By decomposed polygons into convex subsets, and matched the convex subsets, new method of 3D objects construction from slice is proposed. The middle slices can be interpolated by generalized morphologic transformation. The morphology operators have special advantages if used to process two objects construction that have different topologic structure (including holey object and fork object). Experiments show that this method has a smoothness boundary of construction, high precision, lower cost of calculation and no need user alternation. It is a practicably method for 3D object construction and it can be widely used in medicine engineering.