US 5,333,248 AGranted

Method and system for the smooth contouring of triangulated surfaces

AssigneeInternational Business Machines Corporation

InventorAlbert H. J. Christensen

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Abstract

A method and a system in a data processing system for differentially smoothing raw isolines containing linear segments within a triangular mesh which represents a single-valued surface. The triangulation mesh comprises a plurality of triangles. A first centroid is located for a first triangle within the triangular mesh and a second centroid is located for a second adjacent triangle within the triangular mesh which shows a common side with the first triangle. Each centroid includes three medians beginning at the centroid and terminating at one of three vertices of a triangle associated with the centroid. The common side between the two triangles has a first end point and a second end point, and an isoline which traverses the first and the second triangle traverses at least one of the three medians in each triangle. A first point is determined at an intersection of the isoline and a median within the first triangle. A second point is determined at an intersection of the isoline with a median within the second triangle. A third point is determined at an intersection of the isoline with the common side. The isoline is replaced within the triangle formed by the first point, the second point, and the third point with a selected curve, such as a pair of parabolic lines.

Claims20

Dependent claims

A method in a data processing system for differentially smoothing isolines, wherein each isoline is comprised of a plurality of angular successions of linear segments within a triangular mesh representing a measurable feature of a physical object and wherein said triangular mesh comprises a plurality of non-overlapping triangles, said method comprising the data processing system implemented steps of:

locating a first centroid for a first triangle within said triangular mesh and a second centroid for a second triangle within said triangular mesh utilizing said data processing system, wherein said isolines within said triangular mesh are comprised of data produced by measuring said measurable feature of said physical object and wherein each centroid includes three medians, each median connecting said centroid with one of three vertices of a triangle associated with said centroid exclusive of said other two medians, wherein said first and second triangle have a common side, said common side having a first end point and a second end point, wherein an isoline traverses said first and said second triangle and traverses at least one of said three medians in each triangle;
determining a first point utilizing said data processing system, wherein said first point comprises an intersection of said isoline and a median within said first triangle;
determining a second point utilizing said data processing system, wherein said second point comprises an intersection of said isoline with a median within said second triangle;
determining a third point utilizing said data processing system, wherein said third point comprises an intersection of said isoline with said common side;
and
thereafter replacing said isoline located within a triangle formed by said first point, said second point, and said third point with a curve utilizing said data processing system, wherein smoothed isolines of said measurable feature of said physical object may be displayed to a viewer.

3 more elements

A data processing system for differentially smoothing isolines, wherein each isoline is comprised of a plurality of angular successions of linear segments within a triangular mesh representing a measurable feature of a physical object and wherein said triangular mesh comprises a plurality of non-overlapping triangles, said data processing system comprising:

a microprocessor including:
locating means for locating a first centroid for a first triangle within said triangular mesh and a second centroid for a second triangle within said triangular mesh, wherein said isolines within said triangular mesh are comprised of data produced by measuring said measurable feature of said physical object and wherein each centroid includes three medians, each median connecting said centroid with one of three vertices of a triangle associated with said centroid exclusive of said other two medians, wherein said first and second triangle have a common side, said common side having a first end point and a second end point, wherein an isoline traverses said first and said second triangle and traverses at least one of said three medians in each triangle;
means for determining a first point, wherein said first point comprises an intersection of said isoline and a median within said first triangles;
means for determining a second point, wherein said second point comprises an intersection of said isoline with a median within said second triangle;
means for determining a third point, wherein said third point comprises an intersection of said isoline with said common side;
and
means for replacing said isoline located within a triangle formed by said first point, said second point, and said third point with a curve;
and
a video display terminal coupled to said microprocessor, wherein smoothed isolines of said measurable feature of said physical object may be displayed to a viewer.

6 more elements

Dependencies are inferred from the claim text.