SplinesTo preserve the ability to print different strands in different colors when #3DPrinting, we must keep them separate. When #CNCMilling a block of wood or other material, we don't need to keep the strands separate.
To accommodate both kinds of output, I suggest that you keep the strands separate until the very end, and perform a #booleanUnion at the last possible stage after making a copy of the separate strands.
The topmost part of the diagram shows what the strands look like after a boolean union. Much of the internal structure is absorbed in the channel block, and overlapping parts of individual strands are eliminated.
The magenta curve from https://pixelfed.social/p/Splines/798252244743520392 is also shown here. Note that the location of the red cutting planes has changed slightly — Instead of 40 units from the origin, the first cutting plane is located at 39 because I ran into another limit that we must avoid.
Also, we need two blocks 120 units and 32 units long (not 24 units as was erroneously mentioned earlier). Turns out that cutting the strands at 32 units from the first cut puts us at 71 units from origin, and we run into another limit that destroys the #airtight properties of the cut solids. To get around that, we place the second cutting plane at 72 from origin to get a block 33 units long. The last cutting plane is at 159 units from origin, and when used with the first cutting plane it gives us a block 120 units long.
The lower portion of the diagram shows individual strands cut using the cutting planes as described above.
Depending on precision, you might or might not see a #nonmanifoldEdge on the second strand when cutting a length of 33 units. With precision set to 1/10 micron, which is ~100 times finer than current high-end #3DPrinters, I got a non-manifold edge.
Sometimes the fix is easy — Just #explode the solid, and rejoin the tiny surface fragments. Experiment with different precision settings.
Splines (@[email protected])
#Braids #3StrandBraids After we #sweepOneRail with the blue #sweepingCurve on the orange #railCurve for the #braid strand, we cap #planarHoles to get a single #airtight strand. As described in https://pixelfed.social/p/Splines/798015349727305297, the radius of the blue circle is 8 units, and the total height of a strand swept by that circle is 24 units. Half of that is above the #tectonic surface, which is still twice of what #Vignola documented in #RegolaArchitettura. We will apply #nonuniformScaling in the Z direction to reduce the height in half while keeping the length (X) and width (Y) the same. But before we do that we split and discard some of the bottom portion of the strand that is below the tectonic surface and is not needed. The top half of the figure shows the front view of a single strand. The bottom shows the perspective view of the same strand. Note that the orange braid rail starts at the center of the blue sweeping circle which looks like an ellipse in the front view. The orange rail itself looks like a flat sinusoid in the front view, but its beautiful meandering shape is really apparent in the perspective view. The orange rail curve is centered on the "ground" or XY plane, which is also where the #tectonicSurface for the braid is. The amplitude of the orange curve (maximum or minimum from axis of the curve) is 4 units. We need to preserve the geometry of the strand at least up to the bottom of the orange rail. If we split the strand exactly at 4 units below the ground plane, we hit a limit that not all #CAD tools are able to handle. To get around, we extend it past that limit by an arbitrarily small fraction, like 0.2, and discard the portions below. We could have extended it by 0.1 or 0.3 but it wouldn't have mattered. Next, we draw a profile curve for the braid channel which is 32 units wide and its groove is 12 units tall for now. The rims on both sides of the channel are each 8 units wide. Total height of rim and channel is 16.2 units
