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. Bezier curves are the foundation of every vector graphics format (SVG, PDF, EPS, AI) and every modern illustration tool (Illustrator, Figma, Procreate Vector, Affinity Designer). Mastering Bezier-pen-tool work — placing anchor points, adjusting handle directions, balancing curve smoothness against node count — is the single highest-ROI skill for vector textile design.
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.