如何在matlab中绘制地圈？
如何在matlab中绘制地球球体 通过如何在matlab中绘制地圈？,matlab,geometry,surf,Matlab,Geometry,Surf,如何在matlab中绘制地球球体 通过Geosphere我指的是球体上离散点的方式（Geosphere是，例如在3Ds Max中） 在下图中，它显示为球体（左侧）和地球球体（右侧） 在Matlab中有一个函数sphere，它给出了这样一个结果： 我需要得到这样一个地球圈的图像。我有一个矩阵Nx3，有地球圈每个点的xyz坐标 更新： 我只在显示（绘制）geosphere时遇到问题，因为我已经有了每个点的数据-xyz坐标。这就是为什么Gunther Struyf的回答帮助了我，我接受了 这是我通
Geosphere球体地球球体sphere另外，对于计算地球圈的点，感谢下面的回答
@Rody Oldenhuis我有一个函数，可以生成任意精度的球面三角剖分。这是我基于Giacari Luigi的
buildspherefunction [p, t] = TriSphere(N, R)
% TRISPHERE: Returns the triangulated model of a sphere using the
% icosaedron subdivision method.
%
% INPUT:
% N (integer number) indicates the number of subdivisions,
% it can assumes values between 0-inf. The greater N the better will look
% the surface but the more time will be spent in surface costruction and
% more triangles will be put in the output model.
%
% OUTPUT:
% In p (nx3) and t(mx3) we can find points and triangles indexes
% of the model. The sphere is supposed to be of unit radius and centered in
% (0,0,0). To obtain spheres centered in different location, or with
% different radius, is just necessary a traslation and a scaling
% trasformation. These operation are not perfomed by this code beacuse it is
% extrimely convinient, in order of time perfomances, to do this operation
% out of the function avoiding to call the costruction step each time.
%
% NOTE:
% This function is more efficient than the matlab command sphere in
% terms of dimension fo the model/ accuracy of recostruction. This due to
% well traingulated model that requires a minor number of patches for the
% same geometrical recostruction accuracy. Possible improvement are possible
% in time execution and model subdivision flexibilty.
%
% EXAMPLE:
%
% N=5;
%
% [p,t] = TriSphere(N);
%
% figure(1) axis equal hold on trisurf(t,p(:,1),p(:,2),p(:,3)); axis vis3d
% view(3)
% Author: Giaccari Luigi Created:25/04/2009%
% For info/bugs/questions/suggestions : giaccariluigi@msn.com
% ORIGINAL NAME: BUILDSPHERE
%
% Adjusted by Rody Oldenhuis (speed/readability)
% error traps
error(nargchk(1,1,nargin));
error(nargoutchk(1,2,nargout));
if ~isscalar(N)
error('Buildsphere:N_mustbe_scalar',...
'Input N must be a scalar.');
end
if round(N) ~= N
error('Buildsphere:N_mustbe_scalar',...
'Input N must be an integer value.');
end
% Coordinates have been taken from Jon Leech' files
% Twelve vertices of icosahedron on unit sphere
tau = 0.8506508083520400; % t = (1+sqrt(5))/2, tau = t/sqrt(1+t^2)
one = 0.5257311121191336; % one = 1/sqrt(1+t^2) (unit sphere)
p = [
+tau +one +0 % ZA
-tau +one +0 % ZB
-tau -one +0 % ZC
+tau -one +0 % ZD
+one +0 +tau % YA
+one +0 -tau % YB
-one +0 -tau % YC
-one +0 +tau % YD
+0 +tau +one % XA
+0 -tau +one % XB
+0 -tau -one % XC
+0 +tau -one]; % XD
% Structure for unit icosahedron
t = [
5 8 9
5 10 8
6 12 7
6 7 11
1 4 5
1 6 4
3 2 8
3 7 2
9 12 1
9 2 12
10 4 11
10 11 3
9 1 5
12 6 1
5 4 10
6 11 4
8 2 9
7 12 2
8 10 3
7 3 11 ];
% possible quick exit
if N == 0, return, end
% load pre-generated trispheres (up to 8 now...)
