Method and apparatus for discrete mesh filleting and rounding through ball pivoting
View Patent ↗A method and apparatus for rounding a sharp edge of a model of an object is disclosed whereby a ball is propagated in a desired direction along the edge to be smoothed. The position of the ball at each point in its propagation is noted and, as a result, a virtual tunnel through which the ball passed may be constructed. Points on the sides of the surface of the object in proximity to the sharp edge are then projected onto the virtual tunnel by connecting with a line each point in proximity to the sharp edge to the center of the tunnel. New projected points are created at each position on the surface of the tunnel where the lines intersect that surface. The original points along the sharp edge are then hidden or deleted and the points along the virtual tunnel are connected via well-known surface reconstruction methods. In this way, a sharp edge of a triangle mesh model are advantageously smoothed.
1. A method for rounding an edge between two sides of a surface, said surface comprising a plurality of points connected to form a triangle mesh, said method comprising:
moving a representation of a ball parallel to said edge in a predetermined direction;
defining, by a processor, a virtual tunnel as a function of a plurality of positions of said ball as said ball moves parallel to said edge;
identifying a plurality of projected points by projecting a plurality of edge points to a surface of said virtual tunnel; and
connecting said projected points in said plurality of projected points;
wherein a radius of said ball is selected in a way such that no point disposed on either of said two sides is positioned inside a volume of said ball; and
wherein the virtual tunnel contacts the two sides defining a line on each side.
2. The method of claim 1 wherein said step of identifying a plurality of projected points comprises:
identifying a plurality of intersections of a plurality of lines with said surface of said virtual tunnel, said plurality of lines comprising lines between said plurality of edge points and a center of said virtual tunnel; and
disposing points on said surface of said virtual tunnel at each intersection in said plurality of intersections.
3. The method of claim 1 wherein said step of connecting said projected points comprises growing a triangle mesh.
4. The method of claim 1 wherein the representation of the ball is moved parallel to said edge at a distance from the edge such that a surface of the ball contacts said two sides.
5. The method of claim 1 wherein the plurality of edge points projected to a surface of said virtual tunnel to identify a plurality of projected points are the set of points between the line on each side and the edge.
6. An apparatus for use in rounding an edge between two sides of a surface of a model, said surface comprising a plurality of points connected to form a triangle mesh, said apparatus comprising:
means for moving a representation of a ball parallel to said edge in a predetermined direction;
means for defining a virtual tunnel as a function of a plurality of positions of said ball as said ball moves parallel to said edge;
means for identifying a plurality of projected points by projecting a plurality of edge points to a surface of said virtual tunnel; and
means for connecting said projected points in said plurality of projected points;
wherein a means for selecting a radius of said ball comprises means for selecting said radius in a way such that no point disposed on either of said two sides is positioned inside a volume of said ball; and
wherein the virtual tunnel contacts the two sides defining a line on each side.
7. The apparatus of claim 6 wherein said means for identifying a plurality of projected points comprises:
means for identifying a plurality of intersections of a plurality of lines with said surface of said virtual tunnel, said plurality of lines comprising lines between said plurality of edge points and a center of said virtual tunnel; and
means for disposing points on said surface of said virtual tunnel at each intersection in said plurality of intersections.
8. The apparatus of claim 6 wherein said means for connecting said projected points comprises means for growing a triangle mesh.
9. The apparatus of claim 6 wherein the representation of the ball is moved parallel to said edge at a distance from the edge such that a surface of the ball contacts said two sides.
10. The apparatus of claim 6 wherein the plurality of edge points projected to a surface of said virtual tunnel to identify a plurality of projected points are the set of points between the line on each side and the edge.
11. A computer readable medium storing computer program instructions which, when executed by a processor, define steps for rounding an edge between two sides of a surface of a model, said surface comprising a plurality of points connected to form a triangle mesh, said steps comprising:
moving a representation of a ball parallel to said edge in a predetermined direction;
defining a virtual tunnel as a function of a plurality of positions of said ball as said ball moves parallel to said edge;
identifying a plurality of projected points by projecting a plurality of edge points to a surface of said virtual tunnel; and
connecting said projected points in said plurality of projected points;
wherein computer program instructions for selecting a radius of said ball comprise computer program instructions for selecting said radius in a way such that no point disposed on either of said two sides is positioned inside a volume of said ball; and
wherein the virtual tunnel contacts the two sides defining a line on each side.
12. The computer readable medium of claim 11 wherein said computer program instructions defining the step of identifying a plurality of projected points comprise computer program instructions defining the steps of:
identifying a plurality of intersections of a plurality of lines with said surface of said virtual tunnel, said plurality of lines comprising lines between said plurality of edge points and a center of said virtual tunnel; and
disposing points on said surface of said virtual tunnel at each intersection in said plurality of intersections.
13. The computer readable medium of claim 11 wherein said computer program instructions defining the step of connecting said projected points comprise computer program instructions defining the step of growing a triangle mesh.
14. The computer readable medium of claim 11 wherein the representation of the ball is moved parallel to said edge at a distance from the edge such that a surface of the ball contacts said two sides.
15. The computer readable medium of claim 11 wherein the plurality of edge points projected to a surface of said virtual tunnel to identify a plurality of projected points are the set of points between the line on each side and the edge.