Improved Maximum Angle Estimate for Longest-Edge Bisection

Abstract

In this note we construct an upper estimate on the maximum angles of triangles generated by the longest-edge bisection algorithms applied to a triangle. This upper bound considerably improves upon one inherited from the well-known minimum angle estimation, thus providing tighter two-sided estimation of the angles generated by bisections. This estimate also guarantees the validity of the maximum angle condition, widely used in finite element analysis and computer graphics.