if N <= 8
S = load(['TriSphere', num2str(N), '.mat'],'pts','idx');
p = S.pts; t = S.idx;
if nargin == 2, p = p*R; end
return
else
% if even more is requested (why on Earth would you?!), make sure to START
% from the maximum pre-loadable trisphere
S = load('TriSphere8.mat','pts','idx');
p = S.pts; t = S.idx; clear S; N0 = 10;
end
% how many triangles/vertices do we have?
nt = size(t,1); np = size(p,1); totp = np;
% calculate the final number of points
for ii=N0:N, totp = 4*totp - 6; end
% initialize points array
p = [p; zeros(totp-12, 3)];
% determine the appropriate class for the triangulation indices
numbits = 2^ceil(log(log(totp+1)/log(2))/log(2));
castToInt = ['uint',num2str(numbits)];
% issue warning when required
if numbits > 64
warning('TriSphere:too_many_notes',...
['Given number of iterations would require a %s class to accurately ',...
'represent the triangulation indices. Using double instead; Expect ',...
'strange results!']);
castToInt = @double;
else
castToInt = str2func(castToInt);
end
% refine icosahedron N times
for ii = N0:N
% initialize inner loop
told = t;
t = zeros(nt*4, 3);
% Use sparse. Yes, its slower in a loop, but for N = 6 the size is
% already ~10,000x10,000, growing by a factor of 4 with every
% increasing N; its simply too memory intensive to use zeros().
peMap = sparse(np,np);
ct = 1;
% loop trough all old triangles
for j = 1:nt
% some helper variables
p1 = told(j,1);
p2 = told(j,2);
p3 = told(j,3);
x1 = p(p1,1); x2 = p(p2,1); x3 = p(p3,1);
y1 = p(p1,2); y2 = p(p2,2); y3 = p(p3,2);
z1 = p(p1,3); z2 = p(p2,3); z3 = p(p3,3);
% first edge
% -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
% preserve triangle orientation
if p1 < p2, p1m = p1; p2m = p2; else p2m = p1; p1m = p2; end
% If the point does not exist yet, calculate the new point
p4 = peMap(p1m,p2m);
if p4 == 0
np = np+1;
p4 = np;
peMap(p1m,p2m) = np;%#ok
p(np,1) = (x1+x2)/2;
p(np,2) = (y1+y2)/2;
p(np,3) = (z1+z2)/2;
end
% second edge
% -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
% preserve triangle orientation
if p2 < p3; p2m = p2; p3m = p3; else p2m = p3; p3m = p2; end
% If the point does not exist yet, calculate the new point
p5 = peMap(p2m,p3m);
if p5 == 0
np = np+1;
p5 = np;
peMap(p2m,p3m) = np;%#ok
p(np,1) = (x2+x3)/2;
p(np,2) = (y2+y3)/2;
p(np,3) = (z2+z3)/2;
end
% third edge
% -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
% preserve triangle orientation
if p1 < p3; p1m = p1; p3m = p3; else p3m = p1; p1m = p3; end
% If the point does not exist yet, calculate the new point
p6 = peMap(p1m,p3m);
