On a previous thread, David posted that A+t*(B-A) was the expression for any linear curve in any number of dimensions. I was not sure, but I figured that A and B must be vectors, and t was a parameter, and made the below definition to try it out. (lots of components to draw a line, but I'm just trying to understand the equation)
I had been searching for advice
on some geometry topics worth exploring for a class, and now I'm in the class and the teacher wants me to start by learning about splines in general (not nurbs). I just spent the day learning linear spline interpolation, then quadratic, then cubic. I didn't try working them by hand yet, but I'm getting the concepts. It seems cubic is the lowest degree where you can get C2 continuity, which makes it smooth. I read over parameterization and how that simplifies the number of equations. I read about space curves, and then the differences between Hermite, Catmull-Rom, and Cardinal spline, but then got tired and had a cocktail.
So I guess I'm looking for any direction or advice on how to understand parametric curves in 3d space, and how they can be defined (splines or otherwise). Thanks!!!