We recover the essential geometry of #primaryCurves using #curveFitting by trial and error — a human endeavor by "eye" and heuristics — not to be confused with mathematical curve fitting by regression analysis.
The heights of rectangles labeled N, P, Q, and R are 128, 80, 80, and 48, respectively. P is halfway between N and R, and Q is halfway between P and R.
The curve labeled S is the counterpart to the curve labeled O in the previous post. The purpose of these curves will be explained when we derive the #secondaryCurves from the primary curves.
For now, just note that curve O in the previous post is derived by simple proportion arithmetic. Width of N is 112 units and width of R is 28 units [https://pixelfed.social/p/Splines/793169876757012827]. Since the gap between start of curve O and the curve closest to it is 32 units at the front, the gap at the rear is 32*28/112 = 8, and 16 in the middle.
Curve S is derived in a slightly different manner because, unlike curve O where we knew the starting point, we know neither the start nor the end of curve S. Instead, we look at another clue that Vignola left for us — The 4 long leaves emanating from the rear and spreading towards the front on each bell shape. So we divide the front height of N and rear height of R into 4, giving us the start of S at 32 units from the top (miraculously in agreement with the start of curve O) in front and 12 units in the rear.
The top profile curve does not seem to "fit" Vignola's sketch. First, this is a hand sketch. Second, I tried to fit the curve more closely, but the design broke down later. Third, realize that if we fit the curve more closely to what's in the sketch, this will be the ONLY curve to have a tangent at the inflection point (switch from convex to concave) that is neither horizontal nor vertical.
Splines #ReverseEngineer #ImageScans for #restoration.
Show moreThis is a side view from #Vignola's #RegolaArchitettura at https://archive.org/details/gri_33125008229458/page/n39/mode/2up.
We recover the essential geometry of #primaryCurves using #curveFitting by trial and error — a human endeavor by "eye" and heuristics — not to be confused with mathematical curve fitting by regression analysis.
The heights of rectangles labeled N, P, Q, and R are 128, 80, 80, and 48, respectively. P is halfway between N and R, and Q is halfway between P and R.
The curve labeled S is the counterpart to the curve labeled O in the previous post. The purpose of these curves will be explained when we derive the #secondaryCurves from the primary curves.
For now, just note that curve O in the previous post is derived by simple proportion arithmetic. Width of N is 112 units and width of R is 28 units [https://pixelfed.social/p/Splines/793169876757012827]. Since the gap between start of curve O and the curve closest to it is 32 units at the front, the gap at the rear is 32*28/112 = 8, and 16 in the middle.
Curve S is derived in a slightly different manner because, unlike curve O where we knew the starting point, we know neither the start nor the end of curve S. Instead, we look at another clue that Vignola left for us — The 4 long leaves emanating from the rear and spreading towards the front on each bell shape. So we divide the front height of N and rear height of R into 4, giving us the start of S at 32 units from the top (miraculously in agreement with the start of curve O) in front and 12 units in the rear.
The top profile curve does not seem to "fit" Vignola's sketch. First, this is a hand sketch. Second, I tried to fit the curve more closely, but the design broke down later. Third, realize that if we fit the curve more closely to what's in the sketch, this will be the ONLY curve to have a tangent at the inflection point (switch from convex to concave) that is neither horizontal nor vertical.