How Vector Graphics Work: Paths, Curves and Coordinates
A technical but accessible explanation of how vector graphics represent shapes using mathematical paths, Bezier curves and coordinate systems.
Vector graphics seem almost magical — images that stay perfectly sharp no matter how large you make them. But the underlying technology is elegant and surprisingly accessible. This article explains how vector graphics work from the ground up.
Raster vs Vector: The Fundamental Difference
Raster images are grids of pixels. Each pixel has a fixed colour. When you zoom in on a raster image, you see the individual pixels. When you scale a raster image up, the software has to interpolate between existing pixels, which leads to blur. Vector images, by contrast, store mathematical descriptions of shapes. They contain no pixels. Instead, they contain instructions: draw a line from point A to point B, draw a circle of radius R at position X,Y. These instructions produce the same sharp result at any scale.
Coordinate Systems
Vector graphics use a coordinate system to position elements. In SVG, the default coordinate system places the origin (0,0) at the top-left corner, with x increasing to the right and y increasing downward. A rectangle might be defined as x=10, y=20, width=100, height=50 — meaning it starts 10 units from the left edge and 20 units from the top.
Paths and Bezier Curves
The most powerful element in vector graphics is the path. A path is a sequence of drawing commands: move to a point, draw a line to another point, draw a curve to another point. Curves are most commonly represented as Bezier curves, named after French engineer Pierre Bézier. A cubic Bezier curve is defined by four points: a start point, an end point, and two control points that influence the shape of the curve. By combining straight segments and Bezier curves, you can describe virtually any shape.
Fills and Strokes
Vector shapes have two visual properties: fill (the colour or pattern inside the shape) and stroke (the outline around the shape). Both can be solid colours, gradients, or patterns. The stroke has additional properties: width, dash pattern, line cap (how the ends of open paths look), and line join (how corners are rendered).
How Vectorization Works
Vectorization (or image tracing) is the process of converting a raster image to a vector. The algorithm analyzes the pixel colours, identifies regions of similar colour, and generates vector paths that trace the boundaries between those regions. This is a complex computational problem — the algorithm must balance accuracy (how closely the paths match the original pixels) against simplicity (keeping the number of path nodes manageable).
Vector graphics are a fundamentally different way of representing images — one that trades pixel-level detail for infinite scalability and editability. Understanding how they work makes you a better designer, developer, and digital fabricator.
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