The marching method produces for any starting point a polygon on the intersection curve.
2.
Thus the intersection curve, which theory says must be a quartic, contains four double points.
3.
For the general case, literature provides algorithms, in order to calculate points of the intersection curve of two surfaces.
4.
If the intersection curve consists of two parts, the algorithm has to be performed using a second convenient starting point.
5.
As the intersection curves away from the exit, the path of an exiting vehicle is relatively straight, and so the motorist may often not slow substantially.
6.
Instead, one can construct intersections of a tubular elliptic LCS with select 2D planes, and fit a surface numerically to a large number of these intersection curves.
7.
Hirsch extends this argument to " any " surface of revolution generated by a conic, and shows that intersection with a bitangent plane must produce two conics of the same type as the generator when the intersection curve is real.
8.
The "'surface-to-surface intersection ( SSI ) problem "'. is a basic problem in computer-aided geometric design : Given two intersecting surfaces in R 3, compute all parts of the intersection curve.
9.
In 3D flows, instead of solving the Frobenius PDE ( see table above ) for hyperbolic LCSs, an easier approach is to construct intersections of hyperbolic LCSs with select 2D planes, and fit a surface numerically to a large number of such intersection curves.
10.
The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example : a ) the intersection of two planes, b ) plane section of a quadric ( sphere, cylinder, cone, etc . ), c ) intersection of two quadrics in special cases.
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