How to stretch a texture like a bed sheet on a mesh?

You need to specify for each point of the mesh (right), a u,v coordinate of the texture (left).

The UV_MAPPING mode allows to do it easily.

Start by choosing the UV_MAPPING mode and select the texture you want to apply.

Click all the points around the area you want to cover, clockwise.

In case of a bad click, press the Del key to erase the last point.

Go around and click on the very first point again, to close the perimeter.

A line 1 16 then appears, showing the number of points in the perimeter.

Map some points of the mesh to the texture.

To do this, click on a point in the mesh (clic 1), then click on the texture where you want it to match (clic 2).

You don't need to do this for all the points, just 3 points minimum. Choose points that are well apart, for example the point at the very top, the point at the very right, and the point at the very bottom.

The points you have selected appear in white, the others are calculated and appear in gray. If you want to deselect a point, click on the button C at the bottom.

If you move a point of the texture left, you see that the texture moves automatically on the whole mesh.

If you have a large mesh, you can create several perimeters. Simply click on NEW to start another one. Click on ZERO to delete one.

If your mesh has an inner side you can check the box recto/verso and the texture will be applied to the other side too.

For a more precise positioning, you can enlarge the texture: right-click on the texture to bring up a ZOOM menu.

TEXTURE_UV mode offers a more primitive way to change the UV of a polygon.

First click on a pyramid of a polygon.

Then click on one of the cubes that indicates a point on the polygon.

You see at the top the U,V values for that point that you can change.

By clicking on the RESET UV button, all the UVs of the polygon are remapped to a 1 x 1 square.