Even if the surf graph is converted to emf, the image quality is not good.
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Richard Quist on 17 Dec 2021
When generating vector output (such as EMF or PDF files, or when copying EMF or PDF to the clipboard) MATLAB uses a heuristic to determine how to export the content. In your specific case I would guess that the heuristic has chosen to embed the surface plot as an image. You can override the heuristic by doing one of the following:
% Assuming fig is the handle to the figure you are trying to save...
% set the figure's Renderer property to 'painters' before using File->Save As:
set(fig, 'Renderer', 'painters');
% In R2020a and later, use the exportgraphics command and specify the 'ContentType' as 'vector':
exportgraphics(fig, 'output.emf', 'ContentType', 'vector');
% use the print command and include the '-painters' option:
print(fig, 'output.emf', '-painters');