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[JernejL]

Here's my contribution, Centripetal Catmul-Rom function - feel free to use it:

const alpha = 0.5; //set from 0-1

type
  TCurveSegment = array of Vector;

var
	testsegment: TCurveSegment;
	outpoints: TCurveSegment;

function interpolateCurve(points: TCurveSegment; var outpoints: TCurveSegment; amountOfPoints: integer): Vector;

implementation

function GetT(t: single; p0: Vector; p1: Vector): single;
var
    a, b, c: single;
begin
    a := power((p1.x - p0.x), 2.0) + power((p1.y - p0.y), 2.0);
    b := power(a, 0.5);
    c := power(b, alpha);

    result := (c + t);

end;


// todo: to calculate length, use https://en.wikipedia.org/wiki/Arc_length

// Centripetal Catmul-Rom
// https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline

function interpolateCurve(points: TCurveSegment; var outpoints: TCurveSegment; amountOfPoints: integer): Vector;
var
    t0, t1, t2, t3: single;
    segment_length: single;
    t: single;
    A1, A2, A3, B1, B2, C: Vector;
begin

    t0 := 0.0;
    t1 := GetT(t0, points[0], points[1]);
    t2 := GetT(t1, points[1], points[2]);
    t3 := GetT(t2, points[2], points[3]);

    segment_length := ((t2 - t1) / amountOfPoints);

    t := t1;

    while (true) do
    begin

        A1.x := (t1 - t) / (t1 - t0) * points[0].x + (t - t0) / (t1 - t0) * points[1].x;
        A1.y := (t1 - t) / (t1 - t0) * points[0].y + (t - t0) / (t1 - t0) * points[1].y;

        A2.x := (t2 - t) / (t2 - t1) * points[1].x + (t - t1) / (t2 - t1) * points[2].x;
        A2.y := (t2 - t) / (t2 - t1) * points[1].y + (t - t1) / (t2 - t1) * points[2].y;

        A3.x := (t3 - t) / (t3 - t2) * points[2].x + (t - t2) / (t3 - t2) * points[3].x;
        A3.y := (t3 - t) / (t3 - t2) * points[2].y + (t - t2) / (t3 - t2) * points[3].y;

        B1.x := (t2 - t) / (t2 - t0) * A1.x + (t - t0) / (t2 - t0) * A2.x;
        B1.y := (t2 - t) / (t2 - t0) * A1.y + (t - t0) / (t2 - t0) * A2.y;

        B2.x := (t3 - t) / (t3 - t1) * A2.x + (t - t1) / (t3 - t1) * A3.x;
        B2.y := (t3 - t) / (t3 - t1) * A2.y + (t - t1) / (t3 - t1) * A3.y;

        C.x := (t2 - t) / (t2 - t1) * B1.x + (t - t1) / (t2 - t1) * B2.x;
        C.y := (t2 - t) / (t2 - t1) * B1.y + (t - t1) / (t2 - t1) * B2.y;

        setlength(outpoints, length(outpoints) + 1);
        outpoints[high(outpoints)] := C;

        t := t + segment_length;

        if not (t < t2) then
            break;

    end;

end;

initialization

// setlength(testsegment, 4);
//
// testsegment[0]:= makevector2(5,6);
// testsegment[1]:= makevector2(3,4);
// testsegment[2]:= makevector2(3,2);
// testsegment[3]:= makevector2(5,2);
//
// interpolateCurve(testsegment, outpoints, 10);
//
// info(length(outpoints));