bilinear interpolation of a 3D graph

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Hi,

I am trying to do an interpolation between the lines for find the ball velcoity.

Eg, for a given and interpolated x and y, how do i find the z?

The data is persented in colombs for x and y at a given value, z. for which there are 10 colombs for x and y.

The z values for each a generated using the 'ones' function.

I appreciate that i have "hard loaded" in the data. but this is for a university project and have little experience with coding in general. but some understanding of how to interpolate in a table would be greatly appreciated

% Figure properties

figure1 = figure('Color',[1 1 1]);

grid on

hold on

title('Golf Ball Aeroynamics');

xlabel('Spin Rate, [R.P.M]');

ylabel('Drag Coefficent, C_D');

zlabel('Ball Velocity [m/s]');

% Load variables from file

u14ms = [10.0181584038799,0.497489996266905;1048.57744598596,0.465912907853750;1866.50469521945,0.368711068058607;2815.18206925372,0.407423263914084;3741.62610823528,0.410999691385817;4679.15315568930,0.520915473810196;6258.19729101443,0.547523261903284];

u21p9ms = [-0.159115527488822,0.356936519024359;1016.16683700188,0.290223662227460;1808.11541645867,0.299366073247347;2816.67530728093,0.351016197436142;3738.14392611444,0.367539121000365;4676.55222879764,0.444165487142678;6251.28188539660,0.458752709116708];

u30p5ms = [-2.49076998801287,0.270014766270655;970.525159924220,0.264338013836057;1859.98095859237,0.265145219146669;2803.92770559781,0.307556851016285;3744.09851873935,0.317604384594470;4669.24515418907,0.370190230481464;6257.62814701226,0.394022676585451];

u39ms = [6.92152544580862,0.264465306258049;970.525159924220,0.264338013836057;1860.00543790429,0.264220513138833;2823.26636201580,0.277039104826533;3740.15122969201,0.291713228357884;4679.63662209975,0.327652530155452;6253.99908901989,0.356110342247008];

u47p2ms = [-2.34389411648379,0.264466530223645;965.867970831152,0.265263331826690;1860.00543790429,0.264220513138833;2823.24188270388,0.277963810834368;3744.97977396853,0.284314968312405;4666.20359968282,0.310084951954979;6250.17419653215,0.325595655971247];

u55p5 = [-2.17253893303321,0.257993588168799;970.525159924220,0.264338013836057;1860.00543790429,0.264220513138833;2818.63365223466,0.277039716809331;3740.37154349930,0.283390874287368;4675.73829167625,0.299911961903196;6246.00659367752,0.308026853805178];

u64ms = [2.50912947195603,0.256143564170330;965.892450143074,0.264338625818855;1859.98095859237,0.265145219146669;2828.19282354001,0.265942020749714;3740.54289868275,0.276917932232522;4676.03204341930,0.288815489809175;6255.54128567095,0.297853863753395];

u72p8ms = [2.60704671964208,0.252444740138990;965.892450143074,0.264338625818855;1864.63814768544,0.264219901156035;2823.58459307078,0.265017926724677;3740.59185730659,0.275068520216852;4676.25235722660,0.280493135738659;6260.39430925938,0.289530897700081];

u81p1ms = [2.60704671964208,0.252444740138990;970.525159924220,0.264338013836057;1860.00543790429,0.264220513138833;2823.56011375886,0.265942632732512;3740.64081593044,0.273219108201181;4676.32579516236,0.277719017715153;6255.90847534977,0.283983273635868];

u89ms = [2.75392259117115,0.246896504091979;970.525159924220,0.264338013836057;1860.00543790429,0.264220513138833;2828.19282354001,0.265942020749714;3740.73873317812,0.269520284169841;4685.71361128426,0.273094263710382;6260.68806100244,0.278434425606060];

a = ones(1,7)'*14;

b = ones(1,7)'*21.9;

c = ones(1,7)'*30.5;

d = ones(1,7)'*39;

e = ones(1,7)'*47.2;

f = ones(1,7)'*55.5;

g = ones(1,7)'*64;

h = ones(1,7)'*72.8;

i = ones(1,7)'*81.1;

j = ones(1,7)'*89;

hold on

% Plots

x = ([u14ms(:,1),u21p9ms(:,1),u30p5ms(:,1),u39ms(:,1),u47p2ms(:,1),u55p5(:,1),u64ms(:,1),u72p8ms(:,1),u81p1ms(:,1),u89ms(:,1)]); % Spin

y = ([u14ms(:,2),u21p9ms(:,2),u30p5ms(:,2),u39ms(:,2),u47p2ms(:,2),u55p5(:,2),u64ms(:,2),u72p8ms(:,2),u81p1ms(:,2),u89ms(:,2)]); % Lift Coeffcient

z = ([a,b,c,d,e,f,g,h,i,j]); % Velocity

surf(x,y,z);

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Answer 1

Star Strider on 5 Jan 2022

Edited: Star Strider on 5 Jan 2022

Open in MATLAB Online

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Missing data, so I can’t run the code to demonstrate the approach.

Since the data appear to be gridded (not scattered), the griddedInterpolant function is likely the most appropriate approach. For any ‘x’ and ‘y’ within the grid, it is the possible to return ‘z’.

If the data are initially scattered, use the scatteredInterpolant function instead. For any ‘x’ and ‘y’ within the grid, it is the possible to return ‘z’.

EDIT — (5 Jan 2022 at 13:26)

Having the data and the rest of the relevant code makes this possible, however the interpolation functions are having problems with the data. I opted for scatteredInterpolant here because the data appear to be such.

I took two approaches — the first with the original data and interpolation, and the second with an interpolated mesh and the same interpolation. The results are not as good as I would have liked them to be, since scatteredInterpolant usually gives better results.

Neverhteless, this is an appropriate way to interpolate the data, although there are similar approaches that could be worth experimenting with (although I doubt they would give different results).