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Reconstructing and analyzing surfaces in 3-space

Sun, Jian
http://rave.ohiolink.edu/etdc/view?acc_num=osu1184337519

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Computer and Information Science.
One often analyzes surfaces through their induced structures such as the convex hull or the homology group. It is important to derive appropriate induced structures. If they are too complicated, it becomes hard to extract the information about the original surface from them. If they are too simple, little or nothing about the surface can be inferred from them. To analyze surfaces computationally, it is important that the induced structures can be computed efficiently. In this work, we address two induced structures for surfaces: curve-skeletons and handle and tunnel loops. We give formal definitions for both structures and propose algorithms to compute them. One can also reverse the direction, namely, given an induced structure, how to recover the original surface. It is hard, sometimes impossible, to recover the surface exactly. We often seek to obtain an approximation with bounded error. The problem of reconstructing surfaces from their sample points is such an example. This problem has been studied for almost three decades though there are still many open gaps. In this work, we focus on how to handle sample points when they are contaminated with noise. We define a smooth surface out of the noisy sample points by using a technique called moving least squares. We prove that under a non-uniform sampling condition, this smooth surface approximates the sampled surface correctly in terms of topology and geometry. The effectiveness of the proposed algorithms is demonstrated through numerous examples and experimental results.
Tamal Dey (Advisor)
150 p.
Computer Science
Surface Reconstruction; Geodesics; Curve-skeleton.

Recommended Citations

Citations

  • Sun, J. (2007). Reconstructing and analyzing surfaces in 3-space [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1184337519

    APA Style (7th edition)

  • Sun, Jian. Reconstructing and analyzing surfaces in 3-space. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1184337519.

    MLA Style (8th edition)

  • Sun, Jian. "Reconstructing and analyzing surfaces in 3-space." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1184337519

    Chicago Manual of Style (17th edition)

osu1184337519
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© 2007, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.