Using matrices to create 3D rendering

Hello,

I am currently working on a project for my Multivariable calculus class, where we have to turn a set of data into a 3D model.

I currently have mapped out the US and put in the data points for each state, then turned that into a matrix. However, once the matrix is in my code I get the error messages

Error using griddedInterpolant

The grid vectors do not define a grid of points that match the given values.

Error in interp2>makegriddedinterp (line 228)

F = griddedInterpolant(varargin{:});

Error in interp2 (line 128)

F = makegriddedinterp({X, Y}, V, method,extrap);

Error in practice (line 36)

zc = interp2(x,y,z,xi,yi,'cubic');

This is the code I currently have

x=0:50;
y=0:50;
z = [0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
   ;0	0	0	24609	24609	24609	24609	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
;0	0	0	24609	24609	24609	24609	24609	27130	31065	31065	31065	31065	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	31925	31295	0	0
;0	0	0	24609	24609	24609	24609	24609	27130	31065	31065	31065	31065	31065	31065	31065	0	0	0	0	0	31915	31915	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	31295	31295	31295	0
;0	0	0	27321	27321	27321	27321	27321	27321	31065	31065	31065	31065	31065	31065	31065	0	0	0	0	0	31915	31915	31915	31915	31915	0	0	0	0	0	0	0	0	0	0	0	0	0	31295	31295	31295	0
;0	0	27321	27321	27321	27321	27321	27130	27130	31065	31065	31065	31065	31065	31065	31065	0	0	0	0	0	31915	31915	31915	31915	0	0	0	0	0	0	0	0	0	0	0	0	0	28662	36367	31295	0	0
;0	0	27321	27321	27321	27321	27321	27130	27130	27130	31065	31065	31065	31065	31065	31065	31362	31362	31362	31362	31362	31915	31915	31915	30059	30059	30059	0	0	27532	27532	0	0	0	0	0	30346	30346	28662	36367	0	0	0
;0	0	22744	27321	27321	27321	27321	27130	27130	27130	27130	25378	25378	25378	25378	25378	31362	31362	31362	31362	31362	31915	31915	31915	30059	30059	30059	30059	0	27532	27532	0	0	0	30346	30346	30346	30346	31563	31563	0	0	0
;0	22744	22744	22744	24128	24128	24128	27130	27130	27130	27130	25378	25378	25378	25378	25378	31362	31362	31362	31362	31362	31915	31915	31915	31915	30059	30059	30059	0	27532	27532	27532	0	30346	30346	30346	30346	30346	31217	35494	0	0	0
;0	22744	22744	22744	24128	24128	24128	24128	19975	19975	19975	25378	25378	25378	25378	25378	26585	26585	26585	26585	26585	29801	29801	29801	29801	29801	30059	30059	0	27532	27532	27532	30351	35759	35759	35759	35759	29878	0	0	0	0	0
;0	22744	22744	22744	24128	24128	24128	24128	19975	19975	19975	25378	25378	25378	25378	25378	26585	26585	26585	26585	26585	26585	29801	29801	29801	29801	29271	29271	29562	29562	30351	30351	30351	35759	35759	35759	35759	29878	0	0	0	0	0
;0	0	22744	22744	24128	24128	24128	24128	19975	19975	19975	19975	26520	26520	26520	26520	26520	26585	26585	26585	26585	26585	29801	29801	29801	29271	29271	29271	29562	29562	30351	30351	30351	27708	27455	27455	27455	33838	0	0	0	0	0
;0	0	22744	22744	22744	24128	24128	24128	19975	19975	19975	19975	26520	26520	26520	26520	26520	28776	28776	28776	28776	28776	28776	27532	27532	27532	29271	29271	29562	29562	30351	30351	27708	27708	27708	29296	27455	0	0	0	0	0	0
;0	0	22744	22744	22744	22744	24128	24128	19975	19975	19975	19975	26520	26520	26520	26520	26520	28776	28776	28776	28776	28776	28776	27532	27532	27532	29271	29271	29562	29562	28910	28910	27708	27708	29296	29296	29296	29296	0	0	0	0	0
;0	0	0	22744	22744	22744	24128	23447	23447	23447	23447	21373	21373	21373	21373	21373	21373	28776	28776	28776	28776	28776	28776	27532	27532	27532	27532	29271	28910	28910	28910	28910	28910	25562	25562	25562	25562	25562	0	0	0	0	0
;0	0	0	0	22744	22744	22744	23447	23447	23447	23447	21373	21373	21373	21373	21373	25856	25856	25856	25856	25856	25856	25856	27532	27532	27532	27532	26981	26981	26981	26981	26981	26981	25562	25562	25562	25562	25562	0	0	0	0	0
;0	0	0	0	22744	22744	22744	23447	23447	23447	23447	21373	21373	21373	21373	21373	26292	26292	26292	25856	25856	25856	25856	26859	26859	26859	26859	26981	26981	26981	26981	27657	30123	30123	30123	30123	25562	0	0	0	0	0	0
;0	0	0	0	22744	22744	23447	23447	23447	23447	23447	21373	21373	21373	21373	21373	26292	26292	26292	25856	25856	25856	25856	26859	26859	26859	29384	29384	31275	31275	31275	27657	27657	30123	30123	30123	0	0	0	0	0	0	0
;0	0	0	0	0	0	0	23447	23447	23447	23447	21373	21373	21373	21373	21373	26292	26292	26292	26292	26292	26292	26292	26292	26859	26859	29384	29384	31275	31275	31275	27657	27657	27657	30123	30123	0	0	0	0	0	0	0
;0	0	0	0	0	0	0	0	0	23447	23447	21373	21373	21373	21373	21373	26292	26292	26292	26292	26292	26292	26292	26292	27138	27138	29384	29384	31275	31275	31275	27657	27657	27657	27657	0	0	0	0	0	0	0	0
;0	0	0	0	0	0	0	0	0	0	0	0	0	26292	26292	26292	26292	26292	26292	26292	26292	26292	26292	26292	27138	27138	29384	29384	31275	31275	31275	27657	27657	27657	24461	0	0	0	0	0	0	0	0
;0	0	0	0	26008	26008	26008	26008	0	0	0	0	0	0	26292	26292	26292	26292	26292	26292	26292	26292	26292	26292	27138	27138	27138	27138	31275	24461	24461	24461	24461	24461	24461	0	0	0	0	0	0	0	0
;0	0	0	26008	26008	26008	26008	26008	26008	0	0	0	0	0	0	0	0	26292	26292	26292	26292	26292	26292	26292	27138	27138	27138	27138	0	0	0	0	0	24461	24461	24461	0	0	0	0	0	0	0
;0	0	0	0	26008	26008	26008	26008	26008	0	0	26092	0	26092	0	0	0	0	26292	26292	26292	26292	0	0	0	0	0	0	0	0	0	0	0	0	24461	24461	0	0	0	0	0	0	0
;0	0	0	26008	26008	26008	26008	26008	26008	0	0	0	0	0	26092	26092	0	0	0	26292	26292	0	0	0	0	0	0	0	0	0	0	0	0	0	0	24461	24461	0	0	0	0	0	0
;0	0	0	0	26008	26008	26008	26008	26008	0	0	0	0	0	26902	26092	0	0	0	26292	26292	0	0	0	0	0	0	0	0	0	0	0	0	0	0	24461	24461	0	0	0	0	0	0
;0	0	0	0	26008	0	0	0	0	26008	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
;0	0	0	0	26008	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
;0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
];
xi=0:0.5:50;
yi=0:0.5:50;
[xi,yi] = meshgrid(xi,yi);
zc = interp2(x,y,z,xi,yi,'cubic');
mesh(xi,yi,zc)

