Method and apparatus for non-shrinking mesh smoothing using local fitting
View Patent ↗A method and apparatus for the smoothing of a mesh surface is disclosed whereby neighboring vertices of a target vertex are identified, for example, by identifying the neighboring vertices within a desired distance from the target vertex. A normal of the target vertex is determined as a function of, for example, the features of a set of neighbor triangles corresponding to the set of neighboring vertices. A local coordinate system is then established. Unknowns in a quadratic surface function are then solved as a function of the position of the neighboring vertices with respect to the local coordinate system and new x and y coordinates in the local coordinate system are determined for the target vertex. These new x and y coordinates are entered into the quadratic surface function to obtain a new smoothed z coordinate for the target vertex.
1. A method for smoothing a triangle mesh surface, said triangle mesh surface comprising a target vertex to be smoothed, said method being performed by a processor and comprising:
identifying a plurality of neighboring vertices in said triangle mesh surface as a function of a position of said target vertex;
determining a position of said target vertex and a position of each vertex in said plurality of neighboring vertices in a coordinate system associated with said target vertex;
determining a surface function as a function of said position of said target vertex and said position of each vertex in said plurality of neighboring vertices; and
determining a new position of said target vertex as a function of said surface function;
wherein said step of determining a new position of said target vertex comprises determining a new x coordinate and a new y coordinate of said target vertex as a function of the x coordinates and the y coordinates of said vertices in said plurality of neighboring vertices, respectively; and
wherein a z coordinate for said target vertex is determined by inputting said new x coordinate and said new y coordinate of said target vertex into said surface function.
2. The method of claim 1 wherein said step of identifying a plurality of neighboring vertices comprises identifying the neighboring vertices within a desired distance of said target vertex.
3. The method of claim 1 wherein said local coordinate system is determined in a way such that the target vertex is positioned at the origin of the local coordinate system and the z axis is determined as a function of a normal to said target vertex.
4. The method of claim 3 wherein said normal to said target vertex is determined as a function of at least one feature of a neighboring triangle in said triangle mesh surface.
5. The method of claim 4 wherein said at least one feature comprises a normal of said neighboring triangle and a surface area of said neighboring triangle.
6. The method of claim 1 wherein said step of determining a surface function comprises determining at least a first unknown of said surface function using a singular value decomposition technique.
7. The method of claim 1 wherein said new x coordinate of said target vertex is determined as an average of the x coordinates of said vertices in said plurality of neighboring vertices and said new y coordinate of said target vertex is determined as an average of the y coordinates of said vertices in said plurality of neighboring vertices.
8. The method of claim 1 wherein said surface function comprises a quadratic function.
9. An apparatus for use in smoothing a triangle mesh surface, said triangle mesh surface comprising a target vertex to be smoothed, said apparatus comprising:
means for identifying a plurality of neighboring vertices in said triangle mesh surface as a function of a position of said target vertex;
means for determining a position of said target vertex and a position of each vertex in said plurality of neighboring vertices in a coordinate system associated with said target vertex;
means for determining a surface function as a function of said position of said target vertex and said position of each vertex in said plurality of neighboring vertices; and
means for determining a new position of said target vertex as a function of said surface function;
wherein said means for determining the new position of said target vertex comprises means for determining a new x coordinate and a new y coordinate of said target vertex as a function of the x coordinates and the y coordinates of said vertices in said plurality of neighboring vertices, respectively; and
wherein the apparatus is adapted to determine a z coordinate for said target vertex by inputting said new x coordinate and said new y coordinate of said target vertex into said surface function.
10. The apparatus of claim 9 wherein said means for identifying a plurality of neighboring vertices comprises means for identifying the neighboring vertices within a desired distance of said target vertex.
11. The apparatus of claim 9 wherein the target vertex is positioned at the origin of the local coordinate system and the z axis corresponds to a normal to said target vertex.
12. The apparatus of claim 9 wherein said means for determining a new x coordinate of said target vertex comprises means for determining said new x coordinate as an average of the x coordinates of said vertices in said plurality of neighboring vertices and said means for determining a new y coordinate of said target vertex comprises means for determining said new y coordinate as an average of the y coordinates of said vertices in said plurality of neighboring vertices.
13. The apparatus of claim 9 wherein said surface function comprises a quadratic function.
14. A non-transitory computer readable medium comprising computer program instructions which, when executed by a processor, define steps for smoothing a triangle mesh surface, said triangle mesh surface comprising a target vertex to be smoothed, said steps comprising:
identifying a plurality of neighboring vertices in said triangle mesh surface as a function of a position of said target vertex;
determining a position of said target vertex and a position of each vertex in said plurality of neighboring vertices in a coordinate system associated with said target vertex;
determining a surface function as a function of said position of said target vertex and said position of each vertex in said plurality of neighboring vertices;
determining a new position of said target vertex as a function of said surface function, said computer program instructions defining the step of determining a new position of said target vertex comprising computer program instructions defining the step of determining a new x coordinate and a new y coordinate of said target vertex as a function of the x coordinates and the y coordinates of said vertices in said plurality of neighboring vertices, respectively; and
determining a z coordinate for said target vertex by inputting said new x coordinate and said new y coordinate of said target vertex into said surface function.
15. The computer readable medium of claim 14 wherein said computer program instructions defining the step of identifying a plurality of neighboring vertices comprise computer program instructions defining the step of identifying the neighboring vertices within a desired distance of said target vertex.
16. The computer readable medium of claim 14 further comprising computer program instructions defining the step of determining said local coordinate system in a way such that the target vertex is positioned at the origin of the local coordinate system and the z axis is determined as a function of a normal to said target vertex.
17. The computer readable medium of claim 16 further comprising computer program instructions defining the step of determining the normal to said target vertex as a function of at least one feature of a neighboring triangle in said triangle mesh surface.
18. The computer readable medium of claim 17 wherein said at least one feature comprises a normal of said neighboring triangle and a surface area of said neighboring triangle.
19. The computer readable medium of claim 14 wherein said computer program instructions defining the step of determining a surface function comprise computer program instructions defining the step of determining at least a first unknown of said surface function using a singular value decomposition technique.
20. The computer readable medium of claim 14 further comprising computer program instructions defining the steps of:
determining said new x coordinate of said target vertex as an average of the x coordinates of said vertices in said plurality of neighboring vertices; and
determining said new y coordinate of said target vertex as an average of the y coordinates of said vertices in said plurality of neighboring vertices.
21. The computer readable medium of claim 14 wherein said surface function comprises a quadratic function.