if p6 == 0
np = np+1;
p6 = np;
peMap(p1m,p3m) = np;%#ok
p(np,1) = (x1+x3)/2;
p(np,2) = (y1+y3)/2;
p(np,3) = (z1+z3)/2;
end
% allocate new triangles
% refine indexing
% p1
% /\
% /t1\
% p6/____\p4
% /\ /\
% /t4\t2/t3\
% /____\/____\
% p3 p5 p2
t(ct,1) = p1; t(ct,2) = p4; t(ct,3) = p6; ct = ct+1;
t(ct,1) = p4; t(ct,2) = p5; t(ct,3) = p6; ct = ct+1;
t(ct,1) = p4; t(ct,2) = p2; t(ct,3) = p5; ct = ct+1;
t(ct,1) = p6; t(ct,2) = p5; t(ct,3) = p3; ct = ct+1;
end % end subloop
% update number of triangles
nt = ct-1;
end % end main loop
% normalize all points to 1 (or R)
p = bsxfun(@rdivide, p, sqrt(sum(p.^2,2)));
if (nargin == 2), p = p*R; end
% convert t to proper integer class
t = castToInt(t);
end % funciton TriSphere
函数[p，t]=三球体（N，R）
%TRISPHERE：返回使用
%二十面体细分法。
%
%输入：
%N（整数）表示细分的数量，
%它可以假定值在0-inf之间。N越大，效果越好
%但是，更多的时间将花在表面施工和维护上
%将在输出模型中放置更多三角形。
%
%输出：
%在p（nx3）和t（mx3）中，我们可以找到点和三角形索引
%这是模型的一部分。球体应具有单位半径，并以
% (0,0,0). 获取位于不同位置中心的球体，或使用
%不同的半径，只是需要一个平移和缩放
%转换。这些操作不是由该代码执行的，因为它是
%按照时间性能的顺序，非常方便地执行此操作
%函数外避免每次调用构造步骤。
%
%注:
%此函数比中的matlab命令球体更有效
%模型尺寸术语/重建精度。这是由于
%受良好训练的模型，该模型需要少量的修补程序
%同样的几何重构精度。可能的改进是可能的
%实时执行和模型细分灵活性。
%
%例如：
%
%N=5；
%
%[p，t]=三球（N）；
%
%图（1）三曲面上的轴相等保持（t，p（：，1），p（：，2），p（：，3））；三维轴
%视图（3）
%作者：Giacari Luigi创作：25/04/2009%
%有关信息/错误/问题/建议：giaccariluigi@msn.com
%原名：BUILDSPHERE
%
%由Rody Oldenhuis调整（速度/可读性）
%错误陷阱
错误（nargchk（1,1，nargin））；
错误（nargoutchk（1,2，nargout））；
如果~isscalar（N）
错误（'Buildsphere:N\u必须是\u标量'，。。。
“输入N必须是标量。”）；
结束
如果是圆形（N）~=N
错误（'Buildsphere:N\u必须是\u标量'，。。。
“输入N必须是整数值。”）；
结束
%坐标取自Jon Leech的档案
%单位球面上二十面体的十二个顶点
tau=0.850650883520400；%t=（1+sqrt（5））/2，tau=t/sqrt（1+t^2）
一=0.5257311121191336；%1=1/sqrt（1+t^2）（单位球面）
p=[
+tau+1+0%ZA
-tau+1+0%ZB
-τ-1+0%ZC
+τ-1+0%ZD
+1+0+tau%YA
+1+0-τ%YB
-1+0-τ%YC
-1+0+tau%YD
+0+tau+1%XA
+0-tau+1%XB
+0-tau-1%XC
+0+tau-1]；%除息的
%单位二十面体的结构
t=[
5 8 9
5 10 8
6 12 7
6 7 11
1 4 5
1 6 4
3 2 8
3 7 2
9 12 1
9 2 12
10 4 11
10 11 3
9 1 5
12 6 1
5 4 10
6 11 4
8 2 9
7 12 2
8 10 3
7 3 11 ];
%可能的快速退出
如果N==0，返回，结束
%加载预生成的三球体（现在最多8个…）
如果N 64
警告（'TriSphere:注释太多'，。。。
[“给定的迭代次数将需要%s类才能准确执行”，。。。
'表示三角剖分索引。改为使用double；Expect'，。。。
“奇怪的结果！”）；
castToInt=@double；
其他的
castToInt=str2func（castToInt）；
结束
%细化二十面体N次
对于ii=N0:N
%初始化内部循环
t=t；
t=零（nt*4,3）；
%使用稀疏。是的，它在循环中较慢，但对于N=6，大小为
%已经~10000x1000，每增加一次增长4倍
%增加氮；它的内存太大，无法使用零（）。
peMap=稀疏（np，np）；
ct=1；
%通过所有旧三角形循环
对于j=1:nt
%一些辅助变量
p1=已知（j，1）；
p2=已知（j，2）；
p3=已告知（j，3）；
x1=p（p1,1）；x2=p（p2,1）；x3=p（p3,1）；
y1=p（p1,2）；y2=p（p2,2）；y3=p（p3,2）；
z1=p（p1,3）；z2
function [p, t] = TriSphere(N, R)
% TRISPHERE: Returns the triangulated model of a sphere using the
% icosaedron subdivision method.
