如何用数学软件画一个“圣诞树”?

function christmas
% Anselm Ivanovas, anselm.ivanovas@student.unisg.ch
%Basically just a nice plot for some christmas fun.
%3D Plot of a hhristmas tree with some presents and snow
%% setup
snow=800; % number of snow flakes [0 .. 5000]

%% draw tree
h=0:0.2:25; %vertical grid
[X,Y,Z] = cylinder(tree(h)); %produce a tree formed cylinder
Z=Z*25; %scale to the right heigth
%add some diffusion to the surface of the tree to make it look more real
treeDiffusion=rand(126,21)-0.5;%some horizontal diffusion data
%add diffusion to the grid points
for cnt1=1:21

for cnt2=16:126%starting above the trunk
%get the angle to always diffuse in direction of the radius
angle=atan(Y(cnt2,cnt1)/X(cnt2,cnt1));
%split the diffusion in the two coordinates, depending on the angle
X(cnt2,cnt1)=X(cnt2,cnt1)+cos(angle)*treeDiffusion(cnt2,cnt1);
Y(cnt2,cnt1)=Y(cnt2,cnt1)+sin(angle)*treeDiffusion(cnt2,cnt1);
%some Vertical diffusion for each point
Z(cnt2,cnt1)=Z(cnt2,cnt1)+(rand-0.5)*0.5;
end

end
%draw the tree
surfl(X,Y,Z,'light')
%% View and format
%Use as nice green color map (darker at the bottom, lighter at the top)
r=(0.0430:(0.2061/50):0.2491)';%red component
g=(0.2969:(0.4012/50):0.6981)';%green component
b=(0.0625:(0.2696/50):0.3321)';%blue component
map=[r,g,b];%join in a map
for cnt=1:6
%change the lower part to brown for the trunk
map(cnt,:)=[77,63,5]/265;
end
colormap(map)%set the map
view([-37.5,4])%Change the view to see a little more of the Actual 3D tree
lighting phong %some nice lighting
shading interp %remove grid and smoothen the surface color
axis equal %takes care of display in the right proportion
axis([-10 10 -10 10 0 30]) %give some more axis space (for the snow later)
axis off %but don't show axis
hold on %to draw the rest
title('Merry Christmas 知乎er')%self explaining
%% Presents
%Draw some presents around the tree (each with random color)
drawPresent(2,-4,0,3,3,2);
drawPresent(-4,3,0,2,3,1.5);
drawPresent(5,3,0,4,3,3);
drawPresent(-14,-5,0,6,3,1);
drawPresent(-9,-10,0,2,2,2);
drawPresent(0,4,0,4,3,3);
drawPresent(-6,-13,0,3,3,3);
%% Snow
%create some random 3D coordinates for the snow (amount as in setup above)
snowX=(rand(snow,1)*25-12.5);
snowY=(rand(snow,1)*25-12.5);
snowZ=(rand(snow,1)*27);
%Note:Some flakes will end up IN the tree but just can't be seen then
plot3(snowX,snowY,snowZ,'w*')%plot coordinates as white snow flakes
hold off%Done
end % of function

%% ============= private functions
function r=tree(h)%Gives a profile for the tree
for cnt=1:length(h)

if(h(cnt)==0)%no Width at the bottom. Ensures a "closed" trunk
r(cnt)=0;
end
%smaller radius for the trunk
if (h(cnt)>0 && h(cnt)<=3)
r(cnt)=1.5;
end
%reduce radius gradually from 8 to 0. Note: will only work with a trunk heigth
%of 3 and a whole tree heigth of 25. Scale the height of the tree in
%the "draw tree" section, since the cylinder command will return a 1
%unit high cylinder anyway
if(h(cnt)>3)
r(cnt)=8-(h(cnt)-3)*0.3636;
end
end
end % of function
%Draws a present with the given coordinate + size in a random color
%Note:Given coordinates apply to the lower front + left corner of the
%present (the one closest to the viewer) as seen in the plot
function drawPresent(dx,dy,dz,scalex,scaley,scalez)
%the standard present coordinates
presentX=[0.5 0.5 0.5 0.5 0.5; 0 1 1 0 0; 0 1 1 0 0; 0 1 1 0 0; 0.5 0.5 0.5 0.5 0.5];
presentY=[0.5 0.5 0.5 0.5 0.5; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0.5 0.5 0.5 0.5 0.5];
presentZ=[0 0 0 0 0; 0 0 0 0 0; 0.5 0.5 0.5 0.5 0.5; 1 1 1 1 1; 1 1 1 1 1];
%draw some presents with random colors
%scale present and move it to the right place and get the plot handle
myHandle=surf((presentX*scalex+dx),(presentY*scaley+dy), (presentZ*scalez+dz));
%some random color map
randColorMap(:,:,1)=repmat(rand,[5,5]);%r component
randColorMap(:,:,2)=repmat(rand,[5,5]);%g component
randColorMap(:,:,3)=repmat(rand,[5,5]);%b component
%Assign colormap just to the plot handle object of the present, so the tree
%does not change color
set(myHandle,'CData',randColorMap)
shading interp %Nice shding + without grid
end % of function

L <-  matrix(
    c(0.03,  0,     0  ,  0.1,
        0.85,  0.00,  0.00, 0.85,
        0.8,   0.00,  0.00, 0.8,
        0.2,  -0.08,  0.15, 0.22,
        -0.2,   0.08,  0.15, 0.22,
        0.25, -0.1,   0.12, 0.25,
        -0.2,   0.1,   0.12, 0.2),
    nrow=4)
# ... and each row is a translation vector
B <- matrix(
    c(0, 0,
        0, 1.5,
        0, 1.5,
        0, 0.85,
        0, 0.85,
        0, 0.3,
        0, 0.4),
    nrow=2)

prob = c(0.02, 0.6,.08, 0.07, 0.07, 0.07, 0.07)

# Iterate the discrete stochastic map 
N = 1e5 #5  #   number of iterations 
x = matrix(NA,nrow=2,ncol=N)
x[,1] = c(0,2)   # initial point
k <- sample(1:7,N,prob,replace=TRUE) # values 1-7 

for (i in 2:N) 
  x[,i] = crossprod(matrix(L[,k[i]],nrow=2),x[,i-1]) + B[,k[i]] # iterate 

# Plot the iteration history 
png('card.png')
par(bg='darkblue',mar=rep(0,4))    
plot(x=x[1,],y=x[2,],
    col=grep('green',colors(),value=TRUE),
    axes=FALSE,
    cex=.1,
    xlab='',
    ylab='' )#,pch='.')

bals <- sample(N,20)
points(x=x[1,bals],y=x[2,bals]-.1,
    col=c('red','blue','yellow','orange'),
    cex=2,
    pch=19
)
text(x=-.7,y=8,
    labels='Merry',
    adj=c(.5,.5),
    srt=45,
    vfont=c('script','plain'),
    cex=3,
    col='gold'
)
text(x=0.7,y=8,
    labels='Christmas',
    adj=c(.5,.5),
    srt=-45,
    vfont=c('script','plain'),
    cex=3,
    col='gold'
)
dev.off()