How to create a Matlab pumpkin in R? - r

Question

I am trying to replicate the following visual with the following Matlab code:
% Pumpkin
[X,Y,Z]=sphere(200);
R=1-(1-mod(0:.1:20,2)).^2/12;
x=R.*X; y=R.*Y; z=Z.*R;
c=hypot(hypot(x,y),z)+randn(201)*.03;
surf(x,y,(.8+(0-(1:-.01:-1)'.^4)*.3).*z,c, 'FaceColor', 'interp', 'EdgeColor', 'none')
% Stem
s = [ 1.5 1 repelem(.7, 6) ] .* [ repmat([.1 .06],1,10) .1 ]';
[t, p] = meshgrid(0:pi/15:pi/2,0:pi/20:pi);
Xs = -(.4-cos(p).*s).*cos(t)+.4;
Zs = (.5-cos(p).*s).*sin(t) + .55;
Ys = -sin(p).*s;
surface(Xs,Ys,Zs,[],'FaceColor', '#008000','EdgeColor','none');
% Style
colormap([1 .4 .1; 1 1 .7])
axis equal
box on
material([.6 1 .3])
lighting g
camlight
I am working on the bottom but have not gotten very far (see here for reference). The code that I have is:
library(pracma)
library(rgl)
sphere <- function(n) {
dd <- expand.grid(theta = seq(0, 2*pi, length.out = n+1),
phi = seq(-pi, pi, length.out = n+1))
with(dd,
list(x = matrix(cos(phi) * cos(theta), n+1),
y = matrix(cos(phi) * sin(theta), n+1),
z = matrix(sin(phi), n+1))
)
}
# Pumpkin
sph<-sphere(200)
X<-sph[[1]]
Y<-sph[[2]]
Z<-sph[[3]]
R<- 1-(1-seq(from=0, to=20,by=0.1))^2/12
x<-R * X
y<-R * Y
z<-Z * R
c<-hypot(hypot(x,y),z)+rnorm(201)*0.3
persp3d(x,y,(0.8+(0-seq(from=1, to=-1, by=-0.01)^4)*0.3)*z,col=c)
and it gives me the following.
What is it that's going wrong in my present code? What would be a suggested fix?

Answer 1

As #billBokeey mentioned, there's a missing mod modulo operator function for periodic scaling factors.
In addition, the scaling on the z-axis 0.8 + (0-seq(from=1, to=-1, by=-0.01)^4) * 0.3 doesn't go well with the output from your sphere function. We maybe use Z[1,] to replace seq(from=1, to=-1, by=-0.01). phi = seq(-pi, pi, length.out = n+1)) shoud be seq(-pi/2, pi/2, length.out = n+1)) instead.
Finally, the color c needs to be convert to RGB code for persp3d.
Here's the result look like from the code below.
library(rgl)
sphere <- function(n) {
dd <- expand.grid(theta = seq(0, 2*pi, length.out = n+1),
phi = seq(-pi/2, pi/2, length.out = n+1))
with(dd,
list(x = matrix(cos(phi) * cos(theta), n+1),
y = matrix(cos(phi) * sin(theta), n+1),
z = matrix(sin(phi), n+1))
)
}
# Unit ball
sph <- sphere(200)
X <- sph[[1]]
Y <- sph[[2]]
Z <- sph[[3]]
# scaling
R <- 1 - (1 - seq(from=0, to=20, by=0.1) %% 2) ^ 2 / 12 # Modulo Operator %%
R2 <- 0.8 + (0 - seq(from=1, to=-1, by=-0.01)^4)*0.2 # didn't match with the order of z from sphere function
#R2 <- 0.8 - Z[1,]^4 * 0.2
x <- R * X # scale rows for wavy side
y <- R * Y # scale rows for wavy side
z <- t(R2 * t(Z)) # scale columns by transpose for flat oval shape
# color according to distance to [0,0,0]
hypot_3d <- function(x, y, z) {
return(sqrt(x^2 + y^2 + z^2))
}
c_ <- hypot_3d(x,y,z) + rnorm(201) * 0.03
color_palette <- terrain.colors(20) # color look-up table
col <- color_palette[ as.numeric(cut(c_, breaks = 20)) ] # assign color to 20 levels of c_
persp3d(x, y, z, color = col, aspect=FALSE)