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SplinesContinued from https://pixelfed.social/p/Splines/808187718454868394
Explode the wedge on the top with curved faces and discard everything except the two faces.
Centered on the column axis marked with A, draw two concentric circles parallel to the XY plane — one with radius AB and another with radius AC. Split both circles with the two wedge faces.
Using the edges of the two wedge faces as #rails and using the two arcs BB and CC as #sweepingCurves, perform a #sweepTwoRails operation to generate a concave surface. Join this concave surface with the two faces.
The shape we just produced still has an open hole between the two arcs BB and CC. Cap this #planarHole to create an #airtight wedge shape with curved faces. As always, check for #nakedEdges and #nonManifoldEdges.
Align the wedge shape and the two 16 units thick spirals from the previous post. Then rotate both 45° about the column axis. Rotate and copy them again at 90° about the column axis until you have the curved volutes on all four corners.
Explode the wedge on the top with curved faces and discard everything except the two faces.
Centered on the column axis marked with A, draw two concentric circles parallel to the XY plane — one with radius AB and another with radius AC. Split both circles with the two wedge faces.
Using the edges of the two wedge faces as #rails and using the two arcs BB and CC as #sweepingCurves, perform a #sweepTwoRails operation to generate a concave surface. Join this concave surface with the two faces.
The shape we just produced still has an open hole between the two arcs BB and CC. Cap this #planarHole to create an #airtight wedge shape with curved faces. As always, check for #nakedEdges and #nonManifoldEdges.
Align the wedge shape and the two 16 units thick spirals from the previous post. Then rotate both 45° about the column axis. Rotate and copy them again at 90° about the column axis until you have the curved volutes on all four corners.
Splines (@Splines@pixelfed.social)
Revolutionary #Volutes The two large blue circles at the bottom marked with A and B are from the floor plan for #ModernIonicCapital shown in https://pixelfed.social/p/Splines/807782440025967685. The larger one has a radius of 296 units, while the smaller one is 16 less, at 280. Both are centered at x = 416. Both are then rotated ±45° about the column axis to give us the four red circles. The small blue circle with radius 120 units is for the column neck. The two red circles in the back are shown extruded vertically as cylinders. The other two haven't yet been extruded because we want to see the rest of the structure from the front. The two tube or #torus-like structures are obtained by revolving the trimmed #spiral #volute outlines from https://pixelfed.social/p/Splines/808043616946914228 about the vertical axis located at x = 416. Only the bottom tube maintains the interior shape of the spiral. With this setup, vertically extrude the two remaining red curves in the front so they are at least as high as the top of the upper tube. Next, perform a #booleanDifference between the top tube and the two extrusions marked A. Keep the wedge shape of the top tube on the left side and discard the remaining portion of the tube from the right. Then, perform a boolean difference between the bottom tube and the two extrusions marked B. With the wedge shape of the bottom tube on the left side, perform a further #booleanIntersection with the two extrusions marked A. This will produce two curved spirals that are 16 units thick. Discard the remaining portions of the bottom tube as well as all the red extrusions. After these operations, we are left with one wedge shape with curved faces and two spirals that are 16 units thick, also with curved faces. The next step is to convert the outer surface of the wedge shape from convex to concave.
Left side of this diagram shows the #profileCurves for the cap of #ModernIonicCapital from the front. The right side shows a perspective view of the cap surfaces obtained by revolving the profile curves about their respective axes and after some of those have been trimmed away
The measurements for the floor plan of the modern ionic capital are given in https://pixelfed.social/p/Splines/807782440025967685 with further links to relevant pages in #Scarlata's book at the bottom.
I won't bore you with the bottom portion of the modern #capital because it is very similar to that of the classic capital shown in https://pixelfed.social/p/Splines/792124787573855518. A significant difference is that the bottom #ovolo is shorter, with a total height of 32 units instead of 40
For the cap, we need two identical copies of a single profile curve that is 30 units wide and 48 units tall. The curves marked by A and B in the diagram are oriented in the same direction and are spaced 100 units from each other.
The bottom of profile curve A lines up with the neck of the #columnShaft at 120 units from the column axis. The revolution axis for this curve is located at 416 units from the column axis at the center of the largest circle in the floor plan.
