# How to calculate plane corner vertices from plane origin point and plane normal?

I have an origin point, and normal vector of a 3D plane. I want to calculate 4 vertices to use as the corners of a 2 triangle quad to render the plane.

• Looks like you're kind of missing a vector here. Without it, there is an infinite possibility of placement (as if you would "rotate" your quad around that normal vector). – Vaillancourt Mar 6 at 3:20
• could I get a second vector parallel to the plane by getting a perpendicular vector to the normal? using dot or cross ? – kevzettler Mar 6 at 20:16
• Jay gives you a solution for what you propose; this will give you a quad. If that's all you need, thats great! It may not be oriented the way you want. I suggest you try it and either comment on the answer, edit your question or post a follow up question if you need something more precise. – Vaillancourt Mar 6 at 20:52

Find a point on the plane a other than the origin, o. The vector a - o lies on the plane, so is guaranteed perpendicular to the plane normal. Normalise the vector a - o and call it x.
Take the cross product of x and the plane normal and call it y. y is guaranteed to be perpendicular to both x and the plane normal.
The four points of a square are now o + x, o + y, o - x, o - y.