Method and system for the smooth contouring of triangulated surfaces

摘要

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.