The Horizon Measure: A New Look at Curvature

Graduate Project

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_projects/vm40z0078

Descriptions

Attribute Name	Values
Creator	Mills, Arthur M.
Abstract	An important problem in computer graphics is to determine where contour lines and ridges appear in a surface constructed from a triangle mesh. In this presentation we will investigate a new answer to this problem – the horizon measure. The horizon measure determines the likelihood of contour lines to appear in a triangle on a mesh surface. Using classical results from spherical geometry we can obtain a closed-form formula for the horizon measure of a mesh triangle. The connections between the horizon measure and the Gaussian curvature of a surface will be discussed, as well as the applications of the horizon measure to computer graphics.
Resource Type	Capstone Project
Date Issued	2021-02-19
Degree Level	Master's
Degree Name	Master of Science (M.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2020
Advisor	Escher, Christine M.
Committee Member	Guo, Ren Zhang, Eugene
Academic Affiliation	Mathematics
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

Thumbnail	Title	Date Uploaded	Visibility	Actions
	horizon_measure.pdf	2021-02-19	Public	Download