Abstract: It is an important problem to compute the geodesics on
a surface in many fields. To find the geodesics in practice, however,
the traditional discrete algorithms or numerical approaches can only
find a list of discrete points. The first author proposed in 2010 a new,
elegant and accurate method, the geodesic-like method, for
approximating geodesics on a regular surface. This paper will present
by use of this method a computation of the Bezier geodesic-like curves
on spheres.
Abstract: This paper proposes a method to improve the shortest
path problem on a NURBS (Non-uniform rational basis spline) surfaces.
It comes from an application of the theory in classic differential
geometry on surfaces and can improve the distance problem not only
on surfaces but in the Euclidean 3-space R3 .