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Splines<a href="https://pixelfed.social/discover/tags/Milestone4?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone4</a> — <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicScroll</a> <a href="https://pixelfed.social/discover/tags/ModulatingSpirals?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#ModulatingSpirals</a> <a href="https://pixelfed.social/p/Splines/792906324854792619" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/792906324854792619</a> <a href="https://pixelfed.social/discover/tags/ReverseEngineer?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#ReverseEngineer</a> <a href="https://pixelfed.social/discover/tags/ImageScans?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#ImageScans</a> <a href="https://pixelfed.social/p/Splines/793215298082967733" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793215298082967733</a> <a href="https://pixelfed.social/discover/tags/ScrollSurface?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#ScrollSurface</a> <a href="https://pixelfed.social/discover/tags/scaffolding?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#scaffolding</a> <a href="https://pixelfed.social/p/Splines/793597613908557570" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793597613908557570</a> <a href="https://pixelfed.social/discover/tags/SecondaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#SecondaryCurves</a> <a href="https://pixelfed.social/p/Splines/794105734853818690" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/794105734853818690</a> <a href="https://pixelfed.social/discover/tags/Sweeping?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sweeping</a> with <a href="https://pixelfed.social/discover/tags/TertiaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#TertiaryCurves</a> <a href="https://pixelfed.social/p/Splines/794203007066866034" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/794203007066866034</a> <a href="https://pixelfed.social/discover/tags/Smoothness?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Smoothness</a> with <a href="https://pixelfed.social/discover/tags/SurfaceBlend?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#SurfaceBlend</a> https://pixelfed.social/p/Splines/794868875707070193 Solid <a href="https://pixelfed.social/discover/tags/Scroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Scroll</a> https://pixelfed.social/p/Splines/795276076797088402 <a href="https://pixelfed.social/discover/tags/Milestone3?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone3</a> — <a href="https://pixelfed.social/discover/tags/IonicColumn?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicColumn</a> https://pixelfed.social/p/Splines/792803978865652429 <a href="https://pixelfed.social/discover/tags/Milestone2?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone2</a> — Classic <a href="https://pixelfed.social/discover/tags/IonicEntablature?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicEntablature</a> https://pixelfed.social/p/Splines/791021871062069787 <a href="https://pixelfed.social/discover/tags/Milestone1?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone1</a> — <a href="https://pixelfed.social/discover/tags/IonicPedestal?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicPedestal</a> https://pixelfed.social/p/Splines/790752092700055739

Splines<a href="https://pixelfed.social/discover/tags/SeeFeelTouchHug?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#SeeFeelTouchHug</a> In both <a href="https://pixelfed.social/discover/tags/art?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a> and <a href="https://pixelfed.social/discover/tags/engineering?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#engineering</a>, one must be able to both <a href="https://pixelfed.social/discover/tags/see?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#see</a> and <a href="https://pixelfed.social/discover/tags/feel?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#feel</a> things that might not be there (yet). We were able to "see" the outlines of the <a href="https://pixelfed.social/discover/tags/scroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#scroll</a> surface from <a href="https://pixelfed.social/discover/tags/imageScans?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#imageScans</a> of <a href="https://pixelfed.social/discover/tags/Vignola?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Vignola</a>'s sketches in <a href="https://pixelfed.social/p/Splines/793169876757012827" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793169876757012827</a> and <a href="https://pixelfed.social/p/Splines/793215298082967733" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793215298082967733</a>. Vignola's images are on a 2-dimensional surface, as are the outlines we extracted from them. We believe the scroll surface also exists, but it is not yet manifest in 3-dimensional space. So, like a visually impaired person, we try to "feel" our way to the scroll surface using the outlines as our <a href="https://pixelfed.social/discover/tags/walkingStick?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#walkingStick</a>. This diagram is identical to that in <a href="https://pixelfed.social/p/Splines/793493316852849994" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793493316852849994</a> but with the rear ends of the horizontal <a href="https://pixelfed.social/discover/tags/primaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#primaryCurves</a> marked with R1, R5, and R3, which are paired with F1, F5, and F3, respectively. We know that the scroll surface must <a href="https://pixelfed.social/discover/tags/touch?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#touch</a> the tangent points T1, T2, and so on in front, as well corresponding tangent points in the rear (not shown here to reduce clutter). In <a href="https://pixelfed.social/p/Splines/792906324854792619" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/792906324854792619</a>, I mentioned that a scroll starts with a volute in front and is <a href="https://pixelfed.social/discover/tags/modulated?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#modulated</a> 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. In other words, it is not sufficient for the scroll surface to "touch" the <a href="https://pixelfed.social/discover/tags/volute?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#volute</a> <a href="https://pixelfed.social/discover/tags/spirals?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#spirals</a> just in the front and rear. It must also "hug" the intermediate <a href="https://pixelfed.social/discover/tags/modulatingSpirals?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#modulatingSpirals</a>. I will first show this technique with 4 modulating spirals using rectangles M, N, P, Q, and R as their frame, and add more later on. Intuitively, we know that if we use curve F3-R3 as our walking stick on the straight vertical extrusion of that curve, we will feel the scroll surface *somewhere* on that extrusion along every point from front to back. We can narrow it down further by excluding portions above and below as we approach rectangle R in the rear.

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