I need to draw arc through three points in three-dimensional space. Can you please help me out?

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Siddharth Behal 2022-10-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1832628-i-need-to-draw-arc-through-three-points-in-three-dimensional-space-can-you-please-help-me-out

编辑： Matt J 2022-10-22

采纳的回答： Matt J

在 MATLAB Online 中打开

x_i = [0,5,20];

y_i = [0,0,0];

z_i = [20,5,0];

P1 = [x_i(1);y_i(1);z_i(1)]

P1 = 3×1

0 0 20

P2 = [x_i(2);y_i(2);z_i(2)]

P2 = 3×1

5 0 5

P3 = [x_i(3);y_i(3);z_i(3)]

P3 = 3×1

20 0 0

v1 = cross(P2-P1,P3-P1);

v1 = v1/norm(v1)

v1 = 3×1

0 -1 0

syms x y z

P0 = [x;y;z];

eqn1 = dot(P0-P1,v1) == 0

eqn1 =

eqn2 = dot(P0-(P2+P1)/2,P2-P1) == 0

eqn2 =

eqn3 = dot(P0-(P3+P1)/2,P3-P1) == 0

eqn3 =

[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [x, y, z])

A =

B =

P_centre = linsolve(A,B)

Warning: Solution does not exist because the system is inconsistent.

P_centre =

Can you please tell me where I am going wrong?

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Siddharth Behal 2022-10-22

Thank you so much, Torsten. I really appreciate your help.

Siddharth Behal 2022-10-22

Also, do you know how can I plot this arc? I just need the arc between three points instead of the circle

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采纳的回答

Matt J 2022-10-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1832628-i-need-to-draw-arc-through-three-points-in-three-dimensional-space-can-you-please-help-me-out#answer_1080938

编辑：Matt J 2022-10-21

在 MATLAB Online 中打开

I would suggest this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

x_i = [0,5,20];
y_i = [0,0,0];
z_i = [20,5,0];
P1 = [x_i(1),y_i(1),z_i(1)];
P2 = [x_i(2),y_i(2),z_i(2)];
P3 = [x_i(3),y_i(3),z_i(3)];
pfit=planarFit([P1;P2;P3]');
 xy=pfit.R(:,2:3)'*pfit.XYZ;
 cfit=circularFit(xy);
 C=cfit.sample(0:360);
XYZ =num2cell( pfit.R(:,2)*C{1} + pfit.R(:,3)*C{2} + pfit.normal'*pfit.distance  ,2);
scatter3(x_i,y_i,z_i,'filled','r','SizeData',50);
line(XYZ{:}); axis equal
xlabel x, ylabel y, zlabel z

2 个评论
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Siddharth Behal 2022-10-22

Is there a way to draw only the arc between three points instead of the entire circle?

Matt J 2022-10-22

编辑：Matt J 2022-10-22

在 MATLAB Online 中打开

pfit=planarFit([P1;P2;P3]');
 xy=pfit.R(:,2:3)'*pfit.XYZ;
 cfit=circularFit(xy);
 xy=xy-cfit.center';
 t1=atan2d(xy(2,1),xy(1,1));
 t2=atan2d(xy(2,3),xy(1,3));
 C=cell2mat(cfit.sample(linspace(t1,t2)));
XYZ = num2cell( pfit.R(:,2)*C(1,:) + pfit.R(:,3)*C(2,:) + pfit.normal'*pfit.distance  ,2);
scatter3(x_i,y_i,z_i,'filled','r','SizeData',50);
line(XYZ{:}); axis equal
xlabel x, ylabel y, zlabel z

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