The ? "'r " "'k " are " virtual displacements ", by definition they are infinitesimal changes in the configuration of the system consistent with the constraint forces acting on the system " at an instant of time ", i . e . in such a way that the constraint forces maintain the constrained motion.
22.
The first term in D'Alembert's principle above is the virtual work done by the non-constraint forces "'N " "'k " along the virtual displacements " ? " "'r " "'k ", and can without loss of generality be converted into the generalized analogues by the definition of generalized forces
23.
Unlike regular displacement which arises from differentiating with respect to time parameter " t " along the path of the motion ( thus pointing in the direction of the motion ), virtual displacement arises from differentiating with respect to the parameter " ? " enumerating paths of the motion varied in a manner consistent with the constraints ( thus pointing at a fixed time in the direction tangent to the constraining manifold ).
24.
"' Parallax mapping "'( also called "'offset mapping "'or "'virtual displacement mapping "') is an enhancement of the bump mapping and normal mapping techniques implemented by displacing the texture coordinates at a point on the rendered polygon by a function of the view angle in tangent space ( the angle relative to the surface normal ) and the value of the height map at that point.
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