【摘要】 平面实体间的碰撞检测中,经常需要讨论二次曲线间的位置关系.根据切点既是交点,又是最近/最远距离点的性质,结合结式理论推导出若干代数多项式,并用来判定平面椭圆与二次曲线间的位置关系.该方法直观简单,仅需要简单四则运算,可以直接应用于判别运动曲线间的位置关系.最后的实例及其比较表明,该方法应用范围广,结果也稳定.更多还原

【Abstract】 Position relationship problem between two quadratic curves is usually discussed in collision detection problem between two coplanar objects.Combining with the resultant theory and the observation that the tangent point is not only an intersection point but also the closest point,several polynomial discriminants are obtained to classify all possible cases of the position relationship between an ellipse and a quadratic curve.Our method is very intuitive and simple where only simple operations such as addition,subtraction and multiplication are involved.The method could also be used in position relationship problem between two moving quadratic curves.Examples have been presented to show that the new method is robust and feasible in various applications.更多还原