The generalized focal surfaces are a surface interrogation
method.
The idea of generalized focal surfaces is quite related to hedgehog
diagrams. In stead of drawing surface normals proportional to a
function value, only the point on the surface normal proportional to
the function is drawn. The loci of all these points is the
generalized focal surface.
This method was introduced by Hagen and Hahmann (1992), and is based
on the concept of focal surfaces which are known from line geometry.
The focal surfaces are the loci of all focal points of an special line
congruence, the normal congruence.
Generalized focal surfaces consists of variational surface offstes: where kappa_max, kappa_min are the principal curvatures of the given surface X and f is a real valued function. - convexity test
detection of flat points detection of surface irregularities visualization of curvature behaviour visualization of technical smoothness visualization of $C^2$- and $C^3$-discontinuities test of technical aspects |

Convexity test
the intersection of the surface with its focal surface indicate the line of zero Gaussian curvature variable offset factor: f = kappa_max * kappa_min vrml2.0 |
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C2-continuity test on hair dryer surface
The gaps in the focal surface (right) indicate the curvature discontinuity. variable offset factor: f = kappa_max^2 + kappa_min^2 |
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continuity testleft: C2-discont. surface right: C3-discont. surface |
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C-1 (left) and C0-continuous (right) focal surfaces. |

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