# Extending an orthogonal set of vectors (graphics application?)

Sorry if this is OT, but I'm wondering if there's a specific graphics technique in which it is required to extend a preexisting orthogonal set of vectors (not necessarily to a full basis, but perhaps so). In a matrix theory lecture, the prof said that this computation has a real-world application, but I can't remember him saying what it was. Could be computer graphics, could be a lot of things. I realize that it is only an issue in a high-dimensional space. For example, if you had two orthogonal vectors in 3-space, you could compute their cross product cheaply. I asked at Math SE, and it was not appreciated.

TLDR: Just need the application, if any. You don't have to say how it is computed, but feel free to if you like. I'll read it. I know that orthogonal vectors are often easier to work with than oblique vectors, and other very general math facts like that.

• To name a few: computing triangle normals, creating a basis for normal mapping or scattering rays in path tracing, computing the lookAt matrix (usually for a camera). Apr 20, 2020 at 7:09
• Do you only want to know about higher dimensions? Because I know a few uses in 3D, starting with one or two vectors, but don't remember ever needing this for higher dimensions. Apr 20, 2020 at 14:57
• @Olivier No, 3D is fine. Please name them. Apr 21, 2020 at 1:17
• @lightxbulb Much appreciated! Apr 21, 2020 at 1:17
• It has similar uses to look at in robotics an mechanism design. It has uses in optimisation. Apr 21, 2020 at 22:46