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