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The AIM@SHAPE Glossary

Alphabetical list of terms


gaussian curvature
An intrinsic property of a space independent of the coordinate system used to describe it. The Gaussian curvature equals the product of the principal curvatures.
generalised focal surface
The locus of all points of a normal congruence proportional to a curvature function value at these points. It is quite related to hedgehog diagram. Instead of drawing surface normals proportional to a function value, all the points on the surface normals proportional to the function value are drawn.
A topologically invariant property of a surface defined as the largest number of non-intersecting simple closed curves that can be drawn on the surface without separating it. Roughly speaking, it is the number of holes in a surface.?
geodesic path
It is a line which connect two points on a curved surface with minimum path length.
geometric continuity
Two Ck curves or surfaces join at a boundary with geometric continuity Gk if it is possible to a reparametrise both the curves or surfaces with a unique map such that the derivatives of the component functions agree. For k=0, it coincides with C0, for k=1, it is a continuity of the tangent plane, for k=2, it is a continuity of curvature.
gridded elevation model
A gridded elevation model is a DTM defined by a domain partition into a cell complex in which the 2-cells are squares.



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