I have just started learning MATLAB this year, so all the help I can get would be appreciated.

Thank you

Answer 1

[Walter Roberson]

Your z is 29 x 43. When you call interp2(x, y, z, ...) then length(x) must match size(z,2) and length(y) must match size(z,1) so length(x) must be 43 and length(y) must be 29. But you define both x and y as 0:50 which is length(51).

If you have 29 y values that are intended to span from 0 to 50, then use linspace(0, 50, 29) to create the coordinates.

[Sylvia Costa]

Hello,

I have changed my code as to what you have reccomended,

x=0:42;
y=0:28;

and

xi=0:0.1:42;
yi=0:0.1:28;

which allows the program to run, so thank you!

Also had to reverse the data, as it came out as a mirrored version from my original program.

The simmulation also seems to show some negative values on the graph (despite not putting negative values in the matrix), would there be a way to fix that or is that just natural?

(I inserted a photo of the graph below)

[Walter Roberson]

You have some steep edges. cubic interpolation near them results in some values near -4866, and spline interpolation results in some values near -11827, and makima interpolation results in some values near -2682. None of those interpolation methods expect sudden flatness: they all expect local curvature.

It works the other way too: those interpolations also produce overshoot on the peaks.

You can use 'linear' as the interpolation and it will not give any negative values.... but the result will also look pretty blocky.

You might want to try

zt = z;
zt(zt == 0) = nan;
zc = interp2(x, y, z, xi, yi, 'cubic');
zc(isnan(zc)) = 0;
mesh(xi, yi, zc)

This would treat the non-zero region as being separate from the region of 0. You would not get any edge interpolation down to zero, and so no undershoot to negatives.