Function Repository Resource:

# ApproximatedCurve

Get an approximation to a parametric curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["ApproximatedCurve"][c,{t,t0,tf,n}] computes a line of n points approximating the parametric curve c with t from t0 to tf. ResourceFunction["ApproximatedCurve"][c,{t,t0,tf,n},"type"] gives a result based on "type".

## Details and Options

Possible values of "type" are: "Coordinates", "Point", "Line", "PointLine", "Arrow", "Polygon", "BezierCurve", "BSplineCurve", "Tube", "BSplineCurveTube", "Region" or "DiscretizeRegion".

## Examples

### Basic Examples (5)

Approximate cycles around a figure-eight curve:

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Approximate the curve with lines:

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Show the lines:

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Define a curve in three dimensions:

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Polygonal approximation to a curve:

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Different approximation to a curve:

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Convert points in the following closed curve into a tube. It requires less file space than a full parametrization plot:

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### Applications (6)

Get a curve similar to a handwritten curve:

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Using AnglePath gives a different curve:

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Define an epicycloid:

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Modify it using Accumulate:

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Make a spline from the points of a curve:

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Make a design from an epicycloid:

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Define an epicycloid:

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Get a region:

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Test if it is a region:

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Discretize the region:

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Compute some properties:

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Create and visualize a nephroid:

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### Properties and Relations (5)

A crude approximation to arc length:

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Successive approximation to arc length versus the number of steps:

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Forced undersampling with MaxRecursion and PlotPoints:

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Create a similar result using ApproximatedCurve:

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A polygon gives a similar result to FilledCurve:

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Generalize CirclePoints:

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Distances between successive points are different:

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Show the curve using points:

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Approximate a nephroid:

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Enrique Zeleny

## Version History

• 1.0.0 – 24 April 2020