%
% INPUT:
% N (integer number) indicates the number of subdivisions,
% it can assumes values between 0-inf. The greater N the better will look
% the surface but the more time will be spent in surface costruction and
% more triangles will be put in the output model.
%
% OUTPUT:
% In p (nx3) and t(mx3) we can find points and triangles indexes
% of the model. The sphere is supposed to be of unit radius and centered in
% (0,0,0). To obtain spheres centered in different location, or with
% different radius, is just necessary a traslation and a scaling
% trasformation. These operation are not perfomed by this code beacuse it is
% extrimely convinient, in order of time perfomances, to do this operation
% out of the function avoiding to call the costruction step each time.
%
% NOTE:
% This function is more efficient than the matlab command sphere in
% terms of dimension fo the model/ accuracy of recostruction. This due to
% well traingulated model that requires a minor number of patches for the
% same geometrical recostruction accuracy. Possible improvement are possible
% in time execution and model subdivision flexibilty.
%
% EXAMPLE:
%
% N=5;
%
% [p,t] = TriSphere(N);
%
% figure(1) axis equal hold on trisurf(t,p(:,1),p(:,2),p(:,3)); axis vis3d
% view(3)
% Author: Giaccari Luigi Created:25/04/2009%
% For info/bugs/questions/suggestions : giaccariluigi@msn.com
% ORIGINAL NAME: BUILDSPHERE
%
% Adjusted by Rody Oldenhuis (speed/readability)
% error traps
error(nargchk(1,1,nargin));
error(nargoutchk(1,2,nargout));
if ~isscalar(N)
error('Buildsphere:N_mustbe_scalar',...
'Input N must be a scalar.');
end
if round(N) ~= N
error('Buildsphere:N_mustbe_scalar',...
'Input N must be an integer value.');
end
% Coordinates have been taken from Jon Leech' files
% Twelve vertices of icosahedron on unit sphere
tau = 0.8506508083520400; % t = (1+sqrt(5))/2, tau = t/sqrt(1+t^2)
one = 0.5257311121191336; % one = 1/sqrt(1+t^2) (unit sphere)
p = [
+tau +one +0 % ZA
-tau +one +0 % ZB
-tau -one +0 % ZC
+tau -one +0 % ZD
+one +0 +tau % YA
+one +0 -tau % YB
-one +0 -tau % YC
-one +0 +tau % YD
+0 +tau +one % XA
+0 -tau +one % XB
+0 -tau -one % XC
+0 +tau -one]; % XD
% Structure for unit icosahedron
t = [
5 8 9
5 10 8
6 12 7
6 7 11
1 4 5
1 6 4
3 2 8
3 7 2
9 12 1
9 2 12
10 4 11
10 11 3
9 1 5
12 6 1
5 4 10
6 11 4
8 2 9
7 12 2
8 10 3
7 3 11 ];
% possible quick exit
if N == 0, return, end
% load pre-generated trispheres (up to 8 now...)
if N <= 8
S = load(['TriSphere', num2str(N), '.mat'],'pts','idx');
p = S.pts; t = S.idx;
if nargin == 2, p = p*R; end
return
else
% if even more is requested (why on Earth would you?!), make sure to START
% from the maximum pre-loadable trisphere
S = load('TriSphere8.mat','pts','idx');
p = S.pts; t = S.idx; clear S; N0 = 10;
end
% how many triangles/vertices do we have?
nt = size(t,1); np = size(p,1); totp = np;
% calculate the final number of points
for ii=N0:N, totp = 4*totp - 6; end
% initialize points array
p = [p; zeros(totp-12, 3)];
% determine the appropriate class for the triangulation indices
numbits = 2^ceil(log(log(totp+1)/log(2))/log(2));
castToInt = ['uint',num2str(numbits)];
% issue warning when required
if numbits > 64
warning('TriSphere:too_many_notes',...
