SplinesThe slab height depends on the roundness of the egg and whether we have a concave design or not. If we are using a concave base, then top half of the egg is eliminated. For a fully round egg, that means the concave variant must scoop out up to 16 units deep. The dart slab will match the egg slab in depth.
To create the 3-dimensional shape of the dart, first #rotate the fin profile 90° in 3D space along the straight line at the bottom of the fin so that the rotated profile is perpendicular to the two #sweepRails for the dart.
Using the two sweep rails and the perpendicular fin profile, #sweepTwoRails to develop the surface of the dart. Remember to close the planar hole at the end of the fin to get a solid #airtight object. As always, check for #nakedEdges and #nonmanifoldEdges to stave off problems later.
#Extrude the bottom of the dart until it is flush with the bottom of the oval slab.
Two details worth noting in the dart design are:
1. The most exaggerated portions of the dart fin are sliced off when the eggs are sliced. After slicing, the size of the fin is roughly in proportion to the rims of the eggs on both sides.
2. There is a gap between the dart arrow and the oval slab. See the gap between points R and T in https://pixelfed.social/p/Splines/796961505955555432. This gap is necessary and will automatically close when we transfer the egg and dart to the #doublyCurved surface of the #ovolo on the #capital of the #IonicColumn. That is because the Ovolo is shaped like a bowl whose top has a bigger radius than the bottom. As a result, the motif will be warped, and its bottom will be condensed to fit the smaller radius at the bottom, closing the gap in the process.
If you plan to use the eggs and darts motif on a linear surface where there is no warping, experiment with the arrow and tip for a pleasing result.
Splines (@[email protected])
#EggsAndDarts continuation of https://pixelfed.social/p/Splines/796958366767133979 Successive egg slabs are 1/2 part or 4 units away from each other. So the thinnest part of the dart is 4 units. The tip of the dart is at point P, which is 22 units from the major axis for the egg slab. The inside egg is 4 parts or 32 units wide, and we will start with the dart fin also at 32 units wide, even though a portion of the fin will be sliced off when the egg is sliced by the red cutting plane. To find the start and end of the fin, draw a vertical line from P of length µ/2 or 72 units. Offset that line on both sides by 16 units. Mark the intersections of these lines with the outline of the largest ellipse with points A and B. Draw an oval centered on AB with major radius 16 units and minor radius 2/5 of that, or 6.4 units. Divide each arc of the oval into 5 equal parts and mark AD and EF at 2/5 of that. Copy the oval from its top point C to D as well as E. Mark the intersection of the copies at F. Trim the 3 ovals to get 4 arcs AD, DF, FE, and EB. Join them and close the curve with a straight line from A to B. Draw a square 12 x 12 whose bottom edge is centered on P. From each of the top 2 corners, draw a circle with diameter 4 units, shown by RS. #Reflect point P using the major egg axis as a #mirror to get point Q. Draw a #circleThrough3Points P, Q, and R. The origin of the circle, point O should be 3.5 units directly below the base of the large oval. Draw a vertical line up from S to where it is tangent to the side of the large oval. Trim the straight line and arcs to get the left profile of the dart starting with A, passing through S and T, and ending at P. Join all 4 segments and reflect them using the line PC as the mirror. These mirrored copies are the #rails along which we will sweep the fin of the dart with #sweepTwoRails operation to create the dart, but we must orient the fin to be perpendicular to the rails first