2006 Ohio Student Research Forum

Abstract

Interpolation of Unknown Function Values of Meshes
Ilsa Bolano
Ohio State University
Department of Computer Science & Engineering
Mentor(s): Dr. Yusu Wang

In the area of computer graphics meshes are used to represent surfaces. The vertices of the mesh have function values associated with them to provide more information about the surface that the mesh is representing. There are situations where there are only few vertices of a mesh that have known function values. When this happens then the rest of the vertices’ function values need to be interpolated. This research project focused on one specific method that involved the so-called Laplacian interpolation technique.

Before programming could begin, background research was done to understand the topology of meshes more thoroughly. After this phase was completed, code to manipulate mesh that was provided by the mentor was studied. This was done to ensure that the code would be properly used when it came time to write the program to interpolate the unknown function values. The process to code the program was then begun. The algorithm of interpolation being researched was taken from the article “Fair Morse Functions for Extracting Topological Structure of a Mesh” and modified to fit the research project. This involved reading the article and extracting the pertinent information that could be applied to the research project. Once this phase was completed then programming the interpolation functions began.

Programming the interpolation of the function values of the meshes required modifying the code provided, obtaining code to work with matrices, and writing the code to perform the interpolation operations that had been obtained from the previous phase. The code provided by the mentor need to be modified because it did not include the option of a vertex not having a function value associated with it. The programming language C++ does not provide a library to work with matrices thus one needed to be obtained in order to work with the interpolation algorithm. The code for interpolating was then written and tested. Once completed error testing was done to measure the precision of the answers produced by the interpolation algorithm.

The results of the interpolation algorithm can be visualized and graphically shown. This can be done in a future research project. Depending on the results of the error checking, if the interpolation algorithm is precise or not, more research can be done to study the behavior of the algorithm in different settings.