Question on Local Max-Entropy shape functions and their derivatives at corner particle

I am using Smoothed Particle Hydrodynamics (SPH) with dual particle
approach (please look at the figures in the .ppt file I have attached) to simulate High
Velocity impact phenomena.

The shape function values being 1 at the corner particle and zero at the other particles makes the Jacobian to evaluate the gradients of shape function inconvenient (the jacobian becomes a zero matrix). 

The slides explain my problem more clearly.

Kindly go through them and help me.