d3.curveLinear(context) Produces a polyline through the specified points.

d3.curveCatmullRomOpen(context) Produces a cubic Catmull–Rom spline using the specified control points and the parameter alpha, which defaults to 0.5, as proposed by Yuksel et al. Unlike curveCatmullRom, one-sided differences are not used for the first and last piece, and thus the curve starts at the second point and ends at the penultimate point.

d3.curveCatmullRomClosed(context) Produces a closed cubic Catmull–Rom spline using the specified control points and the parameter alpha, which defaults to 0.5, as proposed by Yuksel et al. When a line segment ends, the first three control points are repeated, producing a closed loop.

d3.curveCatmullRom(context) Produces a cubic Catmull–Rom spline using the specified control points and the parameter alpha, which defaults to 0.5, as proposed by Yuksel et al. in On the Parameterization of Catmull–Rom Curves, with one-sided differences used for the first and last piece.

d3.curveCardinalOpen(context) Produces a cubic cardinal spline using the specified control points. Unlike curveCardinal, one-sided differences are not used for the first and last piece, and thus the curve starts at the second point and ends at the penultimate point. The default tension is 0.

d3.curveCardinalClosed(context) Produces a closed cubic cardinal spline using the specified control points. When a line segment ends, the first three control points are repeated, producing a closed loop. The default tension is 0.

d3.curveCardinal(context) Produces a cubic cardinal spline using the specified control points, with one-sided differences used for the first and last piece. The default tension is 0.

d3.curveBundle(context) Produces a straightened cubic basis spline using the specified control points, with the spline straightened according to the curve’s beta, which defaults to 0.85. This curve is typically used in hierarchical edge bundling to disambiguate connections, as proposed by Danny Holten in Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data. This curve does not implement curve.areaStart and curve.areaEnd; it is intended to work with d3.line, no

d3.curveBasisOpen(context) Produces a cubic basis spline using the specified control points. Unlike basis, the first and last points are not repeated, and thus the curve typically does not intersect these points.

d3.curveBasisClosed(context) Produces a closed cubic basis spline using the specified control points. When a line segment ends, the first three control points are repeated, producing a closed loop with C2 continuity.