The problem of minimum translational distance(MTD for short) of convex polyhedra is always an active subfield of computer graphics.The current distance algorithms are deficient in such requirements as stability

realizability

accuracy and efficiency more or less.In order to overcome these limitations

the generalized separable plane is introduced based on the definition of MTD and a new algorithm of the MTD problem using nonlinear programming is presented in the paper.This algorithm is carried out as follow.Firstly

the MTD measure is determined by defining the optimal generalized separable plane-pair.Secondly

the problem of searching the optimal plane-pair is equivalent with nonlinear programming problem under some transforms.Finally

a nonlinear optimization software is used to solve the equivalent model

and therefore MTD measure is determined by the solution.The results show that the proposed algorithm performs linearly with the size of model and over the other algorithms in most of the tests.Besides

it can provide both an accurate measure and the witness vector in a few iterations

which are gently linear with the vertex number.In addition

the implementation is simple and reliable

because only the information of vertex is required and the cycle can be avoided.So

it is a fast and efficient distance algorithm.