The #shaft of an #Ionic column is not perfectly cylindrical but gradually tapers off in the top 2/3 of the shaft. As such, the #primaryProfileCurve is not a straight line, nor is it composed of regular arcs. Instead, it is a complex amalgam of straight lines, circular arcs, and #NURBS curves, where the fancy acronym stands for an even fancier name — "Non-Uniform Rational B-Splines."
So, the promise [https://pixelfed.social/p/Splines/789956327130679640] was that we were going to get through this by drawing just straight lines and arcs. How are we going to draw NURBS? The answer is that we won't. The #CAD program will, as long as we give it sufficient information to carry out the task.
There are three NURBS curves in the profile shown in the plan. The longest and the most important one is between the points marked C through J. There is a smaller one between B and C, and an even smaller one between J and K.
While all three NURBS curves are mathematically similar, the information we must provide to the CAD program for the longest one is different from the other two short ones, and the operations the CAD program carries out to construct the longest one and the other two curves is also different.
This brings us to two new operations — #interpolate or "fit through points," and #blend shapes (existing curves or surfaces). When you choose a CAD program, make sure it supports NURBS, #interpolation, and #blending.
Starting at the bottom of the shaft, point A is 144 units from the #columnAxis, and so is point B, which is also 768 units higher than A. Starting with C through J, the points gradually move closer to the axis until J is exactly µ * 5/6, or 120 units from the axis. These points are equidistant vertically — all 192 units apart. However the horizontal distance is non-uniform.
In the next post we will mark the 8 points C through J using using one arc and 8 straight lines — I will keep my promise.
Splines Plan for #ColumnShaft of #IonicColumn
Show moreThe #shaft of an #Ionic column is not perfectly cylindrical but gradually tapers off in the top 2/3 of the shaft. As such, the #primaryProfileCurve is not a straight line, nor is it composed of regular arcs. Instead, it is a complex amalgam of straight lines, circular arcs, and #NURBS curves, where the fancy acronym stands for an even fancier name — "Non-Uniform Rational B-Splines."
So, the promise [https://pixelfed.social/p/Splines/789956327130679640] was that we were going to get through this by drawing just straight lines and arcs. How are we going to draw NURBS? The answer is that we won't. The #CAD program will, as long as we give it sufficient information to carry out the task.
There are three NURBS curves in the profile shown in the plan. The longest and the most important one is between the points marked C through J. There is a smaller one between B and C, and an even smaller one between J and K.
While all three NURBS curves are mathematically similar, the information we must provide to the CAD program for the longest one is different from the other two short ones, and the operations the CAD program carries out to construct the longest one and the other two curves is also different.
This brings us to two new operations — #interpolate or "fit through points," and #blend shapes (existing curves or surfaces). When you choose a CAD program, make sure it supports NURBS, #interpolation, and #blending.
Starting at the bottom of the shaft, point A is 144 units from the #columnAxis, and so is point B, which is also 768 units higher than A. Starting with C through J, the points gradually move closer to the axis until J is exactly µ * 5/6, or 120 units from the axis. These points are equidistant vertically — all 192 units apart. However the horizontal distance is non-uniform.
In the next post we will mark the 8 points C through J using using one arc and 8 straight lines — I will keep my promise.