Extracting values from a Bézier curve in Mathematica

given a list of points I've created a Bézier curve, and now I would like to understand how to extract a "middle point" from a curve or get a list of points (not the input ones, the interpolated ones)

• Please can you include a simple example of what you have done using Mathematica code we can copy and work with?
– Hugh
Jul 27 '21 at 16:41
• You should use the BezierFunction[your_points][i], where i is parameter (in range 0-1) which is proportional to the path along your curve. Jul 27 '21 at 16:52
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Here we provided an example which indicate that we can not use BezierFunction or BSplineFunction since it is different from BezierCurve.( Although for a single Bezier curve which only contain two control points that they are the same.)

pts = {{0, 0}, {1, -1}, {3, -1}, {3, 3}, {4, 1}, {5, 1}, {6, 0}};
a = Graphics[{BezierCurve[pts], Dotted, Line[pts], Red, Point[pts]}];
b = ParametricPlot[BezierFunction[pts[[1 ;; 4]]][t], {t, 0, 1},
PlotStyle -> Yellow];
c = ParametricPlot[BezierFunction[pts[[4 ;; 7]]][t], {t, 0, 1},
PlotStyle -> Green];
d = ParametricPlot[BezierFunction[pts[[1 ;; 7]]][t], {t, 0, 1},
PlotStyle -> Red];
Show[a, b, c]
Show[a, b, c, d] The red one is BezierFunction and the yellow+green is the BezierCurve.

• It seems that the Arrow and Arrowheads function give the correct position at all the cases.
pts = {{0, 0}, {1, -1}, {3, -1}, {3, 3}, {4, 1}, {5, 1}, {6,
0}}; Table[ 