Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curve appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory. We also provide a semi-algorithm to check their validity. Finally, we present experiments, some of which are not reachable by other methods, and discuss the efficiency of our method.

隔离平面曲线的奇点是计算其拓扑的第一步。为此，数值方法是有效的，但通常没有经过认证。我们有兴趣开发用于隔离奇异点的经过认证的数值算法。为此，我们将注意力集中在平面曲线的特殊情况上，该特殊情况是较大尺寸的平滑曲线的投影。这种类型的曲线自然出现在机器人应用程序和科学可视化中。在这种情况下，我们表明奇异性可以由规则的平方系统编码，该平方的系统可以使用经过验证的数值方法来隔离其解。我们的分析以假设为条件，这些假设使用横向理论证明是通用的。我们还提供了一个半算法来检查其有效性。最后，我们提出实验