GNAL/scad/spiral/spiral_6.scad

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D=300; // start diameter
N=1; // number of spirals
FN=100;
$fn=FN;
R = (D + (N * 2.095)) / 2;
module ShapeToExtrude ()
{
bottom = 1.2;
top = .3;
top_offset = (bottom - top);
h = 2.2;
// Build in +x space. The outside edge of this shape must follow the extrusion path, or there will be open seams..
polygon ( points= [
[0, 0],
[top_offset, h],
[bottom, h],
[bottom, 0]
]);
}
module InwardSpiral (StepSize, Steps, StartRadius, Pitch, ShapeX) {
for (i=[0 : Steps - 1]) {
// This could be made more computationally efficient
// by collapsing intermediate values and by doing only
// essential calculations inside the loop, but for now
// let's just leave it easy to read.
ThisTheta = StepSize * i;
NextTheta = StepSize * (i + 1);
ThisRadius = StartRadius - i * (Pitch * (StepSize / 360));
// Spiral step approximated by arc of radius ThisRadius,
// passing through the start and end points calculated here.
NextRadius = StartRadius - (i + 1) * (Pitch * (StepSize / 360));
ThisX = ThisRadius * sin(ThisTheta);
ThisY = ThisRadius * cos(ThisTheta);
NextX = NextRadius * sin(NextTheta);
NextY = NextRadius * cos(NextTheta);
DeltaX = NextX - ThisX;
DeltaY = NextY - ThisY;
SlopeToNext = DeltaY / DeltaX;
BisecSlope = -1 / SlopeToNext;
ThisXYToBisector = sqrt(DeltaX * DeltaX + DeltaY * DeltaY) / 2;
BisectX = ThisX + (DeltaX / 2);
BisectY = ThisY + (DeltaY / 2);
BisectToCentre = sqrt(pow(ThisRadius, 2) - pow(ThisXYToBisector, 2));
AbsXComponent = sqrt(pow(BisectToCentre, 2) / ( 1 + pow(BisecSlope, 2)));
XComponent = NextY < ThisY ? AbsXComponent: -AbsXComponent;
YComponent = XComponent * BisecSlope;
CentreX = BisectX - XComponent;
CentreY = BisectY - YComponent;
ExtrudeAngle = -2 * acos(BisectToCentre / ThisRadius);
ArcOrientation = NextY < ThisY ? atan(BisecSlope) - (ExtrudeAngle / 2) : -180 + atan(BisecSlope) -(ExtrudeAngle / 2);
translate([CentreX, CentreY, 0]) {
rotate ([0, 0, ArcOrientation]) {
rotate_extrude (angle=ExtrudeAngle, $fn=300) translate ([ThisRadius - ShapeX, 0, 0])ShapeToExtrude();
}
}
}
}
module spiral () {
SPIRALROTATION=N * 360;
SPIRALSTEPS=180;
INITIALRADIUS= 300 / 2 ;
PITCH=2.095;
XMAXSHAPE=2;
InwardSpiral (
SPIRALROTATION/SPIRALSTEPS,
SPIRALSTEPS,
INITIALRADIUS,
PITCH,
XMAXSHAPE);
}
spiral();