Got wrong normal vector

Question

AI-CHI Chang 2022-8-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1777300-got-wrong-normal-vector

评论： AI-CHI Chang 2022-8-14

I wrote a code presented the scatter points on a peak function, and now I want to solve for unit normal vectors at those points.

ok...maybe this is a math problem...why I got a result looks like tangetial vector...

The arrow on the surrounding flat plant looks good but the peak's normal vectors obviously wrong.

% function handler

f = @(x,y)2*(1-x).^2.*exp(-(x.^2) - (y+1).^2) ...

- 5*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ...

- 1/3*exp(-(x+1).^2 - y.^2); % z

rng('default');

ds = 0.0005;

range = (-2:ds:2)';

width = 4;

x = -width+(width-(-width))*rand(length(range),1); %

y = -width+(width-(-width))*rand(length(range),1); % r = a + (b-a).*rand(N,1)

z = f(x,y);

p = [x y z];

p_origin = p;

num_pt = size(p,1);

syms s t

f1 = 2*(1-s).^2.*exp(-(s.^2) - (t+1).^2) ...

- 5*(s/5 - s.^3 - s.^5).*exp(-s.^2-t.^2) ...

- 1/3*exp(-(s+1).^2 - t.^2);

dfs = diff(f1,s);

dft = diff(f1,t);

normal_x = matlabFunction(dfs);

normal_y = matlabFunction(dft);

normal = [normal_x(x,y),normal_y(x,y),-ones(num_pt,1)];

norm_nor = sqrt(sum(normal.*normal,2));

normal = bsxfun(@rdivide,normal,norm_nor);

% draw arrow

x=p(:,1);

y=p(:,2);

z=p(:,3);

u=normal(:,1);

v=normal(:,2);

w=normal(:,3);

plot3(x,y,z,'b.');

axis equal;

grid on;

view(45,15);

hold on;

quiver3(x,y,z,u,v,w,'r','LineWidth',1,'MaxHeadSize',5);

6 个评论
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Bruno Luong 2022-8-10

Your normal is alright just your graphic representation tricks your brain.

AI-CHI Chang 2022-8-10

yeah...then i think my problem is solved

thank you very much !! :D

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Answer 1

David Goodmanson 2022-8-12

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1777300-got-wrong-normal-vector#answer_1025365

编辑：David Goodmanson 2022-8-12

在 MATLAB Online 中打开

Hi AC,

You were quite right in your suspicions of the 3d plot, which looks fishy. You might call this a configuration control issue. You have two independent functions, f and f1, that are supposed to represent the same thing. That carries some risk in programming. The two functions are supposed to be identical with x <--> s, y <--> t. But if you compare their second lines,

- 5*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ...   % f 
- 5*(s/5 - s.^3 - s.^5).*exp(-s.^2-t.^2) ...   % f1

you can see that there is a problem with the y.^5 term. I'm not sure which version is correct, but if you change y.^5 to x.^5, or if you change s.^5 to t.^5, in both cases the normal vectors in the plot are pretty clearly normal.