We consider the problem of constructing a C1 piecewise quadratic interpolant, Q, to positional and gradient data defined at the vertices of a tessellation of n-simplices in IRn . The key to the interpolation scheme is to appropriately subdivide each simplex to ensure that certain necessary geometric constraints are satisfied by the subdivision points. We establish these constraints using the Bernstein							
						
							
					 															
					Tatyana Sorokina, Andrew J. Worsey