To solve the problem of improving the quality of triangulation and its optimum speed

some exports have proposed many methods

whereas there is too much calculation and determining in these prevail methods

which has been a key question. The paper presents the algorithm for triangulation and its optimum based on angle of chord mapping parameters

and it introduces the conception of angle of chord and proves its property. And triangulation optimum is actually diagonal selection of convex quadrangle. In a convex quadrangle including two triangles

it shows the facts that angle of chords are mapped to become mapping parameters on the perpendicular bisector of two adjacent triangles' common edge

then the paper proves that mapping parameters has the same triangulation determining quality as angles of chord own one. Consequently triangulation and locale optimum is turned to a problem of mapping parameters' determining. Theoretic analysis and practicing show that the implementation of the method is very easy

the computation of mapping parameters is simple and convenient

and its result is credible; the angle of chord mapping parameter determining method has avoided calculating the angles or radiuses distances

which are necessary in conventional methods. The angle of chord mapping parameter determining method improves evidently calculation efficiency.