Derivative estimation of triangular patch by using cubic least square method

Smooth surface reconstruction of scattered data built from Delaunay triangulation need the partial derivatives to be defined at the vertices of the triangles for all the data points. Partial derivatives at the vertices of triangular elements and at the midpoint of each side usually are unavailable therefore it is a needed to approximate the derivatives information at the vertices and at the midpoint of each side. The common method use to estimate partial derivatives was the quadratic approximation of least square method. This research focused to estimate partial derivatives by using cubic approximation of least square method and compare the surface obtained between quadratic and cubic approximation. The research also implement the use of interpolating surface of cubic Bezier triangular patch. The result of the study shows comparison of interpolating surface produced by different type of functions for quadratic and cubic least square. The maximum and minimum error was also calculated and maximum error between quadratic and cubic least square was generated when using saddle function while the minimum error is on the exponential function

Filling sharp features on corner of triangular mesh by using Enhanced Advancing Front Mesh (EAFM) method

Repairing an incomplete polygon mesh constitutes a primary difficulty in 3D model construction, especially in the computer graphics area. The objective of hole-filling methods is to keep surfaces smoothly and continually filled at hole boundaries while conforming with the shapes. The Advancing Front Mesh (AFM) method was normally used to fill simple holes. However, there has not been much implementation of AFM in handling sharp features. In this paper, we use an AFM method to fill a holes on sharp features. The Enhanced Advancing Front Mesh (EAFM) method was introduced when there was a conflict during triangle creation. The results of the study show that the presented method can effectively improve the AFM method, while preserving the geometric features and details of the original mesh

Filling simple holes of triangular mesh by using Enhanced Advancing Front Mesh (EAFM) method

Triangular meshes are extensively used to represent 3D models. Some surfaces cannot be digitised due to various reasons such as inadequacy of the scanner, and this generally occurs for glossy, hollow surfaces and dark-coloured surfaces. This cause triangular meshes to contain holes and it becomes difficult for numerous successive operations such as model prototyping, model rebuilding, and finite element analysis. Hence, it is necessary to fill these holes in a practical manner. In this paper, the Enhanced Advancing Front Mesh (EAFM) method was introduced for recovering missing simple holes in an object. The first step in this research was to extract the feature vertices around a hole on a 3D test data function. Then the Advancing Front Mesh (AFM) method was used to fill the holes. When conflicts occurred during construction of the triangle, the EAFM method was introduced to enhance the method. The results of the study show that the enhanced method is simple, efficient and suitable for dealing with simple hole problems