In
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal ...
, the Loop method for
subdivision surfaces
In the field of 3D computer graphics, a subdivision surface (commonly shortened to SubD surface) is a curved surface represented by the specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface ...
is an approximating subdivision scheme developed by Charles Loop in 1987 for
triangular meshes. Prior methods, namely
Catmull-Clark and
Doo-Sabin (1978), focused on
quad meshes.
Loop subdivision
surfaces
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space.
Surface or surfaces may also refer to:
Mathematics
*Surface (mathematics), a generalization of a plane which needs not be flat
* Su ...
are defined recursively, dividing each triangle into four smaller ones. The method is based on a
quartic box spline
In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalization of basis splines (B-splines) and are ge ...
. It generates
C2 continuous limit surfaces everywhere except at extraordinary vertices, where they are
C1 continuous.
Applications
Geologists
A geologist is a scientist who studies the solid, liquid, and gaseous matter that constitutes Earth and other terrestrial planets, as well as the processes that shape them. Geologists usually study geology, earth science, or geophysics, althoug ...
have applied Loop subdivision surfaces to model
erosion
Erosion is the action of surface processes (such as water flow or wind) that removes soil, rock, or dissolved material from one location on the Earth's crust, and then transports it to another location where it is deposited. Erosion is di ...
on
mountain faces, specifically in the
Appalachians
The Appalachian Mountains, often called the Appalachians, (french: Appalaches), are a system of mountains in eastern to northeastern North America. The Appalachians first formed roughly 480 million years ago during the Ordovician Period. The ...
.
See also
*
Geodesic polyhedron
*
Catmull-Clark subdivision surface
*
Doo-Sabin subdivision surface
References
* Charles Loop: ''Smooth Subdivision Surfaces Based on Triangles'', M.S. Mathematics thesis, University of Utah, 1987
pdf.
* Jos Stam: ''Evaluation of Loop Subdivision Surfaces'', Computer Graphics Proceedings ACM SIGGRAPH 1998,
pdf
.
* Antony Pugh, ''Polyhedra: a visual approach'', 1976, Chapter 6. ''The Geodesic Polyhedra of R. Buckminster Fuller and Related Polyhedra''
External links
* Homepage o
Charles Loop
3D computer graphics
Multivariate interpolation
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