Curves (lines & paths)
A curve is a row of points strung together into a stroke: the backbone for hair, ribbons, trails, motion paths and shape outlines.
What a curve is
Start with points, a list of positions, one per row. A curve connects those points in order into a single continuous line. The points remain, and @P on each is still readable and editable, but now they describe a path rather than a loose cloud.
That one idea covers a lot of ground:
Hair and fur, many short curves, one per strand.
Ribbons and trails, a curve swept into a flat band or tube.
Motion paths, a curve an object travels along over time.
Outlines, the edge of a shape traced as a line.
Curves are smooth (gentle bezier bends between points) or straight (point-to-point segments). Either way the points are the control. Move a point and the curve follows.
Open vs closed
An open curve has two ends: a single hair strand, a brush stroke, the line a comet leaves behind. A closed curve loops back to its start with no gap: a circle, a ring, any outline you intend to fill.
Closing matters for filling a curve, since a closed loop encloses an area, and for sweeping a solid tube with no open end. Many nodes expose a closed toggle to switch between the two.
Curves, shapes and geometry
Analytic shapes, a Circle, Rectangle or Text with the Analytical toggle on, are crisp, resolution-free 2D paths. They are curves underneath, so a shape feeds straight into a curve operation and the conversion is inserted automatically.
Geometry is the other side. A curve is a one-dimensional line, geometry is a surface built from connected faces. Sweeping is the bridge: run a profile along a curve and you get solid geometry.
How a curve draws is a Render Mode control on the node that makes it, Line, Pen, Trail and Ray. Tube sweeps a pipe of real world-space radius. Path adapts to the curve: a flat 2D stroke while the curve stays planar, and a thin camera-facing ribbon once it leaves the plane, so a path promoted into 3D stays thin instead of ballooning. Ray adds None, which builds no visible geometry at all and is the fast choice when you only want the hit data. The stored curve is the same in every case, and the choice rides along as a per-row property. See Rasterizing.
Working with curves
Resampling changes how many points sit along the curve without changing its shape. Add points for smoother deformation or detailed effects, or thin them out to lighten the curve.
Trimming keeps part of a curve, the first 60%, the middle stretch, whatever the shot needs. Animate the trim and the line draws itself on over time.
Sweeping runs a 2D profile along the curve to build something solid. With Sweep you can:
extrude a flat profile into depth,
revolve a profile around an axis (a lathe),
run a profile along the curve like a rail, or
wrap a tube around the curve, for cables, vines and pipes.
Every mode builds full geometry you can light and shade. Turn Analytical on to keep Linear, Path and Tube equation-defined instead. Revolve is always analytic, whatever the toggle says.
Scale, Radius and Twist are not just sliders. Wire an easing curve or a list of numbers into any of them and it becomes a profile read along the sweep: a taper on the cross-section, a radius that swells and thins down a tube, a twist that winds unevenly. The curve you sweep along can carry the same information itself, as a per-anchor @scale that multiplies, a @twist that adds, or a @width that replaces the base radius outright.
Any 2D shape works as a sweep profile or as a sweep path. Draw a circle, set it Analytical, and it is a tube cross-section with no further setup.