Horace - Epistles [Epistularum, Letters], Book 2, ep. 3 "Art of Poetry [Ars Poetica; To the Pisos]," l. 24ff (2.3.24-31) (19 BC) [tr. Howes (1845)] | WIST Quotations

Dear sire, and offspring worthy of your fire! We bards are dupes to what ourselves admire. Would I be brief -- I grow confused and coarse; Who aims at smoothness, fails in fire and force; In him who soars aloft, bombast is found; Who fears to face the tempest, crawls…

Manifold Fitting under Unbounded Noise

Splines (@[email protected])

#IonicVolutes are the sinews of #IonicScrolls. Without #volutes, there would be scrolls, but not #Ionic Scrolls. Each scroll starts with a volute in front and is modulated by as many as six volutes of different shapes and sizes as it reaches the back, with the scroll surface tightly hugging the volutes at each contact point in ALL 3 dimensions. This is a key point to remember before we start #reverseEngineering the first #primaryProfileCurves from old image scans. This diagram shows the #scaffolding we will construct using straight lines and rectangles, first in 2 dimensions, then place them front-to-back in 3 dimensions using precise markers, and finally scale and superimpose the volutes on this scaffolding. All of this will be done before we derive the primary profile curves from the image scans. How did I know about this scaffolding? I didn't. It is not documented anywhere that I'm aware of. I developed this after years of striving to derive the correct shape, and I hope that there are people who can still "see" things I might have missed and help improve the design. So, the actual process went like this: I drew outlines from 2D image scans in the top view, getting close to #Vignola's detailed sketches. Then, I did the same thing with image scans in the side view, and I found that the designs didn't line up. After several iterations, I got the designs to line up in both views, and it was obvious that the bell shape of the scroll would follow the large volute in the front. So, I used the large volute as a "rail" and tried to sweep the primary profile curves on one rail. Big mistake! The undulating shapes of the primary profile curves wobbled wildly on the single rail — The middle, 3/4, and back of the scroll were twisted out of shape! Instead of trying to #sweepOneRail, I decided to clamp down wobbling with another operation called #sweepTwoRails, using volutes at both front and back ends as rails with less wobbling. You will need a #CAD tool to practice.

Functions with average smoothness: structure, algorithms, and learning