What is Bezier curve?
A smooth parametric curve defined by anchor points and control handles. The fundamental building block of vector graphics in SVG, EPS, and PDF.
In detail
A Bezier curve is a smooth curve mathematically defined by 2 anchor points (start, end) and 1-2 control points (handles) that pull the curve away from a straight line between anchors. Cubic Beziers (2 control points) are the default in vector graphics — they can represent any shape from a straight line to a tight S-curve. Vectorization algorithms (VTracer, ImageTracer) work by analyzing raster edges and emitting a sequence of Beziers that approximate the original curves. Stitch sequences for embroidery are sampled from Bezier curves. Even hand-drawn paths in Illustrator are stored as Beziers internally.
Example
A floral leaf outline is vectorized into 8 Bezier curves (4 cubic per leaf side). The whole leaf is described by 8 anchor points and 16 control handles — about 200 bytes vs 50 KB for a raster of the same leaf at 256×256.