from math import *

# translation for the trackball
T = [0,0,0] # use this to initialize camera position and to implement zoom
# rotation for the trackball
R = [[1,0,0,0,
      0,1,0,0,
      0,0,1,0,
      0,0,0,1]]
# old mouse x,y coordinates
oxy = [0,0]

def project(r, x, y):
    """Project an x,y pair onto a sphere of radius r if we are within
    sqrt(2) * r from center OR a hyperbolic sheet if we are farther away."""
    dd = x*x+y*y
    rr = r*r
    if dd < .5 * rr:    # on sphere
        return sqrt(rr - dd)
    else:               # on hyperbola
        return .5 * rr / sqrt(dd)

def rotation(w, h, x, y, ox, oy):
    """Given screen size, new and old mouse coordinates,
    calculate the new rotation for the trackball."""
    # center of the screen
    c = [w/2, h/2]         
    # radius is the half the smaller screen extent
    if w < h: r = c[0]
    else:     r = c[1]
    # mouse point in screen centered coords
    x,y   = x - c[0],  h-1-y - c[1]
    ox,oy = ox - c[0], h-1-oy - c[1]
    # get 3d points by projecting from screen
    p1 = [ox, oy, project(r, ox, oy)]
    p2 = [x, y, project(r, x, y)]
    # the origin is at the center of the sphere
    # calculate the angle between p1 and p2

    # your code here

    # calculate the rotation axis for rotating p1 to p2
    # hint: the axis is perpendicular to both p1 and p2

    # your code here, compound the new rotation with the
    # old one, stored in R
    
def zoom(y, oy):
    """Given old and new y coordinate, modify the
    translation of the trackball for zoom effect."""

    # a good way to implement the zooming is the modify the
    # camera's distance from the origin by a factor of
    # e.g., 2^((y - oy) / 80.0)
    pass
    
def pan(x,y,ox,oy):
    # how far in the viewplane are pixels apart? scale panning accordingly
    pass