how can I find the intersection of two surface

Question

M 2022-9-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1808915-how-can-i-find-the-intersection-of-two-surface

评论： Star Strider 2022-9-23

Hi, I wrote the code below to find the intersection of two surfaces "cdot: and "ctdot", but it has an error : Z must be a matrix, not a scalar or vector.

Could you please tell me how solve it, thanks for any help.

vplc=0.16;

delta=0.1;

Ktau=0.045;

Kc=0.1;

K=0.0075;

Kp=0.15;

gamma=5.5;

Kb=0.4;

alpha0=delta*6.81e-6/(0.002);

alpha1=delta*2.27e-5/(0.002);

Ke=7;

Vs=0.002;

Ks=0.1;

Kf=0.18;

kplc=0.055;

ki=2;

tau_max=0.176;

Vss=0.044;

A=(-(Vss.*c.^2)./(Ks.^2))+((Vs.*K.*gamma.^2.*ct.^2)./(Ks.^2))+alpha0+alpha1.*((Ke.^4)./(Ke.^4+(gamma.*ct).^4));

p=(vplc.*c.^2./(c.^2+kplc.^2))./ki;

h=(-(0.4.*A.*((Kc.^4).*(Kp.^2))./((p.^2.*c.^2.*gamma.*ct.*Kf))));

G1=alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4));

G2=((1-h)./tau_max).*c.^4;

Fc=(4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2);

Fct=((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2);

Fh=(gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4);

cdot=@(ct,c)(((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2)).*(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4)))+((gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4)).*(((1-h)./tau_max).*c.^4);

ctdot=@(ct,c)(-(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4))).*((4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2)));

ct = 0:.1:2.5;

c = 0:.1:2.5;

[Ct,C] = meshgrid(ct,c);

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',2)

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Answer 1

Star Strider 2022-9-20

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1808915-how-can-i-find-the-intersection-of-two-surface#answer_1057455

编辑：Star Strider 2022-9-20

在 MATLAB Online 中打开

MATLAB is case-sensitive so ‘ct’ ~= ‘Ct’ (and so for the others) in the ‘cdot’ and ‘ctdot’ calls.

I would like to run this to demonstrate that, however ‘c’ is nowhere to be found.

vplc=0.16;
delta=0.1;
Ktau=0.045;
Kc=0.1; 
K=0.0075;
Kp=0.15;
gamma=5.5;
Kb=0.4;
vss=0.044;
alpha0=delta*6.81e-6/(0.002);
alpha1=delta*2.27e-5/(0.002);
Ke=7;
Vs=0.002;
Ks=0.1;
Kf=0.18;
kplc=0.055;
ki=2;
tau_max=0.176;
Vss=0.044;
ct = 0:.1:2.5;
c = 0:.1:2.5;
A=(-(vss.*c.^2)./(ks.^2))+((Vs.*K.*gamma.^2.*ct.^2)./(ks.^2))+alpha0+alpha1.*((Ke.^4)./(Ke.^4+(gamma.*ct).^4));
Unrecognized function or variable 'ks'.
p=(vplc.*c.^2./(c.^2+kplc.^2))./ki;
h=(-(0.4.*A.*((Kc.^4).*(Kp.^2))./((p.^2.*c.^2.*gamma.*ct.*Kf))));
G1=alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4));
G2=((1-h)./tau_max).*c.^4;
Fc=(4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2);
Fct=((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2);
Fh=(gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4);
cdot=@(ct,c)(((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2)).*(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4)))+((gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4)).*(((1-h)./tau_max).*c.^4);
ctdot=@(ct,c)(-(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4))).*((4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2)));
% ct = 0:.1:2.5;
% c = 0:.1:2.5;
[Ct,C] = meshgrid(ct,c);
figure
surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))
hold on
contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',2)  

.

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Star Strider 2022-9-20

编辑：Star Strider 2022-9-20

在 MATLAB Online 中打开

vplc=0.16;

delta=0.1;

Ktau=0.045;

Kc=0.1;

K=0.0075;

Kp=0.15;

gamma=5.5;

Kb=0.4;

alpha0=delta*6.81e-6/(0.002);

alpha1=delta*2.27e-5/(0.002);

Ke=7;

Vs=0.002;

Ks=0.1;

Kf=0.18;

kplc=0.055;

ki=2;

tau_max=0.176;

Vss=0.044;

ct = 0:.1:2.5;

c = 0:.1:2.5;

A=(-(Vss.*c.^2)./(Ks.^2))+((Vs.*K.*gamma.^2.*ct.^2)./(Ks.^2))+alpha0+alpha1.*((Ke.^4)./(Ke.^4+(gamma.*ct).^4));

p=(vplc.*c.^2./(c.^2+kplc.^2))./ki;

h=(-(0.4.*A.*((Kc.^4).*(Kp.^2))./((p.^2.*c.^2.*gamma.*ct.*Kf))));

