Re:Why are 2D vector graphics so much harder than 3D?
by romwell on Thursday May 09, 2019 @08:04PM
(#19873779)
Indeed, but the terminology used in mathematics is very clear. So perhaps add this snippet to the article?
Another thing possibly of value: where Bezier curves come from - automotive design. The machines that were tracing these curves out needed to solve the forward problem (where should the tool head be at time t?), and the designers needed an easy way to change the shape of the curve. The Bezier splines were (and still are) a great solution to that problem.
For that reason, it's easy to convert Bezier splines into G-Code for either plotter - or, these days - 3D printer.
Also, sampling the parametric form does give you a polygon (or a polygonal mesh), which is easier to work with. But that's another can of worms.
Another thing possibly of value: where Bezier curves come from - automotive design. The machines that were tracing these curves out needed to solve the forward problem (where should the tool head be at time t?), and the designers needed an easy way to change the shape of the curve. The Bezier splines were (and still are) a great solution to that problem.
For that reason, it's easy to convert Bezier splines into G-Code for either plotter - or, these days - 3D printer.
Also, sampling the parametric form does give you a polygon (or a polygonal mesh), which is easier to work with. But that's another can of worms.