Surfaces with Pythagorean normals along rational curves
An algebraic analysis of components of offsets to irreducible surfaces along rational curves is provided. A simple criterion for deciding if the curve on the surface is (proper/non-proper) PSN is formulated. Surfaces with PSN pencils such that a generic fiber is a proper/non-proper PSN curve are investigated. It is shown that all developable surfaces are PSN pencils (but not necessarily PN surfaces). For non-developable surfaces a method for generating all real parameterizations respecting PSN pencils is designed.
psn pencils psn curves offset surfaces pythagorean surface normals double planes numerical-control machining