Link: https://en.wikipedia.org/wiki/B%C3%A9zier_curve

A Bézier curve […] is a parametric curve used in computer graphics and related fields. A sequence of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape that otherwise has no mathematical representation or whose representation is unknown or too complicated. The Bézier curve is named after French engineer Pierre Bézier (1910–1999), who used it in the 1960s for designing curves for the bodywork of Renault cars. Other uses include the design of computer fonts and animation.

Curvature Beziers: Improving on a timeless recipe

I used these for an Apple II BASIC demo. You can run it online.

20 hgr2 : hcolor = 3 : onerr goto 900
50 read x1, y1, x2, y2, x3, y3
51 hplot x1,y1
65 for n = 0 to 1 step 0.01
70 xa = ((n*x2) + ((1-n)*x1))
75 ya = ((n*y2) + ((1-n)*y1))
80 xb = ((n*x3) + ((1-n)*x2))
85 yb = ((n*y3) + ((1-n)*y2))
100 a = ( ( (1-n) * xa ) + ( (n) * xb ) ) 
110 b = ( ( (1-n) * ya ) + ( (n) * yb ) ) 
120 if a < 0 or a > 279 then 200 
130 if b < 0 or b > 191 then 200 
140 hplot to a,b
200 next n 
210 x1=x3 : y1=y3
215 read x2,y2, x3,y3
220 goto 65 
301 data 140,65,140,65,140,100,125,105,140,105,140,115,145,105,155,115
302 data 150,100,170,85,181,102,170,95,156,106,180,90,192,118,200,160
303 data 156,160,80,160,90,40,100,20,110,40,115,55,125,40,115,25,110
304 data 40,120,60,130,40,120,20,110,40,100,60,90,40,95,25,105,40,95
305 data 55,90,40,100,-10,135,10,150,30,145,55,145,106,150,100,170,85
306 data 181,102,190,75,194,80,200,85,190,105,200,100,195,110,200,115
307 data 192,118,200,160,156,160,150,180,145,190,100,170,140,180,150
308 data 160,150,160,130,155,130,155,125,175,110,180,75,160,115,170,125
309 data 150,120,150,85,130,90,60,130,60,130,60,110,60,110,60,95,60,110,40
900 end