We revisit here a fundamental result on planar triangulations, namely that the flip distance between two triangulations is upper-bounded by the number of proper intersections between their straight-segment edges. We provide a complete and detailed proof of this result in a slightly generalised setting using a case-based analysis that fills several gaps left by previous proofs of the result.

翻译：我们在此重温关于平面三角方位的基本结果,即两个三角方位之间的翻转距离以其直系分层边缘之间的适当交叉点数量为上限。 我们利用基于案例的分析,填补了先前对结果的证明留下的若干空白,完整和详细地证明了这一结果。