How do I plot an intersection of a surface 3D and a plane?

Question

Eric Bernard Dilger 2021-4-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/812510-how-do-i-plot-an-intersection-of-a-surface-3d-and-a-plane

回答： burak ergocmen 2024-2-22

I'm interested to plot the intersection of a 3D surface with a 2D plane (x,y) for differents values of the height z. I need to plot the upper view of this intersection and represent its points as a dark pixel of value1 if they're below the intersection, and as a white pixel of value 0 if they're above. I also need to store this data points in a matricial form so that it represents the (x,y) cutting plane. Any suggestions?

The code below it's a midpoint displacement algorithm that I'm using to plot 3D surfaces.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Eric Bernard Dilger 2021-4-25

H=0.5;

nmax=6;

length=2^nmax+1;

step=2^nmax;

halfstep=step/2;

x=linspace(0,1,length);

y=x;

[x,y]=meshgrid(x,y);

z=zeros(size(x));

for n=1 : nmax

range=2^(-2*n*H);

for i = 1 : step : length - step

for j = 1 : step : length - step

z(i+halfstep,j)=0.5*(z(i,j)+z(i+step,j))+(1-2*rand)*range; % (1+0,5 ; j)

z(i,j+halfstep)=0.5*(z(i,j)+z(i,j+step))+(1-2*rand)*range; % (i ; j+0,5)

z(i+step,j+halfstep)=0.5*(z(i+step,j)+z(i+step,j+step))+(1-2*rand)*range; % (i+1 ; j+0,5)

z(i+halfstep,j+step)=0.5*(z(i,j+step)+z(i+step,j+step))+(1-2*rand)*range; % (i+0.5 ; j+1)

z(i+halfstep,j+halfstep)=0.25*(z(i,j)+z(i+step,j)+z(i,j+step)+z(i+step,j+step))+(1-2*rand)*range;

end

step=step/2;

halfstep=halfstep/2;

p=1;

for i=1 : 2^n +1

q=1;

for j = 1 : 2^n + 1

plotx(i,j) = x(p,q);

ploty(i,j) = y(p,q);

plotz(i,j) = z(p,q);

q = q + step;

end

p = p + step;

end

surf(plotx,ploty,plotz,'facecolor','w')

axis([0 1 0 1 -0.5 0.5])

axis off

shg

pause(0.1)

end

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2021-4-25

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/812510-how-do-i-plot-an-intersection-of-a-surface-3d-and-a-plane#answer_684190

在 MATLAB Online 中打开

Use the contourf function to get the intersection of the plane and the surface, and plot the result —

H=0.5;

nmax=6;

length=2^nmax+1;

step=2^nmax;

halfstep=step/2;

x=linspace(0,1,length);

y=x;

[x,y]=meshgrid(x,y);

z=zeros(size(x));

for n=1 : nmax

range=2^(-2*n*H);

for i = 1 : step : length - step

for j = 1 : step : length - step

z(i+halfstep,j)=0.5*(z(i,j)+z(i+step,j))+(1-2*rand)*range; % (1+0,5 ; j)

z(i,j+halfstep)=0.5*(z(i,j)+z(i,j+step))+(1-2*rand)*range; % (i ; j+0,5)

z(i+step,j+halfstep)=0.5*(z(i+step,j)+z(i+step,j+step))+(1-2*rand)*range; % (i+1 ; j+0,5)

z(i+halfstep,j+step)=0.5*(z(i,j+step)+z(i+step,j+step))+(1-2*rand)*range; % (i+0.5 ; j+1)

z(i+halfstep,j+halfstep)=0.25*(z(i,j)+z(i+step,j)+z(i,j+step)+z(i+step,j+step))+(1-2*rand)*range;

end

step=step/2;

halfstep=halfstep/2;

p=1;

for i=1 : 2^n +1

q=1;

for j = 1 : 2^n + 1

plotx(i,j) = x(p,q);

ploty(i,j) = y(p,q);

plotz(i,j) = z(p,q);

q = q + step;

end

p = p + step;

end

surf(plotx,ploty,plotz,'facecolor','w')

axis([0 1 0 1 -0.5 0.5])

% axis off

shg

pause(0.1)

end

hold on

plane_z = +0.15;

surf(xlim, ylim, plane_z*ones(2), 'FaceColor','b', 'FaceAlpha',0.5) % Plot Plane At 'plane_z'

hold off

xlabel('X \rightarrow', 'Rotation',20)

ylabel('\leftarrow Y', 'Rotation',-25)

zlabel('Z \rightarrow')

ZL = zlim;

figure

[c,h] = contourf(plotx, ploty, plotz, [ZL(1) plane_z]); % Contour Plot At 'plane_z'

colormap(bone(2));

colorbar

axis('equal')

grid

xlabel('X')

ylabel('Y')

Levels = plane_z;

idx = find(c(1,:) == Levels);

Len = c(2,idx);

for k = 1:numel(idx) % Retrieve Contour (x,y) Data

xc{k} = c(1,idx+1:Len(k));

yc{k} = c(2,idx+1:Len(k));

end

Contour_Information = sprintf('Number of different contours at %.2f = %d\n', plane_z, numel(idx))

Contour_Information =

'Number of different contours at 0.15 = 7 '

I altered the code slightly to show the plane in the original surf plot in order to demonstrate that the contour plot creates it correctly.

See the contourf documentation on Contour Matrix M to understand how to get the coordinates of the contours themselves. (This is not trivial, however it is not difficult. I included code that does that and appears to work here.)

I will let you experiment with getting the image and saving it. See the documentation on imwrite for one approach.

.

4 个评论
显示 2更早的评论隐藏 2更早的评论

Eric Bernard Dilger 2021-5-31

Hello buddy! It's me again. Now, I'd like to plot the contourf of this 3D surface with a non-horizontal plane. I could plot the intersection between them, just defining the points of Z_matrix to be different than z_plane*ones(2).

Z_matrix = [0.3 0.3; 1.7 1.7];

surf(xlim, ylim, plane_z*Z_matrix, 'FaceColor','b', 'FaceAlpha',0.5) % Plot Plane At 'plane_z'