimDep, $fn= 32); skin(StemCurve); skin(StemCurve2); // generate smooth trantion to ceiling // translate([0,0,-.001])skin([for (i=[0:stemLayers-1]) transform(translation(StemTranslation(i,keyID))*rotation(StemRotation(i, keyID)), elliptical_rectangle(StemTransform(i, keyID),b= StemRadius(i, keyID), fn=fn))]); // InnerTransform(i, keyID), = CapRoundness(i,keyID),fn=fn) } } //cut for fonts and extra pattern for light? } //Cuts //Fonts if(Legends == true){ #rotate([-XAngleSkew(keyID),YAngleSkew(keyID),ZAngleSkew(keyID)])translate([-0,0,KeyHeight(keyID)-2.0])linear_extrude(height = 1)text( text = "No U", font = "Constantia:style=Bold", size = 3, valign = "center", halign = "center" ); // #rotate([-XAngleSkew(keyID),YAngleSkew(keyID),ZAngleSkew(keyID)])translate([0,-3.5,0])linear_extrude(height = 0.5)text( text = "Me", font = "Constantia:style=Bold", size = 3, valign = "center", halign = "center" ); } //Dish Shape if(Dish == true){ if(visualizeDish == false){ translate([-TopWidShift(keyID),.00001-TopLenShift(keyID),KeyHeight(keyID)-DishHeightDif(keyID)])rotate([0,-YAngleSkew(keyID),0])rotate([0,-90+XAngleSkew(keyID),90-ZAngleSkew(keyID)])skin(FrontCurve); translate([-TopWidShift(keyID),-TopLenShift(keyID),KeyHeight(keyID)-DishHeightDif(keyID)])rotate([0,-YAngleSkew(keyID),0])rotate([0,-90-XAngleSkew(keyID),270-ZAngleSkew(keyID)])skin(BackCurve); } else { #translate([-TopWidShift(keyID),.00001-TopLenShift(keyID),KeyHeight(keyID)-DishHeightDif(keyID)]) rotate([0,-YAngleSkew(keyID),0])rotate([0,-90+XAngleSkew(keyID),90-ZAngleSkew(keyID)])skin(FrontCurve); #translate([-TopWidShift(keyID),-TopLenShift(keyID),KeyHeight(keyID)-DishHeightDif(keyID)])rotate([0,-YAngleSkew(keyID),0])rotate([0,-90-XAngleSkew(keyID),270-ZAngleSkew(keyID)])skin(BackCurve); } } if(crossSection == true) { translate([0,-15,-.1])cube([15,30,15]); } } //Homing dot if(homeDot == true)translate([0,0,KeyHeight(keyID)-DishHeightDif(keyID)-.25])sphere(d = dotRadius); } //------------------stems MXWid = 4.03/2+Tol; //horizontal lenght MXLen = 4.23/2+Tol; //vertical length MXWidT = 1.15/2+Tol; //horizontal thickness MXLenT = 1.25/2+Tol; //vertical thickness function stem_internal(sc=1) = sc*[ [MXLenT, MXLen],[MXLenT, MXWidT],[MXWid, MXWidT], [MXWid, -MXWidT],[MXLenT, -MXWidT],[MXLenT, -MXLen], [-MXLenT, -MXLen],[-MXLenT, -MXWidT],[-MXWid, -MXWidT], [-MXWid,MXWidT],[-MXLenT, MXWidT],[-MXLenT, MXLen] ]; //2D stem cross with tolance offset and additonal transformation via jog //trajectory(); function StemTrajectory() = [ trajectory(forward = 5.25) //You can add more traj if you wish ]; StemPath = quantize_trajectories(StemTrajectory(), steps = 1 , loop=false, start_position= $t*4); StemCurve = [ for(i=[0:len(StemPath)-1]) transform(StemPath[i], stem_internal()) ]; function StemTrajectory2() = [ trajectory(forward = .5) //You can add more traj if you wish ]; StemPath2 = quantize_trajectories(StemTrajectory2(), steps = 10, loop=false, start_position= $t*4); StemCurve2 = [ for(i=[0:len(StemPath2)-1]) transform(StemPath2[i]*scaling([(1.1-.1*i/(len(StemPath2)-1)),(1.1-.1*i/(len(StemPath2)-1)),1]), stem_internal()) ]; module cherry_stem(depth, slop) { D1=.15; D2=.05; H1=3.5; CrossDist = 1.75; difference(){ // outside shape linear_extrude(height = depth) { offset(r=1){ square(outer_cherry_stem(slop) - [2,2], center=true); } } inside_cherry_cross(slop); hull(){ translate([CrossDist,CrossDist-.1,0])cylinder(d1=D1, d2=D2, H1); translate([-CrossDist,-CrossDist+.1,0])cylinder(d1=D1, d2=D2, H1); } hull(){ translate([-CrossDist,CrossDist-.1])cylinder(d1=D1, d2=D2, H1); translate([CrossDist,-CrossDist+.1])cylinder(d1=D1, d2=D2, H1); } } } module choc_stem() { translate([5.7/2,0,-3.4/2+2])difference(){ cube([1.25,3, 3.4], center= true); translate([3.9,0,0])cylinder(d=7,3.4,center = true); translate([-3.9,0,0])cylinder(d=7,3.4,center = true); } translate([-5.7/2,0,-3.4/2+2])difference(){ cube([1.25,3, 3.4], center= true); translate([3.9,0,0])cylinder(d=7,3.4,center = true); translate([-3.9,0,0])cylinder(d=7,3.4,center = true); } } /// ----- helper functions function rounded_rectangle_profile(size=[1,1],r=1,fn=32) = [ for (index = [0:fn-1]) let(a = index/fn*360) r * [cos(a), sin(a)] + sign_x(index, fn) * [size[0]/2-r,0] + sign_y(index, fn) * [0,size[1]/2-r] ]; function elliptical_rectangle(a = [1,1], b =[1,1], fn=32) = [ for (index = [0:fn-1]) // section right let(theta1 = -atan(a[1]/b[1])+ 2*atan(a[1]/b[1])*index/fn) [b[1]*cos(theta1), a[1]*sin(theta1)] + [a[0]*cos(atan(b[0]/a[0])) , 0] - [b[1]*cos(atan(a[1]/b[1])) , 0], for(index = [0:fn-1]) // section Top let(theta2 = atan(b[0]/a[0]) + (180 -2*atan(b[0]/a[0]))*index/fn) [a[0]*cos(theta2), b[0]*sin(theta2)] - [0, b[0]*sin(atan(b[0]/a[0]))] + [0, a[1]*sin(atan(a[1]/b[1]))], for(index = [0:fn-1]) // section left let(theta2 = -atan(a[1]/b[1])+180+ 2*atan(a[1]/b[1])*index/fn) [b[1]*cos(theta2), a[1]*sin(theta2)] - [a[0]*cos(atan(b[0]/a[0])) , 0] + [b[1]*cos(atan(a[1]/b[1])) , 0], for(index = [0:fn-1]) // section Top let(theta2 = atan(b[0]/a[0]) + 180 + (180 -2*atan(b[0]/a[0]))*index/fn) [a[0]*cos(theta2), b[0]*sin(theta2)] + [0, b[0]*sin(atan(b[0]/a[0]))] - [0, a[1]*sin(atan(a[1]/b[1]))] ]/2; function sign_x(i,n) = i < n/4 || i > n-n/4 ? 1 : i > n/4 && i < n-n/4 ? -1 : 0; function sign_y(i,n) = i > 0 && i < n/2 ? 1 : i > n/2 ? -1 : 0;