Equation for sickle shaped plane curve

Question

Is there a parametric equation for a plane curve with the shape of a sickle cell, e.g. half nephroid and half circle? I couldn't find one so far. Thanks!

I'm looking for an equation consisting of sinusoidal functions instead of inverted parabolae.

Answer 1

Found it. If I combine a half nephroid with a half circle, i get a nice sickle curve. R code:

RES = 360
a = 250
R = 2*a
MIDX = 500
MIDY = 500
NODES <- matrix(NA,nrow=0,ncol = 3) 

phi <- seq(pi, 0, -2*pi/RES)

for (i in phi) {
xpos <- MIDX + a*(3*cos(i)-cos(3*i))
ypos <- MIDY + a*(3*sin(i)-sin(3*i))
NODES <- rbind(NODES, c(xpos,ypos))
}

phi <- seq(pi, 0, -2*pi/RES)
for (i in phi) {
xpos <- MIDX + R*cos(i) 
ypos <- MIDY + R*sin(i)
NODES <- rbind(NODES, c(xpos,ypos))
}

plot(NODES)