如何用数学软件画一个“圣诞树”?

程序员文章站 2022-03-13 12:43:07

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可以是字符的，也可以是图形的

相关问题如何用C语言画一个“圣诞树”? - 编程

回复内容：

我只是搬运http://codegolf.stackexchange.com上的答案，原作者是Silvia （@Silvia )，用的是Mathematica。

PD = .5;
s[t_, f_] := t^.6 - f
dt[cl_, ps_, sg_, hf_, dp_, f_, flag_] :=
    Module[{sv, basePt},
           {PointSize[ps],
            sv = s[t, f];
            Hue[cl (1 + Sin[.02 t])/2, 1, .3 + sg .3 Sin[hf sv]],
            basePt = {-sg s[t, f] Sin[sv], -sg s[t, f] Cos[sv], dp + sv};
            Point[basePt],
           If[flag,
              {Hue[cl (1 + Sin[.1 t])/2, 1, .6 + sg .4 Sin[hf sv]], PointSize[RandomReal[.01]],
               Point[basePt + 1/2 RotationTransform[20 sv, {-Cos[sv], Sin[sv], 0}][{Sin[sv], Cos[sv], 0}]]},
              {}]
          }]

frames = ParallelTable[
                       Graphics3D[Table[{
                                         dt[1, .01, -1, 1, 0, f, True], dt[.45, .01, 1, 1, 0, f, True],
                                         dt[1, .005, -1, 4, .2, f, False], dt[.45, .005, 1, 4, .2, f, False]},
                                        {t, 0, 200, PD}],
                                  ViewPoint -> Left, BoxRatios -> {1, 1, 1.3}, 
                                  ViewVertical -> {0, 0, -1},
                                  ViewCenter -> {{0.5, 0.5, 0.5}, {0.5, 0.55}}, Boxed -> False,
                                  PlotRange -> {{-20, 20}, {-20, 20}, {0, 20}}, Background -> Black],
                       {f, 0, 1, .01}];

Export["tree.gif", frames]

Mathematica版本：
打开一个notebook，然后长按CTRL+/,效果如下：

像不像一棵圣诞树呢？这里有用SAS画的圣诞树，翻译成了Mathematica版的

Clear["`*"];
ifs[prob_,A_,init_,max_]:=FoldList[#2.{#[[1]],#[[2]],1}&,init,RandomChoice[prob->A,max]];

L={{{0.03,0},{0,0.1}},{{0.85,0},{0,0.85}},{{0.8,0},{0,0.8}},{{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}}};
B=Map[List,{{0,0},{0,1.5},{0,1.5},{0,0.85},{0,0.85},{0,0.3},{0,0.4}},{2}];

{A,prob,init,max}={N@Join[L,B,3],{2,60,10,7,7,7,7}/100.,{0.,2.},10^5};
pts=ifs[prob,A,init,max];//AbsoluteTiming
Graphics[{{Darker@Green,PointSize@Tiny,Point@pts},{Hue@Random[],PointSize@Large,Point@#}&/@RandomChoice[pts,200]},AspectRatio->1.5]

去年用R画了圣诞树送给教定量入门的教授，改了一下Wiekvoet: Merry Christmas的代码。
（今年直接手动涂色送happy spring的卡片了，不是程序媛搞不出酷炫的东西好桑心） Wolfram Mathematica 算数学软件吧？

还有这个：

算不算抖机灵 = = 鸡汁的我

MATLAB ，名副其实的数学软件。

参考 File Exchange
by Anselm Ivanovas
====================================
%

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

Christmas Tree
R语言能画，但是这种比较有什么意义呢..................................

L 
    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 
    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 

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 
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()