halo I will start with ,ellipse in polar coordinates. bold mean=vectors polar equation:ellipse in 3d major axis = a rem:a>b minor axis = b angle = theta info angle between two lines 1e line : focus and point on the ellipse 2e line : focus and perihelion u,v are unit vector u is direction major axis v is direction minor axis c is vector (orgin to the center of the ellipse) rem: center different from focus for ellipse rem: center=focus only for circle x is vector (orgin to point on the ellipse) x=c+a*cos(theta)u+b*sin(theta)v (1) ? how can you find the relation between euler angles and (1). ? how unit u,v vector related to euler angles. ? how (1) is related to real observation on the sky.