Vectors, nodes and curves
A vector is a path described mathematically: points, and the curves between them. Each point is a node. Fewer, well placed nodes give smooth curves and fast smooth motion. Thousands of nodes give faceted results and a machine that stutters.
What a vector is
A shape described by mathematics rather than by pixels. A circle is a centre and a radius. A curve is a start point, an end point, and control handles that say how it bends between them. Because it is mathematical, it scales without losing quality, and it gives CAM a path to follow.
- Node. A point on the path. Also called an anchor or a control point.
- Segment. The line or curve between two nodes.
- Handle. The control that sets how a Bezier curve bends out of a node.
- Path. The whole chain of nodes and segments.
Open and closed
| Closed vector | Open vector | |
|---|---|---|
| Shape | The path returns to where it started | It has two loose ends |
| Has an inside? | Yes | No |
| Can be pocketed? | Yes | No. There is no inside to clear. |
| Can be V-carved? | Yes | No. There is no width to read. |
| Can be profiled? | Yes, inside or outside | Only on the line |
| Typical cause of an unwanted open vector | Import artefacts, a traced shape that did not close, a node deleted by accident |
This is the single most common reason a toolpath refuses to generate. Most CAM has a tool that shows open vectors and joins them within a tolerance. Run it after every import.
Why node count matters to a machine
CAM converts your path into machine moves. A smooth curve made from a few Bezier segments becomes a few arcs, or a smooth chain of moves the controller can run at full speed. The same curve made from 800 tiny straight segments becomes 800 separate moves, and the controller decelerates at the end of each one.
Consequences you actually see:
- The machine stutters and crawls through detail.
- The cut looks faceted, because each tiny segment is genuinely flat.
- Job time balloons. See jobs that take too long.
- V-carving in particular looks ragged. See bad lettering.
Vector direction
Every closed vector has a direction, clockwise or counter-clockwise. It usually does not matter, because CAM works out climb and conventional from the offset side. It starts to matter when:
- Nested shapes need consistent direction for an island to be recognised.
- Some CAM uses direction to decide which side is material and which is not.
- You are manually controlling cut direction for grain reasons.
Most packages have a command to set direction consistently across a selection. If islands are being cut away or pockets are filling in the wrong place, this is worth checking.