Asymptote

if one can shading a surface according to the specified weights which just like some heat sources?

for the plane, I finded a way, it is similar to the filesurface.asy. Can we draw it without througth the 3D?

the data.txt is :

1      3     4     5
0     1.4    2     3
1.0   1.0    1.0   2.0
0.2   0.3    0.5   0.7
0.5   0.7    0.2   0.4
2     1.5    0.9   1.0

====================================

settings.render=0;

import graph3;
import palette;

size(200);

file in=input("data.txt").line();
real[] x=in;
real[] y=in;

real[][] z=in.dimension(0,0);

surface s=surface(z,(min(x),min(y)),(max(x),max(y)),Spline);

s.colors(palette(s.map(zpart), Rainbow()));

draw(s,nolight);

//draw(planeproject(unitsquare3)*s,nolight);

currentprojection=orthographic(0,0,1);

limits((0,0,0),(1.1*max(x),1.1*max(y),1.1*max(z)));

xaxis3("$x$",OutTicks(),Arrow3(),above=true);
yaxis3("$y$",OutTicks(),Arrow3(),above=true);

for the general surface, I don't know how to do. it seems difficult to constructed the temperature distrubution function real(triple v) according to the specified heat sources.

import palette;
import graph3;

size(200);

currentprojection=orthographic(1,1,1);

triple[] P={
  (2,  0,  0),
  (-2,  0,  0),
  (0,  2,  0),
  (4,  0,  4),
  (0,  4,  4),
  (-4,  0,  4)
};

path3 p1=P[0]..P[2]..P[1];
path3 p2=P[3]..P[4]..P[5];

surface sur=extrude(p1,p2);

real[][] weights={
  {5,15},
  {20,12},
  {10,8},
};

real distribution(triple v){return sin(v.x*v.z);}//??????

sur.colors(palette(sur.map(distribution),Rainbow()));

draw(sur);

draw(planeproject(unitsquare3)*sur);

axes3("$x$","$y$","$z$",Arrow3());

Sorry, I make some mistake in my code, here is the new

settings.render=0;

import graph3;
import palette;

size(200);

file in=input("data.txt").line();
real[] x=in;
real[] y=in;

real[][] z=in.dimension(0,0);

surface s=surface(z,x,y);

s.colors(palette(s.map(zpart), Rainbow()));

draw(s,nolight);

//draw(planeproject(unitsquare3)*s,nolight);

currentprojection=orthographic(0,0,1);

limits((0,0,0),(1.1*max(x),1.1*max(y),1.1*max(z)));

xaxis3("$x$",OutTicks(),Arrow3(),above=true);
yaxis3("$y$",OutTicks(),Arrow3(),above=true);

for the general cace, I constructed another surface and using the map, but it seems not the good way

import palette;
import graph3;
size(200);

currentprojection=perspective(2,-12,6);

triple[] P={
  (2,  0,    0),
  (0,  2,    0),
  (-2, 0,   0),
  (4,  0,    4),
  (0,  4,    4),
  (-4, 0,   4)
};

triple [] Q={
  (2,  0,   10),
  (0,  2,   20),
  (-2, 0,  5),
  (4,  0,   8 ),
  (0,  4,   12),
  (-4, 0,  15)
};

surface p=extrude(P[0]..P[1]..P[2],P[3]..P[4]..P[5]);

surface q=extrude(Q[0]..Q[1]..Q[2],Q[3]..Q[4]..Q[5]);

p.colors(palette(q.map(zpart),Rainbow()));

draw(p);

axes3("$x$","$y$","$z$",Arrow3());