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This paper is devoted to presenting a new approach to determine theintersection of two quadrics based on the detailed analysis of its projectionin the plane (the so called cutcurve) allowing to perform the correspondinglifting correctly. This approach is based on a new computationalcharacterisation of the singular points of the cutcurve and on how this curveis located with respect to the projection of the considered quadrics (whoseboundaries are the so called silhouette curves).

Computing the intersection of two quadrics through projection and lifting