use cinema 4d and take snapshots for emphasis:

  1. Using cinema 4d draw a line segment between (1,2,3) and (3,5,7). What math formula do you use to create this line segment?Draw a line segment between (1,2) and (3,5) without specifically entering coordinates.
  2. Draw a Bezier curve with endpoints at (0,0) and (2,2) and a horizontal tangent at (0,0) and a 45 degree tangent at (2,2). Manipulate this curve so the tangent is 45 degrees at (0,0) and horizontal at (2,2). What formulas from Bezier curves are you using?
  3. Draw a Bezier curve in the front window and use the Lathe object to make a wineglass. Explain how the lathe object works to create the curves and points necessary to triangulate a surface.
  4. Create a cube and select all the vertices. Rotate the vertices by 45 degrees about the z axis. What happens to the cube. From our math theory why does this happen?
  5. Create a cube and move a point.  Triangulate your new figure. Why cant you always break up the surface into rectangles?
  6. Create a cube and extrude a face. How do you think cinema 4d does this? Delete the new face you created. How far in does the hole go.
  7. Create a sphere and move it to (1,0,0). Rotate 90 degrees about the z axis and now rotate 90 degrees around the x axis. Where is the sphere? Is it in the same place if you reverse the order of the rotations? What is mathematically behind your answer?
  8. Create a sphere at point (1000,2000,10000). Create a new camera that is at the origin and points along z axis. Set the H,P,B to 0. Bank the camera 20 degrees in either direction. Look through this camera. What happens to the sphere? What mathematics is behind this? What happens in front window. Is there any difference? How about if the z value is 1000? