This paper shows that an adequate use of vector fields can solve most inconsistencies related to texture mapping that appear in current animation and rendering systems based on implicit objects. The method used is based on the concept of a virtual skin. A skin with its own texture mapping is spread over an implicit object and is constrained to stick to the deformation of the implicit object. A vector field is used to compute the relationship between the motion of the skin and the deformation of the object. Visual and implementation issues are discussed with respect to typical applications of implicit objects in computer graphics.