If you are vectorizing curvy shapes such as contour maps, aerofoils, ship hulls or freeform artwork, it’s a good idea to set your raster to vector conversion software to convert them to a type of vector called a Bezier curve.
Bezier curves are a type of spline vector – a way of mathematically representing smooth, flowing curves. They were defined by Pierre Etienne Bézier (1910 – 1999), who was an engineer and designer at the French car manufacturer Renault for 42 years. Interestingly, Wikipedia states that although Bézier patented the Bezier curve, it is based on de Casteljau’s algorithm, by Paul de Casteljau. de Casteljau worked for rival French car manufacturer Citroën.
What makes Bezier curves so great?
First, they are a simple way of smoothly representing what you might call "irregular" curves. For example, take the raster curve below (black).
It is possible to represent a curve like this using a single Bezier curve, although if you vectorize it using our Scan2CAD raster to vector converter it will most likely be represented by several Bezier curves to keep the fit to the raster image tight. In this example, Scan2CAD has used three bezier curves (blue). The nature of the curves makes it easy for each curve to attach smoothly to the next.
It would be much more difficult to represent this irregular curve using arcs, which, with their fixed radii, are what you might call "regular" curves. To get a smooth representation of the curve using arcs, with each arc attaching smoothly to the next, you would need to use eight arcs (pink).
Second, once created, Bezier curves are very easy to edit. Each curve has a start point, an end point and two control points. The control points are attached to the start and end points by control lines. By manipulating the control points to change the angle and length of the control lines, you can very easily change the shape of the curve.
Bezier curves and CNC software
Although Pierre Bézier was heavily involved in CNC, even designing and producing an early milling and drilling machine, most CNC software does not support Bezier curves.
If you have Scan2CAD, this is not a problem as you can ask Scan2CAD to export the Bezier curves to the DXF file as a series of arcs or line segments, which your CNC software will be able to read. These arcs or line segments will not be as easy to edit as the original Bezier curves but they will retain their smooth fit.
