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Directional developable surfaces and their singularities in Euclidean 3-Space
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The developable surface is a surface that can be unfolded on a plane
without tearing or stretching, which is widely used in many fields of
engineering and manufacturing. This work presents a new version of
developable ruled surfaces in Euclidean 3-space. First, we establish an
adapted frame along a spatial curve, denoted by the quasi-frame. We then
introduce a parametric representation of a developable ruled surface and
call it a directional developable ruled surface. At the core of this
paper, we investigate the existence and uniqueness of such developable
surfaces, then study their classification by singularity theory and
unfolding method. Some examples are given in the final.
Title: Directional developable surfaces and their singularities in Euclidean 3-Space
Description:
The developable surface is a surface that can be unfolded on a plane
without tearing or stretching, which is widely used in many fields of
engineering and manufacturing.
This work presents a new version of
developable ruled surfaces in Euclidean 3-space.
First, we establish an
adapted frame along a spatial curve, denoted by the quasi-frame.
We then
introduce a parametric representation of a developable ruled surface and
call it a directional developable ruled surface.
At the core of this
paper, we investigate the existence and uniqueness of such developable
surfaces, then study their classification by singularity theory and
unfolding method.
Some examples are given in the final.
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