G1=alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4));

G2=((1-h)./tau_max).*c.^4;

Fc=(4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2);

Fct=((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2);

Fh=(gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4);

cdot=@(ct,c)(((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2)).*(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4)))+((gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4)).*(((1-h)./tau_max).*c.^4);

ctdot=@(ct,c)(-(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4))).*((4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2)));

[Ct,C] = meshgrid(ct,c);

figure

surf(Ct,C,cdot(Ct,C))

hold on

surf(Ct,C,zeros(size(C)), 'FaceColor','r', 'FaceAlpha',0.5)

hold off

xlabel('X')

ylabel('Y')

title('cdot')

figure

surf(Ct,C,ctdot(Ct,C))

hold on

surf(Ct,C,zeros(size(C)), 'FaceColor','r', 'FaceAlpha',0.5)

hold off

xlabel('X')

ylabel('Y')

title('ctdot')

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',5)

hold off

xlabel('X')

ylabel('Y')

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',5)

hold off

xlabel('X')

ylabel('Y')

ylim([0 0.2])

zlim([-1 1])

title('Zoomed')

Mtx = cdot(Ct,C)-ctdot(Ct,C);

[minMtx,idx] = min(Mtx(:))

minMtx = 1.8648e-05

idx = 651

[row,col] = ind2sub(size(Mtx), idx)

row = 1

col = 26

idx = find(Mtx == min(Mtx(:)))

idx = 651

[row,col] = ind2sub(size(Mtx), idx)

row = 1

col = 26

I am not certain that the surfaces actually intersect. If so, they do so in a very narrow range of ‘Y’ although likely for all ‘X’ in that region. (I plotted a plane equal to zero in both plots to see if there could be an intersection. Remove it in your plots if you do not want it.) I do not see the intersection even when setting a wider 'LineWidth' ffor the plot3 line. The minimum of the matrix intersections is

, not zero.

The surfaces might intersect if ‘Y’ (here ‘C’) is allowed to become negative for both surfaces. They do not appear to intersect with the present variable definitions.

I will help further as necessary.

.

Star Strider 2022-9-22

编辑：Star Strider 2022-9-22

在 MATLAB Online 中打开

It is relevant here. The simplest option would be to use the view function to rotate the plot to look at it on edge, for example:

view(90,0) % Z(Y)

view(0,0) % Z(X)

depending on what you want. Those can be used with any of the existing surf plots, or others you may want to create with these functions. (Another option is simply to use plot, however that may not be meaningful in this context.)

I have added both of the view options here —

vplc=0.16;

delta=0.1;

Ktau=0.045;

Kc=0.1;

K=0.0075;

Kp=0.15;

gamma=5.5;

Kb=0.4;

alpha0=delta*6.81e-6/(0.002);

alpha1=delta*2.27e-5/(0.002);

Ke=7;

Vs=0.002;

Ks=0.1;

Kf=0.18;

kplc=0.055;

ki=2;

tau_max=0.176;

Vss=0.044;

ct = 0:.1:2.5;

c = 0:.1:2.5;

A=(-(Vss.*c.^2)./(Ks.^2))+((Vs.*K.*gamma.^2.*ct.^2)./(Ks.^2))+alpha0+alpha1.*((Ke.^4)./(Ke.^4+(gamma.*ct).^4));

p=(vplc.*c.^2./(c.^2+kplc.^2))./ki;

h=(-(0.4.*A.*((Kc.^4).*(Kp.^2))./((p.^2.*c.^2.*gamma.*ct.*Kf))));

G1=alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4));

G2=((1-h)./tau_max).*c.^4;

Fc=(4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2);

Fct=((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2);

Fh=(gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4);

cdot=@(ct,c)(((gamma.*Kf.*(c.^4).*(p.^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2)).*(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4)))+((gamma.*Kf.*c.^4.*p.^2.*ct)./(Kb.*Kp.^2.*Ktau.^4)).*(((1-h)./tau_max).*c.^4);

ctdot=@(ct,c)(-(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4))).*((4.*gamma.*Kf).*((c.^3.*p.^2.*h.*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2)));

[Ct,C] = meshgrid(ct,c);

figure

surf(Ct,C,cdot(Ct,C))

hold on

surf(Ct,C,zeros(size(C)), 'FaceColor','r', 'FaceAlpha',0.5)

hold off

xlabel('Ct')

ylabel('C')

title('cdot')

figure

surf(Ct,C,ctdot(Ct,C))

hold on

surf(Ct,C,zeros(size(C)), 'FaceColor','r', 'FaceAlpha',0.5)

hold off

xlabel('Ct')

ylabel('C')

title('ctdot')

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',5)

hold off

xlabel('Ct')

ylabel('C')

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',5)

hold off

view(90,0)

xlabel('Ct')

ylabel('C')

zlabel('Z')

title('Z(C)')

