Add [Constraint]

This tool sets the constrained attribute to true on the selected vertices. If edges or faces are selected, the vertices in the selections will be set to Constrained. Constrained vertices will snap to and stay on the surface of reference meshes while in Constrained to Mesh mode


Remove [Constraint]  

This tool sets the constrained attribute to false on vertices. If edges or faces are selected, the vertices in the selections will be set to unconstrained. Unconstrained vertices will not snap to and stay on the surface of reference meshes regardless of mode.  


Snap [Vertices to Reference Mesh ]

This command snaps all constrained vertices down to the reference mesh. Use this command when you have been working with Constrained to Mesh mode turned off. Turning Constrained to Mesh mode on with not automatically snap constrained vertices down to the mesh.  

A proxy mesh created without constraints, left, setting the vertices set to Constrained, center, the constraints updated using Snap Vertices to Reference Mesh, right

Draw

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