# Curve-to-straight joining problem

Consider this ...

Notice three joins are very good, but one is not so good.

My question: in fact, is the problem shown in fact precisely an example of THE FOLLOWING type of problem, and solution:

https://graphicdesign.stackexchange.com/a/16011/30169

So, indeed, is the total solution correct implementation of the techniques explained there? OR is there a further more complicated problem in this case?

Or, in my naivety is there some other problem? Thank you!

Supplementary question: is there an outstanding article or book, that deals obsessively with achieving perfection in the issues relating to joining straights and curves in splines? Thank you.

The method described in the post you mention is sound and covers mostly the bases.

Mathematically speaking spline handle is the derivate direction of the spline at the joining point and how long it is controls the second derive, or speed of curvature change.

• If the curve segments meet we call it a c0 continuity, which is a sharp corner. This is the general case.

• If the curves meet and their spline tangents align on a line in opposite directions we have a c1 continuous curve.

• If the curves meet and they are c1 continuous AND the spline tangents are equally long we have a c2 continuous curve.

Technically you also have higher order continuities. And the higher the order the better the join can be said to be (tough cubic splines dont have more continuities so this is as far as you can get on Bezier curves in illustrator). In general however 2d graphics do not really cause need for higher than 1 degree continuous when aligning straight and curved and 2 degree when aligning 2 curves. However in 3d it becomes more important as reflections interact with surfaces in a way that makes this more prominent.

• Thanks for that! BTW for some reason it is not possible to add a bounty on the question. Cheers! – Fattie Sep 28 '14 at 3:18
• @JoeBlow you dont have enough reputation. – joojaa Sep 28 '14 at 5:20
• ah gotchya. i had 100 when I put a bounty on the other question. Cheers – Fattie Sep 28 '14 at 5:26