The Spline Tab

[skycowboypaul]

I am sitting here looking at the spline tab. I have played with it a few times but I have never used it. I am wondering, what good is it? What would I use it for? How would I use it. Why and when would I want to convert a spline to a line or arc? What will adding or removing a point from a spline get me? The DC manual doesn't really provide answers to any of these questions. A tutorial on splines, how and where to use them would be very very interesting to me. Okay, I'm done wondering, thanks for reading this boring post

[i44troll]

Paul,

Great question, not boring at all!

When drafting was pencil and paper special tools were required to aid the draftsman in drawing progressive arcs. One of those tools was a strip of wood or rubber that was flexible enough to bend into an enumerable amount of arcs and curves; they called it the spline. Unlike the compass, the spline is free of an arch radius and was used to "interpolate" (to average a series of points) or to "smooth" a line or series of lines and arcs. So, splines are used in any application where you want to create an arc but not necessarily one that you want drawn using a radius. Being a machinist, the best example that I can give you would be the "involute curve" used to define the shape of gear teeth. While this may not be the most practical example it is really not necessary to know what application it is normally used for, but rather, it is more important that you use it enough to find out what it actually does to see if it will be useful for your own drawings.

Chris "i44troll"

[skycowboypaul]

Chris

Did you use any splines when you drew up those doors for me?

Paul

[i44troll]

Paul,

No, I didn't use the spline tool on any of the doors, instead, I used a series of arcs joined together end to end. I rarely use splines because most of my drawings need to have dimensions that are easily interpreted by my students, and splines are not easily dimensioned (except they be converted to lines where the line endpoints can be plotted in X and Y) The tool that I use most when I need to create a "progressive" arc is the "Draw an Elliptical Arc" tool within the circle tab. This little jewel is so useful I use it in nearly all my drawings to created bent arrows to show detail in my drawings. Here's an example......
   
Without the aid of the arrow it would be difficult to squeeze the whole drawing into the confines of the page, plus, I think it looks pretty cool!

Chris "i44troll"

---

<< why would I want to convert a spline to a line or arc? >>

I would change a spline into lines and arcs so that the end points can be easily plotted on a coordinate grid. You cannot define a spline using endpoints and arc centers, but you can define lines and arcs that have a constant radius. The result of the change is a very close representation of the original spline.

<< What will adding or removing a point from a spline get me? >>

Remember, a spline is an "interpolation" of points. Therefore, if you add or delete a "single" point you change the appearance of that line. If we had no way of editing a spline I doubt that very many of us would ever use them at all. When you draw a spline you wont know exactly how that line will come out in appearance. Being able to move a point to a different location gives us a little bit more control in the outcome of that line.

Chris "i44troll"

[Admin 1]

I have used the Spline Tool to create detail 'cut-offs' and 'cut-aways' in some of my drawings.
For an example, see my 'DDs Pavilion' drawing on our Drawings Download Pages.    

Just my penny-and-a-half worth on the subject. lol

Btw i44troll, I like your curvy arrow lines. Another one of those little 'Hints & Tips' that one wouldn't always think about.

Oh hey! Don't forget to submit your vote for my proposed new Hints and Tips forum <here> too!

[williamj]

Okay... I hope this thread isn't closed, so here goes.

I read the thread and I didn't see answer (might have missed it though) to the question in my head. But first a little preliminary...

In plotting a curve on an X,Y graph and connecting the plot points using the spline... does the spline section in between the plot points actually conform to the curve or is it just an approximation?

I.E. If I were to develop the formula for a curve using those plot points would a point derived from that formula land on the spline section for the new point?

I hope this isn't as confusing as it sounds to me,
williamj

[i44troll]

Bill,

I think the actual question was "what is a spline and what is it used for". I think we answered as best we could based entirely on our own personal experiences. If you want to get a little deeper into the subject you would look up words like "NURBS", which is an acronym for "Non-uniform rational basis spline" which is just another way to describe a spline that is generated using computer generated points (control points and "knots"). According to some sources on wiki this was needed in the auto industry so that a spline could be defined mathematically. Before that time a spline was drawn into a model by a designer but was not easily duplicated because the shape was so hard to define. with the advent of computers, and even more specifically CAD, these splines were created using control points (movable points) and knots (stationary points) that can be somewhat defined, even though the lines that were drawn are still only considered interpolated points. trying to do the math would be personally defeating at best since the spline itself is a product of the math....not the other way around. still, here is the formula given from Wiki sources. I wouldn't want to be on that taskforce....
   

Chris "i44troll"

[williamj]

Chris,

Thanks for the reply. I about laughed myself silly when I saw the equations! Why is it I can never seem to find anything easy?

So... I'm pretty much at a loss trying to get a smooth, mathematically correct, curve from an X,Y plot.

I'm thinking that the curve I'm trying to get is quadratic in nature, where Y gets increasingly(I.E. Y is smaller from X1 to X2 than it is from 0 to X1 and smaller yet from X2 to X3 than from X1 to X2) smaller as you increase X and it doesn't appear that Y will ever reach zero no matter how far you go on X. (Now that was one long sentence!)

Thanks again,
williamj

[i44troll]

What are you trying to draw? What's the big picture?

[williamj]

(01-08-2013, 05:12 PM)i44troll Wrote: What are you trying to draw? What's the big picture?

Will try to describe...

an object is located at 0,0 on a grid.
I'm at -1,0 on the same grid facing positive Y - I turn to set my line of sight on the object... 90 deg. from 0.
the object moves to 0,1 and I rotate (maintaining my position at -1,0) and now my line of sight is 45 deg. from 0.
the object moves to 0,2, I turn... line of sight is now 26.5651 deg. from 0. (the angle of my rotation was measure to 4 decimal places (in DeltaCad))
and so on and so on...

I put, not the co-ordinates but, the changes of the object in Y and the changes of my rotation (deg. from 0) into Excel and graphed for the curve.

I was wrong... not quadratic, looks like (according to the world wide web) a version of a "power curve", that's what they're calling it anyway. (who ever "they" are)

It's all for another project I'm working on, proprietary and all that. Wish I could say more.

I still wish I spent more waking hours in math than non-waking hours. :/

williamj