3D Interpretation of Conics and Orthogonality

Abstract

Computational techniques involving conics are formulated in the framework of projective geometry, and basic notions of projective geometry such as poles, polars, and conjugate pairs are reformulated as "computational procedures" with special emphasis on computational aspects. It is shown that the 3D geometry of three orthogonal lines can be interpreted by computing conics. We then describe an analytical procedure for computing the 3D geometry of a conic of a known shape from its projection. Real image examples are also given.