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Separation by Rip shortcut V https://docs.blender.org/manual/en/latest/modeling/meshes/editing/vertices.html#rip-region Rip creates a “hole” in the mesh by making a copy of selected vertices and edges … , still linked to the neighboring non-selected vertices, so that the new edges are borders of the faces on one side, and the old ones, borders of the faces on the other side of the rip. …

2.8x Join all objects (Ctrl+J), in edit mode (Tab) select all vertices except top rim and delete them (X) enable addon TinyCAD and with all vertices selected press (W) > Tiny CAD > XALL Intersect Selected …

Under Overlay Properties in 3D view editor enable Statistics to see from how many vertices your "foam" consists. Add Particle system with the same amount of particles as vertices. … Source > Vertices (disable Random Order). Physics Type > None. Default size 0.1 Size 0.01 …

I don't know what is final purpose of your curved shape, but you can consider to try ... Curve object with Shape > Resolution 8 Geometry > Bevel > Depth to something you like Geometry > Bevel > Resol …

Check if your vertex indices match on both objects. To display them enable as Overlay > Developer > Indices

Knife Project Create your shape (smile) with origin in center of ball, vertices move above ball surface With smile object selected you can rotate around a ball as you like To get aligned view for projection …

Scenario 1 Make one copy of Array real to be able snap extruded vertex and add Array modifier again. Like: Duplicate Array modifier (and disable one of them) Set Count 2 and Apply Enable Snap > Ver …

Add Circle 8 sides (Rotate R 22.5, Extrude E, Scale S, Copy Shift+D, move and scale down, select 4 vertices press F ... …

Snap to Vertex should do the job ... it looks a bit jumpy, but if you switch to edit mode, move all vertices "close" to desired location (not exactly) and move it again from this close position it snaps … If you want to avoid jumps, you can do first step (move vertices closer) without snapping enabled and enable snapping for final move by pressing shortcut Ctrl. …

All shaded as Smooth ... First and third AutoSmooth disabled ... second and fourth enabled ... ... the third would look same as the first, both are shaded smoot the only difference is a topology - to …

In general - each vertex is usually used to store only one color. In your example one vertex consists from three colors. So the only one way to interpolate is to set average color.

I don't think there is a way. In deep history of 2.49, there was a great script of Pildanovak (Fracture) and one of the feature was image used to split object onto a parts according image lines. Curre …

The Hooks (Empties.001 and Empties.002) control curve point's locations and rotations (Tilt), but Curve object (container storing curve data) itself isn't rotating (location and rotation is still the …

Note: Blender has also an operator, you can search Make Planar Faces, that can recalculate them into flat faces, but in cost of distortions of all selected vertices. …

The reason why zoom in/out affects those "fading" vertices is because blender is displaying partially wire inside of a mesh to improve viewport experience for vertices that would be quickly hidden in sharp … This "inside" view is constant for viewport, but actual distances of vertices in viewport are changing. …