['Given number of iterations would require a %s class to accurately ',...
'represent the triangulation indices. Using double instead; Expect ',...
'strange results!']);
castToInt = @double;
else
castToInt = str2func(castToInt);
end
% refine icosahedron N times
for ii = N0:N
% initialize inner loop
told = t;
t = zeros(nt*4, 3);
% Use sparse. Yes, its slower in a loop, but for N = 6 the size is
% already ~10,000x10,000, growing by a factor of 4 with every
% increasing N; its simply too memory intensive to use zeros().
peMap = sparse(np,np);
ct = 1;
% loop trough all old triangles
for j = 1:nt
% some helper variables
p1 = told(j,1);
p2 = told(j,2);
p3 = told(j,3);
x1 = p(p1,1); x2 = p(p2,1); x3 = p(p3,1);
y1 = p(p1,2); y2 = p(p2,2); y3 = p(p3,2);
z1 = p(p1,3); z2 = p(p2,3); z3 = p(p3,3);
% first edge
% -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
% preserve triangle orientation
if p1 < p2, p1m = p1; p2m = p2; else p2m = p1; p1m = p2; end
% If the point does not exist yet, calculate the new point
p4 = peMap(p1m,p2m);
if p4 == 0
np = np+1;
p4 = np;
peMap(p1m,p2m) = np;%#ok
p(np,1) = (x1+x2)/2;
p(np,2) = (y1+y2)/2;
p(np,3) = (z1+z2)/2;
end
% second edge
% -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
% preserve triangle orientation
if p2 < p3; p2m = p2; p3m = p3; else p2m = p3; p3m = p2; end
% If the point does not exist yet, calculate the new point
p5 = peMap(p2m,p3m);
if p5 == 0
np = np+1;
p5 = np;
peMap(p2m,p3m) = np;%#ok
p(np,1) = (x2+x3)/2;
p(np,2) = (y2+y3)/2;
p(np,3) = (z2+z3)/2;
end
% third edge
% -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
% preserve triangle orientation
if p1 < p3; p1m = p1; p3m = p3; else p3m = p1; p1m = p3; end
% If the point does not exist yet, calculate the new point
p6 = peMap(p1m,p3m);
if p6 == 0
np = np+1;
p6 = np;
peMap(p1m,p3m) = np;%#ok
p(np,1) = (x1+x3)/2;
p(np,2) = (y1+y3)/2;
p(np,3) = (z1+z3)/2;
end
% allocate new triangles
% refine indexing
% p1
% /\
% /t1\
% p6/____\p4
% /\ /\
% /t4\t2/t3\
% /____\/____\
% p3 p5 p2
t(ct,1) = p1; t(ct,2) = p4; t(ct,3) = p6; ct = ct+1;
t(ct,1) = p4; t(ct,2) = p5; t(ct,3) = p6; ct = ct+1;
t(ct,1) = p4; t(ct,2) = p2; t(ct,3) = p5; ct = ct+1;
t(ct,1) = p6; t(ct,2) = p5; t(ct,3) = p3; ct = ct+1;
end % end subloop
% update number of triangles
nt = ct-1;
end % end main loop
% normalize all points to 1 (or R)
p = bsxfun(@rdivide, p, sqrt(sum(p.^2,2)));
if (nargin == 2), p = p*R; end
% convert t to proper integer class
t = castToInt(t);
end % funciton TriSphere