In the field of computer visualization

three-dimensional object is usually rendered by triangle meshes

but too many triangle meshes can affect the result of real-time operation

such as shifting

rotation and zooming

most of users can't bear the slowness. So how to simplify the triangle meshes is regarded more and more important. To simplify triangles effectively while not influence the vision effect

based on the traditional method of edge contraction

a new method is presented

which named Two Times of Local Mapping. First

it maps the three-dimensional triangle meshes from three-dimensional space to two-dimensional plane by using Gaussian sphere which can determine the direction of projection. Then on two-dimensional plane

using the traditional edge contraction method

a new contracted point is found in the kernel of a polygon. With the new point

the number of triangles is reduced greatly. After simplification

when mapping the simplified triangles back to three-dimensional space

the error is checked. Two kinds of error are defined to ensure the minimum error. It is proved that the given method is little-error

efficient and without self-intersected

and also it is stable and applicable.