projective space – 3D Vector Projection onto A Viewing screen


we have a 3D tetrahedron, with corners at A=(6,0,0), B=(4,3,9), C=(10,6,6) and
D=(8,8,5).
p

  1. Doable Part. The diagram on the right shows a line C
    parallel to the x-axis, and one side BC of the tetrahedron.
    Find the two vector projections p and q illustrated. q
    p is the projection of BC onto the line. q is the projection
    onto the dotted line joining B to the line. B
  2. Slightly harder, using the above. A 2D viewing screen is between you and the tetrahedron. 3D
    orientation is such that your eye and corner A of the tetrahedron both lie along the x-axis (of 3D space). The
    viewing screen is the plane x=0 (ie, it is the plane containing the y and z axes). The coordinates of your
    eye and one point on the screen are respectively (-6,0,0) and (0,0,0). Use an isomorphic projection to
    project the tetrahedron corners onto the viewing screen. Join the four points. Use solid lines if you can
    see the edge of the actual tetrahedron, and dashed lines if you can’t.
  3. Not difficult, but you have to think. You will not use the projection formula – instead you will use lines in
    3D space. Use a perspective projection to project the tetrahedron corners onto the viewing screen in
  4. Join the four points. Use solid lines if you can see the edge of the actual tetrahedron, and dashed lines if
    you can’t.