On normals of ellipses and ellipsoids

Activity: Talk or presentationTalk at conference or symposiumScience to science


Distance computation is an important issue with applications to path planning, obstacle recognition and collision prevention. To compute distances between complex
objects these objects are often decomposed into elementary and preferably convex
components such as spheres and ellipsoids. Locally extremal distances between such
objects occur on their common normals. In this presentation we discuss the task of
finding all common normals between basic object pairs like point - ellipsoid, straight
line - ellipsoid and ellipsoid - ellipsoid. For each of these pairs we present geometric
proofs for the maximal number of common normals in case of generic relative position of the two objects. To that end we use tools from descriptive geometry, line
geometry and algebraic geometry.
Period6 Sep 20219 Sep 2021
Event title22nd Scientific-professional Colloquium on Geometry and Graphics
Event typeConference
LocationCivo, Croatia
Degree of RecognitionInternational