SplinesAfter we diligently sweep the remaining sections of the #scroll surface as described in https://pixelfed.social/p/Splines/794203007066866034, we get a complete surface ready for a quality check using a #surfaceAnalysis tool known as #environmentMapping.
Environment mapping is similar to #textureMapping that I used in https://pixelfed.social/p/Splines/790701780235593999 to give a marble look to a finished design, except that the purpose of an #environmentMap is not to create a finished design, but just to temporarily wrap an image on a surface to check it by "eye."
Here, we see the scroll surface with a polished gold environment map. For many uses, this surface is adequate. But if you are looking for perfection, you will not be able to ignore the #banding on the scroll surface, precisely at each interstitial location — There are 5 distinct bands from 6 #modulatingSpirals.
The banding is caused by our #tertiaryCurves which are #continuous over the scroll surface, but not #smooth. Mathematically speaking, the tertiary curves are not #continuouslyDifferentiable over their entire length. So, is it time for #quaternaryCurves and sweeping the scroll surface again, section by section?
There is an easier way to achieve a smooth patina on the scroll surface using #surfaceBlend. We used #curveBlend, specifically #tangencyBlend in https://pixelfed.social/p/Splines/791723063470910081 and https://pixelfed.social/p/Splines/791794072490907090, and #arcBlend in https://pixelfed.social/p/Splines/792616677005177924.
To build the scroll surface using surface blends, we keep only the front 5 sections and the rear five section intact. That is because these sections are the most definitionally rich and impart the whole surface its distinctive look.
We discard the bands immediately adjacent to the front and rear bands — ones that are 14 units and 7 units deep. Then we split the remaining middle band that is 25 units deep into 18 and 7, with the larger section biased toward the front.
Environment mapping is similar to #textureMapping that I used in https://pixelfed.social/p/Splines/790701780235593999 to give a marble look to a finished design, except that the purpose of an #environmentMap is not to create a finished design, but just to temporarily wrap an image on a surface to check it by "eye."
Here, we see the scroll surface with a polished gold environment map. For many uses, this surface is adequate. But if you are looking for perfection, you will not be able to ignore the #banding on the scroll surface, precisely at each interstitial location — There are 5 distinct bands from 6 #modulatingSpirals.
The banding is caused by our #tertiaryCurves which are #continuous over the scroll surface, but not #smooth. Mathematically speaking, the tertiary curves are not #continuouslyDifferentiable over their entire length. So, is it time for #quaternaryCurves and sweeping the scroll surface again, section by section?
There is an easier way to achieve a smooth patina on the scroll surface using #surfaceBlend. We used #curveBlend, specifically #tangencyBlend in https://pixelfed.social/p/Splines/791723063470910081 and https://pixelfed.social/p/Splines/791794072490907090, and #arcBlend in https://pixelfed.social/p/Splines/792616677005177924.
To build the scroll surface using surface blends, we keep only the front 5 sections and the rear five section intact. That is because these sections are the most definitionally rich and impart the whole surface its distinctive look.
We discard the bands immediately adjacent to the front and rear bands — ones that are 14 units and 7 units deep. Then we split the remaining middle band that is 25 units deep into 18 and 7, with the larger section biased toward the front.
Splines (@[email protected])
Continuation of https://pixelfed.social/p/Splines/794199123072358090 After you have rebuilt all the #spiral arcs as well as the projected #secondaryCurves into #tertiaryCurves, it is finally time to sweep the scroll surface, but remember to do it one section at a time. Use one section of a spiral arc and the corresponding arc in the next interstitial as #railCurves. Then, #sweepTwoRails, using one section of the tertiary curves on each end of the rails. This diagram shows 5 sections of the swept surfaces in front and 5 sections in the back. The remaining ones will be built similarly but require further processing to make the whole surface smooth.
Dr Sam McMaster
AlexHenderson
Hackster.io
