Automotive a-class explained
“NURBS” and transition theory
NURBS
Non-uniform rational basis splines
nurbs and mesh
There are two types of 3d data that dominate today; mesh and nurbs. There are many other formats, but these two are the most common.
Mesh was the first kind of 3d data used in computer graphics, it is easy to work with and quick to render. A mesh consists of a set of connected points.
Two points connected define a line, and three points define a plane. So a mesh is seen as a lot of connected triangular surfaces.
Nurbs are a little more complicated. They have their origin in drafting (making technical drawings). Drafters needed to have a precise and reproducible way of making complex curves. The answer was a flexible “ruler” called a spline held in place with weights.
At the dawn of the digital era, engineers from Renault and Citroën converted the tool/concept to a digital format, laying the foundation for NURBS surfaces and vector graphics.
Old-school spline ruler
Bezier curve
In this digital version the weights are replaced by points that “pull” on the curve.
Transitioning this concept from curves to surfaces was relatively minor, but the implications for the industry was absolutely revolutionary.
An apt analogy when comparing mesh to nurbs is to compare pixel and vector graphics. You can approximate something curved, but the closer the approximation you need, the more data you will need to describe it.
In the picture to the right the mesh surface is defined with 50 points and is quite jagged. The nurbs surface next to it is defined with 12 points and is perfectly curved no matter what scale.
nurbs and mesh
Transition theory
Beyond the tangent
G0 “Position”
The two edges are touching. G0 is the lowest level of tolerance when surfacing, if the surfaces aren’t touching (within tolerance) you won’t be able to treat them as a solid object.
What’s with the weird stripes?
The weird look in these images is commonly called a “zebra shader”
You can imagine it like the surfaces are completely reflective and are reflecting a wall with black and white stripes on it.
Reflecting a straight line, like the horizon or fluorescent lamps in a garage, is a “worst case scenario”. The zebra shader mimics that so it is a very good way of scrutinizing what a transition between surfaces will look like.
To demonstrate the transitions I will be adding a rounding “fillet” to the edge from first picture.
G1 “Tangent”
The surfaces have the same angle where they meet. This transition is usually “good enough” for most engineering programs.
Unfortunately a tangent transition look pretty sharp/bad. They cause what looks like darker lines at the transition, commonly called tangent lines.
G2 “Curvature”
The surfaces have the same bend (curvature) in the transition
This is typically the transition we strive for in the automotive industry. It looks a lot smoother than a tangent transition. It can however still show a little bit of a tangent line if the surfaces it builds on are too flat.
G3 “Torsion”
The surfaces have the same curvature change in the transition
This transition is pretty much “invisible” it is mostly used for very visible edges, large transitions and flat surfaces.
