Catmull-Rom interpolation on SVG Paths

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To answer your questions directly:

  1. Yes. Catmull-Rom spline is an algorithm to interpolate a series of (x, y, z) points. It will generate a cubic polynomial curve between each two consecutive points.
  2. You cannot direcly use Catmull Rom spline for SVG path. You need to convert it to cubic Bezier curve first.

For a curve segment defined by point P0, P1, P2 and P3 and knot sequence t0, t1, t2, t3, the centripetal Catmull-Rom spline (defined between point P1 and P2) can be computed by the recursive formula provided in https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline. Therefore, I will not elaborate here.

To convert it to cubic Bezier curve, you need to compute the first
derivative at P1 and P2 as 

M1 = (t2-t1)*(c1*(P1-P0)/(t1-t0) + c2*(P2-P1)/(t2-t1))
M2 = (t2-t1)*(d1*(P2-P1)/(t2-t1) + d2*(P3-P2)/(t3-t2))

Where 

 c1 = (t2-t1)/(t2-t0),
 c2 = (t1-t0)/(t2-t0),
 d1 = (t3-t2)/(t3-t1),
 d2 = (t2-t1)/(t3-t1)

Then you can convert it to cubic Bezier curve with 4 control points: Q0, Q1, Q2 and Q3:

Q0 = P1
Q1 = P1 + M1/3
Q2 = P2 - M2/3
Q3 = P2

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