Subdivision Surfaces

Co-authored with Jeppe Oskar Meyer Larsen.

Abstract

In this report we reviewed much of the litterature on subdivision surfaces, which are a new type of surfaces for computer aided geomtric design and computer graphics. We review the theory of tensor-product B-spline surfaces and discuss the shortcomings of these surfaces. We then show how to generalise tensor product surfaces to subdivison surfaces.

We present an implementation of five subdivision surface schemes (Doo-Sabin, Catmull-Clark, Loop, Quadratic NURSS, Cubic NURSS) and compare the properties of the surfaces generated by these schemes.

Subdivison Surface Viewer program

The Subdiv program will display geometric models drawn using subdivision surfaces. The models are specified in MDL or WRL format (WRL file must be specially formatted). The MDL format is described in the report available below.

Tetrahedron-like shape
Once the program is started it will display a wireframe representation of the model. Here is a list of keys that are active in the viewer:

  • O: Toggle between wireframe and surface view.
  • L: Toggle light.
  • H: Toggle face culling.
  • D: Toggle Z test (depth test).
  • P: Toggle perspective.
  • N: Toggle exact normals (only for Loop scheme).
  • Arrow keys: Rotate model.
  • Ctrl+arrow keys: Move model.
  • PgUp/PgDn: Zoom in/out.
  • F11: Do one subdivision less.
  • F12: Do one subdivision more.
  • Esc: Exit program.

Cup
Some of these controls are also available by right clicking the program window. The subdivision scheme used to draw the model can also be changed by right clicking.

In the lower left hand corner of the window the current subdivision scheme and the number of polygons in the subdivided model are indicated.

Download report and software

Download report:

If you have trouble saving the above files to your harddisk, right click the link and choose Save target as….

Download software (please read the installation instructions below)

Installation instructions for the Subdiv program

Download the Subdiv zip file from the link above. Use a program like WinZip to extract the files to a directory.

To launch the program open a command prompt and change to the directory where you unzipped the program. Type

subdiv

model levels, where models is the file name of a geometric model in MDL or WRL format (Only specially formatted WRL files will work), and levels is the number of subdivisions to perform. If you specify too many subdivision levels the program will crash. For most models 4 or 5 subdivision levels should work.

The zip file includes a number of geometric models in MDL and WRL format. The MDL format is specified in the report available above.

See also

New York University Media Research Lab has links to a number of scientific articles about subdivision. A program for calculating and displaying subdivision surfaces is also available for download.

Hugues Hoppe’s home page at Microsoft has a large number of articles about various topics in geomtric modelling, including subdivision surfaces.

Binary Reality gives an application oriented introduction to subdivision surfaces.

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