Since you have a limited set of tools you are not actually doing a classical fitting. What you have is a discrete problem. And since you are looking for a somewhat easily drawn fit, no more that twice segmented for example.

One way to approach this is to find all the points that match your curvature requirements. Then find the point x units away from point on both ends for all of these see how well it matches. If the curvature match at the endpoint is too much off then this isn't a good candidate. If you don't find a good candidate split the problem into two. Once you have found a goodish candidate slide the result to see if relaxing the thing makes the error more symmetric.

Some things to note. Since your french curve is accelerating from one end to another you need to split beziers and b-splines at each span where the curve changes direction. Also be one you've found a good endpoints be sure to check that the halfway isn't too much off.

Now if you want to do a classical fitting like approach then you need to parametrize the sliding and scale of your curve. This is not likely useful since you in fact can not scale your rules at whim.

Or then you could just get a spline, you know one of those things that were used before computers and stuff, and write instructions on how to set up the spline.

Since you have a limited set of tools you are not actually doing a classical fitting. What you have is a discrete problem. And since you are looking for a somewhat easily drawn fit, no more than twice segmented for example.

One way to approach this is to find all the points that match your curvature requirements. Then find the point x units away from point on both ends for all of these and see how well it matches. If the curvature match at the endpoint is too much off then this isn't a good candidate. If you don't find a good candidate split the problem into two. Once you have found a goodish candidate slide the result to see if relaxing the thing makes the error more symmetric.

Some things to note. Since your french curve is accelerating from one end to another you need to split beziers and b-splines at each span where the curve changes direction. Also once you've found good endpoints be sure to check that the halfway isn't too much off.

Now if you want to do a classical fitting like approach then you need to parametrize the sliding and scale of your curve. This is not likely useful since you in fact can not scale your rules at whim.

Or then you could just get a spline, you know one of those things that were used before computers and stuff, and write instructions on how to set up the spline.

Since you have a limited set of tools you are not actually doing a classical fitting. What you have is a discrete problem. And since you are looking for a somwehat easysily drawn fit, no more that twice segmented for example.

One way to approach this is to find all the points that match your curvature requirements. Then find the point x units away from point on both ends for all of these see how well it matches. If the curvature match at the endpoint is too much off then this isnt a good candidate. If you dont find a good candidate split the problem into two. Omce you have found a goodish candidate slide the result to see if relaxing the thing makes the error more symmetric.

Some things to note. Since your french curve is accelerating from one end to another you need to split beziers and b-splines at each span where the curve changes direction. Also be one youve found a good endpoints be sure to check that the halfway isnt too much off.

Now if you want to do a classical fitting like approach then you need to parametrize the sliding and scale of your curve. This is not likely useful since you in fact can not scale your rules at whim.

Or then you could just get a spline, you know one of those things that were used before computers and stuff, and write instructions on how to set up the spline.

Since you have a limited set of tools you are not actually doing a classical fitting. What you have is a discrete problem. And since you are looking for a somewhat easily drawn fit, no more that twice segmented for example.

One way to approach this is to find all the points that match your curvature requirements. Then find the point x units away from point on both ends for all of these see how well it matches. If the curvature match at the endpoint is too much off then this isn't a good candidate. If you don't find a good candidate split the problem into two. Once you have found a goodish candidate slide the result to see if relaxing the thing makes the error more symmetric.

Some things to note. Since your french curve is accelerating from one end to another you need to split beziers and b-splines at each span where the curve changes direction. Also be one you've found a good endpoints be sure to check that the halfway isn't too much off.

Now if you want to do a classical fitting like approach then you need to parametrize the sliding and scale of your curve. This is not likely useful since you in fact can not scale your rules at whim.

Or then you could just get a spline, you know one of those things that were used before computers and stuff, and write instructions on how to set up the spline.