Question

Is possible to draw a quad given its normal vector, a point that is center of the quad and the size of the quad?

I know the equation of a plane with normal vector n=(a,b,c) passing through the point (x_0,y_0,z_0) is given by a(x-x_0)+b(y-y_0)+c(z-z_0)=0. (from here)

But how to find the coordinate of the four vertex of the quad?

Thanks

Answer 1

No, because there are infinite quads that satisfy your condition.

Just assume 1 quad is a solution, and rotate this quad about the normal vector through that center. Now you’ve got a distinct quad that is also a solution.

There are 4×3 = 12 coordinates, so there should be 12 constraints. Yours has only 3+3+1 = 7.

You must specify more conditions.

(Of course it’s possible to draw “a” quad on that plane. Just substitute some numbers for x, y in the plane equation to get z.)