Ubach et al 2013a - Revision history

Julio at 17:56, 5 October 2019

2019-10-05T17:56:19Z

Julio at 17:03, 11 April 2019

2019-04-11T17:03:08Z

Julio: Julio moved page Draft Garcia-Espinosa 406470970 to Ubach et al 2013a

2019-04-11T16:59:05Z

Julio moved page Draft Garcia-Espinosa 406470970 to Ubach et al 2013a

Julio: Created page with " == Abstract == This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshe..."

2019-04-11T16:59:03Z

Created page with " == Abstract == This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshe..."

New page

== Abstract ==

This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshes of triangles do not have normals uniquely defined at the nodes. A widely used technique to compute the normal direction at any given node is to compute the weighted average of the normals of each surrounding triangle. The present study proposes new weighting factors to compute the normal directions at the nodes of the mesh of triangles of a general surface. Previous weights found in the literature used the geometric dimensions of the triangles themselves to design the weighting factors. The new factors are proposed using the triangles’ circumscribed circles dimensions. The new weights provide superior results than the ones obtained by previous best practices for a wide range of surfaces. An advanced framework based on the approachability of smooth surfaces by quadrics is presented and used. This framework helps to understand the improved performance of the presented factors with respect to other factors found in the literature. A comprehensive numerical comparison analysis is performed, and the most precise of all factors is clearly identified.

== Full document ==
<pdf>Media:Draft_Garcia-Espinosa_406470970-2748-document.pdf</pdf>

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 == Abstract ==
 This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshes of triangles do not have normals uniquely defined at the nodes. A widely used technique to compute the normal direction at any given node is to compute the weighted average of the normals of each surrounding triangle. The present study proposes new weighting factors to compute the normal directions at the nodes of the mesh of triangles of a general surface. Previous weights found in the literature used the geometric dimensions of the triangles themselves to design the weighting factors. The new factors are proposed using the triangles’ circumscribed circles dimensions. The new weights provide superior results than the ones obtained by previous best practices for a wide range of surfaces. An advanced framework based on the approachability of smooth surfaces by quadrics is presented and used. This framework helps to understand the improved performance of the presented factors with respect to other factors found in the literature. A comprehensive numerical comparison analysis is performed, and the most precise of all factors is clearly identified.
 == Full document ==
-<pdf>Media:Draft_Garcia-Espinosa_406470970-2748-document.pdf</pdf>
+<pdf>Media:Ubach_et_al_2013a_1899_Accepted version.pdf</pdf>
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