Real time editing of a surface vector field using discrete connections

This video demonstrates a new algorithm for editing direction fields on discrete surfaces that are as smooth as possible everywhere but on a set of isolated singularities of given index. Direction fields are represented via a "discrete connection," i.e., an angle associated with each (dual) edge. These angles are determined by the solution to a linear system, and are globally optimal in the sense that they describe the trivial connection closest to Levi-Civita among all solutions with a prescribed set of singularities. Relative to previous methods our algorithm is highly efficient and surprisingly simple, and can be implemented using standard operations from mesh processing and linear algebra. The solution can be used to construct rotationally symmetric direction fields with a prescribed set of singularities and directional constraints, which are essential in applications such as quadrilateral remeshing, texture synthesis, and "fur" design.

This video is supplementary material from the paper "Trivial Connections on Discrete Surfaces" by Keenan Crane, Mathieu Desbrun, and Peter Schröder. (SGP 2010)

More information can be found at http://users.cms.caltech.edu/~keenan/project_tcods.html

Category:

Science & Technology

Tags:

• 3d modeling
• geometry processing
• vector field design
• computer graphics
• discrete differential geometry

[Lawdrun]

lolmacintosh

[Orbiter144]

oR basically what specs are your computer which you run all these demos on.

[Orbiter144]

What computer are you running this on? cept for it's a MAC >:(

[Zalo10]

Forgive me if I completely misunderstand the purpose of this method, but perhaps another application for this kind of thing would be visualizing how a flood might flow down a hill for emergency planning.