Offset of a bezier-curve

Hello all,

my name is Patrick and I’m pretty new to this forum and OpenGL, too. I hope I posted this topic in the right subforum.

I’m currenty in China, completing my practica for my german diploma. The professor here gave me some stuff to do.

First of all I should draw a bezier curve (3d = surface) with opengl. Although I’m pretty new to OpenGL I think this will be less a problem. The second job is to think about (math. backround) the offset of an beziercurve. And here’s my problem. I found different explanations for ‘offset’. I asked my teacher for computer-graphics in Germany (that’s where I’m from) and he told me it’s something like a blain on the bezier-surface. He thinks that I should summate a difference value on the points of the bezier-surface in a special region… to realize the blain.

To be honest I don’t think thats right, altough I think he knows what he’s talking about. Maybe some ppl of you could think about the offset of a bezier-curve. It’s not really clear to me.

I would be thankfull for any suggestion.

Thanks a lot.


just could do another guesses (mathematician’s view)

“offset” could mean
“translation of the whole curve in target space”
“translation of curve points along normal direction”

the latter is a very local view, but eg. thinking of railway tracks this kind of “offset” describes a very senseful thing…
in 3d space, a local offset would match the meaning of your professors “blain” theory, with the definition in normal space.
for example “bump mapping” simulates this kind of offset, whereas “displacement mapping” realizes it, if you know about one of them.

maybe its best to requery the exact meaning of the assignment.



thanks for your answer. I’m going to ask my professor here in China again, but there are a lot of linguistic differences between us. :wink:

I found some usefull documents on the internet. For example

In this document a way of building offsets of an bezier-curve is described. It looks like the offset it self is just a duplicate of the beziercurve. That makes sence with the first words in the document (about industrial roboters and so on), too.

Again thanks for your help.


Sometimes some piece of code is better than an explanation ^^

As far as i remember, you can also consider that the ‘offset’ is simply a vector that reach your next control point needed to generate the curve.

cool link on the subject: