Finding corresponding values from a 3d Surface

Hello there,

I am having trouble with finding values in a 3D-Surface I have plotted. I guess the solution to this is relatively simple, but I just don't get what to do.

I have created a 3-D surface according to 3 corresponding matrixs, as shown in the code below. This worked fairly well and I do get the exact surface I was looking for (figure 1). Next I plotted the point of my values ang_vel, ang_flex, and Fext(end) (which is 11.5295). Now here is my problem: Corresponding to this point, I would like to know, which y-value it has, when it touches the 3D-surface.

clear
clc
close all

%%EINLESEN DER KRAFTDATEN
Pfad_Programm=cd;
[num, txt]=xlsread('Participant_1_1_NE_alle Trials_MuscleOutput.xlsx',1,'B8:E2015');
daten=xlsread('Participant_1_1_NE_alle Trials_MuscleOutput.xlsx',1); 


Fext=daten(8:end,3)*100;    %_deltoideus_anterior_part1 in %
ang_vel=60;                 %Winkelgeschwindigkeit während des Versuchs
angle_flex=60;              %Ellenbogenflexionswinkel während des Versuchs

torque_male_flex=[56.4 62.9 63.0 60.3 56.4;41.2 43.9 44.7 42.3 35.7;36.1 38.0 38.7 36.8 27.9;32.1 33.9 33.1 29.2 18.7;0 30.0 27.9 21.5 12.0;0 0 25.7 18.4 8.4];
torque_female_flex=[26.2 30.4 32.0 32.4 30.4;20.4 20.8 21.4 20.8 18.3;18.9 19.4 19.9 19.0 15.2;15.9 18.2 17.9 15.6 11.3;0 14.4 15.8 13.2 8.1;0 0 14.1 13.2 8.7];

vel=[0 0 0 0 0;60 60 60 60 60;120 120 120 120 120;180 180 180 180 180;240 240 240 240 240;300 300 300 300 300];
vel2=[300 300 300 300 300;240 240 240 240 240;180 180 180 180 180;120 120 120 120 120;60 60 60 60 60;0 0 0 0 0;];
ang2=[15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110];

figure (1)
surf(ang2,vel2,torque_male_flex);
title('tva surface - male elbow flexion');
xlabel('velocity')
ylabel('angle')
zlabel('torque')
hold on
plot3(angle_flex,ang_vel,Fext(end),'o');

Thanks a lot for helping!

Best regards,

Christian

Answer 1

[Prabhan Purwar]

Hello,

Following code may help:

clc
close all
clear
%Z=11.5295;
ang_vel=60;                 %Winkelgeschwindigkeit während des Versuchs
angle_flex=60;              %Ellenbogenflexionswinkel während des Versuchs
X=angle_flex;
Y=ang_vel;
Z=40;                       %Z value to intersect 
torque_male_flex=[56.4 62.9 63.0 60.3 56.4;41.2 43.9 44.7 42.3 35.7;36.1 38.0 38.7 36.8 27.9;32.1 33.9 33.1 29.2 18.7;0 30.0 27.9 21.5 12.0;0 0 25.7 18.4 8.4];
torque_female_flex=[26.2 30.4 32.0 32.4 30.4;20.4 20.8 21.4 20.8 18.3;18.9 19.4 19.9 19.0 15.2;15.9 18.2 17.9 15.6 11.3;0 14.4 15.8 13.2 8.1;0 0 14.1 13.2 8.7];
vel=[0 0 0 0 0;60 60 60 60 60;120 120 120 120 120;180 180 180 180 180;240 240 240 240 240;300 300 300 300 300];
vel2=[300 300 300 300 300;240 240 240 240 240;180 180 180 180 180;120 120 120 120 120;60 60 60 60 60;0 0 0 0 0;];
ang2=[15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110];
f=createFit(ang2, vel2, torque_male_flex);
title('tva surface - male elbow flexion');
xlabel('velocity')
ylabel('angle')
zlabel('torque')
hold on
plot3(X,Y,Z,'o','MarkerSize',10); %given point
plot3(X,-50:300,Z,'o','MarkerSize',1); %Normal to point
for i=0:0.01:300
val=f(angle_flex,i);
if (round(val,2)==Z)disp('intersection');
    in=i;
end
end
plot3(angle_flex,in,Z,'o','MarkerSize',10) %Intersection point

Kindly include following function created using surface fitting.

function [fitresult, gof] = createFit(ang2, vel2, torque_male_flex)
%CREATEFIT(ANG2,VEL2,TORQUE_MALE_FLEX)
%  Create a fit.
%
%  Data for 'untitled fit 1' fit:
%      X Input : ang2
%      Y Input : vel2
%      Z Output: torque_male_flex
%  Output:
%      fitresult : a fit object representing the fit.
%      gof : structure with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.

