SplinesArcs and lines toil for <a href="https://pixelfed.social/discover/tags/splines?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#splines</a><br>
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2500 years ago, when they had neither computers nor <a href="https://pixelfed.social/discover/tags/CAD?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#CAD</a> tools, designers and architects relied on knowledge of algebra, geometry, and trigonometry for their daily work. It was a mere 350 years ago that Leibniz and Newton brought calculus as a new mathematical tool for design and engineering.<br>
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Before computers arrived, artists, designers, and architects toiled with manual drafting tools to engineer breathtaking masterpieces. "Toil" is not an exaggeration to describe that endeavor, even though I suspect some of them really enjoyed what they were doing. <br>
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<a href="https://pixelfed.social/discover/tags/Scarlata?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#Scarlata</a> compiled an entire book on <a href="https://pixelfed.social/discover/tags/VignolaProportions?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#VignolaProportions</a> with painstaking accuracy and high precision before there were calculators and spreadsheets, making it "easy" to convert from µ to physical units in both English and Metric systems, but the world has moved on, his work is forgotten, and nobody is thankful for his contributions.<br>
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If you have a CAD tool, you need not toil. Simply draw an arc of radius µ = 144 that is centered on the <a href="https://pixelfed.social/discover/tags/columnAxis?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#columnAxis</a> and passes through point B. Then draw a vertical line parallel to the column axis at x = µ * 5/6, or 120 units. Use this line to split the arc and trim away the left portion of the arc. Next, divide the length of the remaining portion of the arc into 8 equal portions using your CAD tool to mark points 1 through 8 as shown. If your CAD tool is able to divide the leftover arc this way, you can just ignore the angular lines radiating from the center. Otherwise, I will show you how to use them as a fallback.<br>
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Now look at point C, which seems like it is vertically above point B, but it is not. It is actually vertically above point 1.<br>
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Draw 7 more vertical lines starting with point 1, then point 2, and so on. Mark point C at 192 units vertically above on line 1, D at 192*2 on line 2, E at 192*3 on line 3, and so on until you reach point J.<br>
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Select these 8 points and use your CAD program to interpolate a free-form NURBS curve to fit these points.