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Implicit surface with a common geodesic in the 3-dimensional space
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The problem of constructining a family of surfaces that share a special geodesic is wellknown. The author of [2] have given a parametric representation of a surface pencil whosemembers share the some geodesic curve. And they rised the question of a possible alternative ofthe problem for implicite surfaces. The aim of this work is to give the necessary and sufficientconditions for a family of implicite surfaces to share a common spacial geodesic. Implicitsurface defined by an equation F (x, y, z) = 0, play an important role in geometric modeling,computer graphics and mathematical physics. In this work we establish the necessary andsufficient conditions for a given parametric curve to be a geodesic on implicit surface.We illustrate by giving some examples.
Title: Implicit surface with a common geodesic in the 3-dimensional space
Description:
The problem of constructining a family of surfaces that share a special geodesic is wellknown.
The author of [2] have given a parametric representation of a surface pencil whosemembers share the some geodesic curve.
And they rised the question of a possible alternative ofthe problem for implicite surfaces.
The aim of this work is to give the necessary and sufficientconditions for a family of implicite surfaces to share a common spacial geodesic.
Implicitsurface defined by an equation F (x, y, z) = 0, play an important role in geometric modeling,computer graphics and mathematical physics.
In this work we establish the necessary andsufficient conditions for a given parametric curve to be a geodesic on implicit surface.
We illustrate by giving some examples.
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