%  Auto-generated by MATLAB on 06-Mar-2020 12:04:25


%% Fit: 'untitled fit 1'.
[xData, yData, zData] = prepareSurfaceData( ang2, vel2, torque_male_flex );

% Set up fittype and options.
ft = 'thinplateinterp';

% Fit model to data.
[fitresult, gof] = fit( [xData, yData], zData, ft, 'Normalize', 'on' );

% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, [xData, yData], zData );
legend( h, 'untitled fit 1', 'torque_male_flex vs. ang2, vel2', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'ang2', 'Interpreter', 'none' );
ylabel( 'vel2', 'Interpreter', 'none' );
zlabel( 'torque_male_flex', 'Interpreter', 'none' );
grid on

Output:

Kindly set

• X,Y and Z values
• Value of precision in round(val,2) to get the precise coordinates for the point of intersection.

Following links may help:

• https://in.mathworks.com/matlabcentral/fileexchange/33073-triangle-ray-intersection (Alternate Method)
• https://in.mathworks.com/help/curvefit/surface-fitting.html (Surface Fitting)
• https://in.mathworks.com/help/curvefit/sfit.html (Sfit)
• https://in.mathworks.com/help/matlab/ref/round.html (Round)

[Christian Gärtner]

Hi Prabhan Purwar,

first, thanks a lot for your answer it is deeply appreciated and already is helping me a lot.

I actually want to find another intersecting point. So you can see which point I am talking about, I modified your code, so the normal to the intersection point is pointing into the right direction.

I also switched the axis "angle" with "velocity", because this is the way I would like it to be.

Still I somehow can't get the intersection point in the direction of the normal, as in the code below, because I am unsure how to change your code. Could you please help me with that? Thanks a lot!

clc
close all
clear
%Z=11.5295;
ang_vel=60;                 %Winkelgeschwindigkeit während des Versuchs
angle_flex=60;              %Ellenbogenflexionswinkel während des Versuchs
X=angle_flex;
Y=ang_vel;
Z=20;                       %Z value to intersect 
torque_male_flex=[56.4 62.9 63.0 60.3 56.4;41.2 43.9 44.7 42.3 35.7;36.1 38.0 38.7 36.8 27.9;32.1 33.9 33.1 29.2 18.7;0 30.0 27.9 21.5 12.0;0 0 25.7 18.4 8.4];
torque_female_flex=[26.2 30.4 32.0 32.4 30.4;20.4 20.8 21.4 20.8 18.3;18.9 19.4 19.9 19.0 15.2;15.9 18.2 17.9 15.6 11.3;0 14.4 15.8 13.2 8.1;0 0 14.1 13.2 8.7];
vel2=[0 0 0 0 0;60 60 60 60 60;120 120 120 120 120;180 180 180 180 180;240 240 240 240 240;300 300 300 300 300];
%vel2=[300 300 300 300 300;240 240 240 240 240;180 180 180 180 180;120 120 120 120 120;60 60 60 60 60;0 0 0 0 0;];
ang2=[15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110;15 40 65 90 110];

%f=createFit(ang2, vel2, torque_male_flex);
f=createFit(vel2,ang2 ,torque_male_flex);

title('tva surface - male elbow flexion');
% xlabel('angle')
% ylabel('velocity')
xlabel('velocity')
ylabel('angle')
zlabel('torque')
hold on
plot3(X,Y,Z,'o','MarkerSize',10); %given point
%plot3(X,-50:300,Z,'o','MarkerSize',1); %Normal to point
plot3(X,Y,0:100,'o','MarkerSize',1); %Normal to point --> this is the direction I would like to find the intersection point, so in this Example I am looking for [60;60;?]

for i=0:0.01:100
%val=f(angle_flex,i);
val=f(angle_flex,i);
if (round(val,2)==Z)disp('intersection');
    in=i;
end
end
%plot3(angle_flex,in,Z,'o','MarkerSize',10) %Intersection point
plot3(angle_flex,ang_vel,in,'o','MarkerSize',10) %Intersection point


% function [fitresult, gof] = createFit(ang2, vel2, torque_male_flex)
function [fitresult, gof] = createFit(vel2, ang2, torque_male_flex)
%CREATEFIT(ANG2,VEL2,TORQUE_MALE_FLEX)
%  Create a fit.
%
%  Data for 'untitled fit 1' fit:
%      X Input : ang2
%      Y Input : vel2
%      Z Output: torque_male_flex
%  Output:
%      fitresult : a fit object representing the fit.
%      gof : structure with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.
%  Auto-generated by MATLAB on 06-Mar-2020 12:04:25
%% Fit: 'untitled fit 1'.
[xData, yData, zData] = prepareSurfaceData( vel2, ang2, torque_male_flex );
% Set up fittype and options.
ft = 'thinplateinterp';
% Fit model to data.
[fitresult, gof] = fit( [xData, yData], zData, ft, 'Normalize', 'on' );
% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, [xData, yData], zData );
%legend( h, 'untitled fit 1', 'torque_male_flex vs. ang2, vel2', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'ang2', 'Interpreter', 'none' );
ylabel( 'vel2', 'Interpreter', 'none' );
zlabel( 'torque_male_flex', 'Interpreter', 'none' );
grid on
end