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MX_DES_Convex.scad
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MX_DES_Convex.scad
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use <scad-utils/morphology.scad> //for cheaper minwoski
use <scad-utils/transformations.scad>
use <scad-utils/shapes.scad>
use <scad-utils/trajectory.scad>
use <scad-utils/trajectory_path.scad>
use <sweep.scad>
use <skin.scad>
/*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;