ListCurvePathPlot

ListCurvePathPlot[{{x₁,y₁},{x₂,y₂},…}]

plots a curve that corresponds to a smooth path through the specified points.

Details and Options

ListCurvePathPlot attempts to reconstruct smooth curves defined by the specified set of points.
The curves are independent of the order in which points are supplied to ListCurvePathPlot.
Curves can "fold over", and do not need to have a single value for a given value.
If the set of points supplied to ListCurvePathPlot follows a given smooth curve sufficiently closely, ListCurvePathPlot will always reconstruct the curve.
ListCurvePathPlot can generate disconnected curves in certain cases.
ListCurvePathPlot has the same options as Graphics, with the following additions and changes:

ColorFunction	Automatic	how to determine the coloring of lines
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
InterpolationOrder	None	the polynomial degree of curves used in joining data points
MaxPlotPoints	Infinity	the maximum number of points to include
Mesh	None	how many mesh points to draw on each line
MeshFunctions	{#3&}	how to determine the placement of mesh points
MeshShading	None	how to shade regions between mesh points
MeshStyle	Automatic	the style for mesh points
Method	Automatic	the method to use for interpolation and data reduction
PlotRange	Automatic	range of values to include
PlotRangeClipping	True	whether to clip at the plot range
PlotStyle	Automatic	graphics directives to determine the style of each line
PlotTheme	$PlotTheme	overall theme for the plot

ListCurvePathPlot yields a curve that fits the data provided, but may not necessarily contain all the points specified by the data.

open allclose all

Randomly sample points on a circle:

Find a smooth curve through the points:

Join the points in the order they were given:

Use a theme with detailed ticks and grid lines:

Use a theme with simple ticks in a bold color scheme:

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