Method and apparatus for encoding a 3D mesh

1. A method for encoding a three-dimensional (3D) mesh, the method comprising:

determining a priority of a gate configuring a 3D mesh based on valence information on boundary vertices, tag information on vertices configuring a patch, and a null patch;

simplifying a 3D mesh by removing a vertex based on the priority of the gate; and

encoding connectivity information of a vertex removed from a plurality of vertices configuring the 3D mesh through the simplifying the 3D mesh,

wherein the simplifying of the 3D mesh comprises:

generating tag information including a plus type on a boundary vertex when a number of vertices connected to the corresponding boundary vertex subsequent to a generation of a triangle is increased or remains the same in comparison to a number of vertices connected to the corresponding boundary vertex prior to the generation of the triangle;

generating tag information including a minus type on the boundary vertex when the number of vertices connected to the corresponding boundary vertex subsequent to the generation of the triangle is reduced in comparison to the number of vertices connected to the corresponding boundary vertex prior to the generation of the triangle; and

determining a higher priority of the gate when tag information on both vertices configuring the gate include minus-plus type or plus-minus type than when tag information on the both vertices configuring the gate include plus-plus type or minus-minus type.

2. The method of claim 1 , wherein the simplifying of the 3D mesh comprises:

removing a front vertex of the gate, based on the priority.

3. The method of claim 2 , wherein the removing of the front vertex comprises:

generating a triangle of the patch, subsequent to the removing of the front vertex;

generating tag information associated with neighboring vertices of the front vertex; and

updating valence information of the neighboring vertices of the front vertex.

4. The method of claim 1 , wherein the determining the priority of a gate comprises:

determining a higher priority to the gate for lower valence information on the both vertices configuring the gate.

5. The method of claim 1 , wherein the simplifying the 3D mesh comprises:

determining a priority of the gate associated with the patch determined to be the null patch to be lower than a priority of the gate associated with the patch determined not to be the null patch.

6. The method of claim 5 , wherein the simplifying the 3D mesh further comprises:

determining the patch associated with the front vertex to be the null patch when the front vertex is a vertex configuring another gate.

7. The method of claim 1 , wherein the simplifying of the 3D mesh comprises:

determining a higher priority of the gate when both vertices configuring the gate include tag information differing from one another than a priority when the both vertices include tag information identical to one another.

8. The method of claim 1 , wherein the simplifying of the 3D mesh comprises:

determining a start gate with a highest priority; and

simplifying the 3D mesh by removing a front vertex of the start gate.

9. The method of claim 1 , wherein the simplifying of the 3D mesh by removing the front vertex of the start gate comprises:

generating a triangle by connecting neighboring vertices of the front vertex subsequent to the removing of the front vertex of the start gate;

determining edges remaining subsequent to the generating of the triangle from among edges configuring an area adjacent to the front vertex of the start gate to be a plurality of subsequent gates; and

determining a priority of the plurality of subsequent gates.

10. An apparatus for encoding a three-dimensional (3D) mesh, the apparatus comprising:

a priority determiner to determine a priority of a gate configuring a 3D mesh based on valence information on boundary vertices, tag information on vertices configuring a patch, and a null patch;

a mesh simplifier to simplify a 3D mesh by removing a vertex based on the priority of the gate; and

a mesh encoder to encode connectivity information on a vertex removed from a plurality of vertices configuring the 3D mesh through the simplifying the 3D mesh,

wherein the mesh simplifier is further configured to:

generate tag information including a plus type on a boundary vertex when a number of vertices connected to the corresponding boundary vertex subsequent to a generation of a triangle is increased or remains the same in comparison to a number of vertices connected to the corresponding boundary vertex prior to the generation of the triangle;

generate tag information including a minus type on the boundary vertex when the number of vertices connected to the corresponding boundary vertex subsequent to the generation of the triangle is reduced in comparison to the number of vertices connected to the corresponding boundary vertex prior to the generation of the triangle; and

determine a higher priority of the gate when tag information on both vertices configuring the gate include minus-plus type or plus-minus type than when tag information on the both vertices configuring the gate include plus-plus type or minus-minus type.

11. The apparatus of claim 10 , wherein the mesh simplifier comprises:

a vertex remover to remove a front vertex of the gate based on the priority.

12. The apparatus of claim 11 , wherein the vertex remover generates a triangle of the patch, subsequent to the removing of the front vertex, generates tag information of a plurality of neighboring vertices connected to the front vertex, and updates valence information of the plurality of neighboring vertices of the front vertex.

13. The apparatus of claim 10 , wherein the priority determiner determines a higher priority to the gate for lower valence information on both vertices configuring the gate.

14. The apparatus of claim 10 , wherein the priority determiner determines a priority of the gate associated with the patch determined to be the null patch to be lower than a priority of the gate associated with the patch determined not to be the null patch.

15. The apparatus of claim 14 , wherein the priority determiner determines the patch associated with the front vertex to be the null patch when the front vertex is a vertex configuring another gate.

16. The apparatus of claim 10 , wherein the mesh simplifier determines a higher priority when both vertices configuring the gate includes tag information differing from one another than a priority when the both vertices includes tag information identical to one another.

17. The apparatus of claim 10 , wherein the mesh simplifier comprises:

a start gate determiner to determine a start gate with a highest priority; and

a vertex remover to remove the front vertex of the start gate.

18. The apparatus of claim 17 , wherein the vertex remover removes the front vertex of the start gate, generates a triangle by connecting neighboring vertices of the front vertex of the start gate, and determines edges remaining subsequent to the generating of the triangle from among edges configuring an area adjacent to the front vertex of the start gate to be a plurality of subsequent gates.

19. The apparatus of claim 18 , wherein the mesh simplifier further comprises:

a priority determiner to determine a priority of the plurality of subsequent gates.