How to draw a rectangle perpendicular to a vector in OpenGL

Question

I'm trying to draw a rectangle perpendicular to vector v:

glPushMatrix()
glTranslatef(v[0], v[1], v[2])
glBegin(GL_QUADS)
glVertex3f( -h, -h, 0)
glVertex3f( h, -h, 0)
glVertex3f( h, h, 0)
glVertex3f( -h, h, 0)
glEnd()

The resulting rectangle sits at the end of vector (I need this), how do I make it perpendicular to this vector?

Answer 1

If the vector v is a in view space, then the x axis points to the left, the y axis points up and z axis points out of the viewport.

Calculate the longitude and latitude - see Geographic coordinate system:

import math

lenXY = math.sqrt(v[0]*v[0] + v[2]*v[2])
lon   = math.atan2(v[0], v[2])
lat   = math.atan2(v[1], -lenXY)

Do a rotation around the x and y axis:

glPushMatrix()
glTranslatef(v[0], v[1], v[2])
glRotatef(math.degrees(lon), 0, 1, 0)
glRotatef(math.degrees(lat), 1, 0, 0)

# [...]

glPopMatrix()