How to draw equally distanced normal lines between two multi-segmented Cubic Bézier splines?

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Hello,

I have two multi-segmented cubic Bézier splines S and S′ that cut off by lines A and B (img.1). The distance between red dots it's their cubic Bézier curves. My question is how to split each of these two splines (S and S′) to equal segments and draw normal lines between those segments points (img.2).

Any ideas? Thankful in advance for any help.

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