We #revolve profile curve A full circle about its revolution axis. Then, we #rotate the resulting surface about the column axis to get 4 identical copies.
We revolve profile curve B full circle about the column axis. Then, we trim the resulting surface along with the 4 others at each intersection to get the side and corner surfaces for the cap of the capital.
We #join the trimmed surfaces, cap #planarHoles to convert them into a closed solid, and verify that the resulting solid is #airtight with no #nakedEdges and no #nonManifoldEdges.
The cap is in the correct final orientation. The volutes will be at 45° angles, but when we construct them, it will be easier to rotate the whole plan 45° so that the #volute #spiral is on the XZ plane.
The measurements for the floor plan of the modern ionic capital are given in https://pixelfed.social/p/Splines/807782440025967685 with further links to relevant pages in #Scarlata's book at the bottom.
I won't bore you with the bottom portion of the modern #capital because it is very similar to that of the classic capital shown in https://pixelfed.social/p/Splines/792124787573855518. A significant difference is that the bottom #ovolo is shorter, with a total height of 32 units instead of 40
For the cap, we need two identical copies of a single profile curve that is 30 units wide and 48 units tall. The curves marked by A and B in the diagram are oriented in the same direction and are spaced 100 units from each other.
The bottom of profile curve A lines up with the neck of the #columnShaft at 120 units from the column axis. The revolution axis for this curve is located at 416 units from the column axis at the center of the largest circle in the floor plan.
We #revolve profile curve A full circle about its revolution axis. Then, we #rotate the resulting surface about the column axis to get 4 identical copies.
We revolve profile curve B full circle about the column axis. Then, we trim the resulting surface along with the 4 others at each intersection to get the side and corner surfaces for the cap of the capital.
We #join the trimmed surfaces, cap #planarHoles to convert them into a closed solid, and verify that the resulting solid is #airtight with no #nakedEdges and no #nonManifoldEdges.
The cap is in the correct final orientation. The volutes will be at 45° angles, but when we construct them, it will be easier to rotate the whole plan 45° so that the #volute #spiral is on the XZ plane.
Splines (@Splines@pixelfed.social)
Plan for the #ModernIonicCapital If the design in https://pixelfed.social/p/Splines/807569519962747338 looks daunting, let me assure you it is far simpler than the work that went into the reconstruction of just the #scroll for the #classicIonicCapital. Be sure to check out #MileStone4 at https://pixelfed.social/p/Splines/795361973789834465. With the modern #IonicCapital, the designers went back to the basics of using just straight lines and circular arcs to define the geometry of the essential elements of the capital. No #braids, #keystones, or #modillions, and no #helix curves or #sinusoids. We start the floorplan for the modern ionic capital with a circle of radius 5/6 of µ (120 when µ = 144) which marks the neck of the #columnShaft. Tangent to this circle is a large circle of radius 296 units centered on the X axis exactly 416 units from the column axis. This is the circle that marks the curve of the #abacus, which is always tangential to the column shaft at the neck. This circle also marks the curved faces of the interior portion of the #volute wedge. Without the raised volute spirals, the interior wedge appears flush with the abacus as they follow the same circular arc. Concentric to this large circle is another circle with a radius of 280 units to mark the extent of the raised volute spirals which are 16 units thick. Another concentric circle of radius 266 units marks the outer edge of the top of the capital. The gap between the outermost large circle and the innermost concentric circle is 30 units, and that is reflected in another pair of circles centered on the column axis with radius of 250 units and 220 units to define the four corners. The capital footprint fits in a square 396 units wide — or 24.75 parts horizontally from axis, per #Scarlata in https://babel.hathitrust.org/cgi/pt?id=mdp.39015031201190&view=1up&seq=45. Use this with the sketch in https://babel.hathitrust.org/cgi/pt?id=mdp.39015031201190&view=1up&seq=142
RikuNKMR3rd raffle art done.
@megfawkes.bsky.social Syn. Please read the alt text too. Took it as an opportunity to polish my writing.
#art #NSFW #OC #succubus #monsterGirl #MegFawkeOCs #airTight #creampie