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',5)

hold off

view(0,0)

xlabel('Ct')

ylabel('C')

zlabel('Z')

title('Z(Ct)')

figure

surf(Ct,C,cdot(Ct,C), cat(3,ones(size(Ct)),ones(size(C)),zeros(size(Ct))), 'DisplayName','cdot')

hold on

surf(C,Ct,ctdot(Ct,C), cat(3,ones(size(Ct)),zeros(size(Ct)),ones(size(C))), 'DisplayName','ctdot')

hold off

view(0,90)

xlabel('Ct')

ylabel('C')

zlabel('Z')

title('Surface C(Ct)')

legend('Location','best')

figure

contour(Ct,C,cdot(Ct,C),20,'m', 'DisplayName','cdot')

hold on

contour(C,Ct,ctdot(Ct,C),20,'c', 'DisplayName','ctdot')

hold off

% view(0,90)

xlabel('Ct')

ylabel('C')

zlabel('Z')

title('Contour C(Ct)')

legend('Location','best')

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',5)

hold off

xlabel('Ct')

ylabel('C')

ylim([0 0.2])

zlim([-1 1])

title('Zoomed')

Mtx = cdot(Ct,C)-ctdot(Ct,C);

[minMtx,idx] = min(Mtx(:))

minMtx = 1.8648e-05

idx = 651

[row,col] = ind2sub(size(Mtx), idx)

row = 1

col = 26

idx = find(Mtx == min(Mtx(:)))

idx = 651

[row,col] = ind2sub(size(Mtx), idx)

row = 1

col = 26

.

Torsten 2022-9-22

编辑：Torsten 2022-9-22

在 MATLAB Online 中打开

vplc=0.16;

delta=0.1;

Ktau=0.045;

Kc=0.1;

K=0.0075;

Kp=0.15;

gamma=5.5;

Kb=0.4;

alpha0=delta*6.81e-6/(0.002);

alpha1=delta*2.27e-5/(0.002);

Ke=7;

Vs=0.002;

Ks=0.1;

Kf=0.18;

kplc=0.055;

ki=2;

tau_max=0.176;

Vss=0.044;

A=@(ct,c) (-(Vss.*c.^2)./(Ks.^2))+((Vs.*K.*gamma.^2.*ct.^2)./(Ks.^2))+alpha0+alpha1.*((Ke.^4)./(Ke.^4+(gamma.*ct).^4));

p=@(ct,c)(vplc.*c.^2./(c.^2+kplc.^2))./ki;

h=@(ct,c)(-(0.4.*A(ct,c).*((Kc.^4).*(Kp.^2))./((p(ct,c).^2.*c.^2.*gamma.*ct.*Kf))));

G1=@(ct,c)alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4));

G2=@(ct,c)((1-h)./tau_max).*c.^4;

Fc=@(ct,c)(4.*gamma.*Kf).*((c.^3.*p(ct,c).^2.*h(ct,c).*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2);

Fct=@(ct,c)((gamma.*Kf.*(c.^4).*(p(ct,c).^2).*h)./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2);

Fh=@(ct,c)(gamma.*Kf.*c.^4.*p(ct,c).^2.*ct)./(Kb.*Kp.^2.*Ktau.^4);

cdot=@(ct,c)(((gamma.*Kf.*(c.^4).*(p(ct,c).^2).*h(ct,c))./(Kb.*Kp.^2.*Ktau.^4))+((Vs.*K.*gamma.^2)./(Ks.^2))-((4.*gamma.^4.*ct.^3.*alpha1.*Ke.^4)./(Ke.^4+(gamma.*ct).^4).^2)).*(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4)))+((gamma.*Kf.*c.^4.*p(ct,c).^2.*ct)./(Kb.*Kp.^2.*Ktau.^4)).*(((1-h(ct,c))./tau_max).*c.^4);

ctdot=@(ct,c)(-(alpha0+(alpha1.*Ke.^4./((gamma.*ct).^4+Ke.^4))).*((4.*gamma.*Kf).*((c.^3.*p(ct,c).^2.*h(ct,c).*ct)./(Kb.*Kp.^2.*Ktau.^4))-(2.*Vss.*c./Ks.^2)));

figure(1)

fimplicit(@(x,y)cdot(x,y),[-2.5 2.5 -2.5 2.5])

figure(2)

fimplicit(@(x,y)ctdot(x,y),[-2.5 2.5 -2.5 2.5])

Torsten 2022-9-23

At least cdot(ct,c) = 0 is empty for ct >=0.

ctdot(ct,c) = 0 gives two implicit curves symmetric to the ct-axis.

Star Strider 2022-9-23

Originally, the objective was to determine the intersection:

figure

surf(Ct,C,cdot(Ct,C)-ctdot(Ct,C))

hold on

contour3(C,Ct,cdot(Ct,C)-ctdot(Ct,C), [0 0], '-r', 'LineWidth',2)

I am not certain where we are at this point.

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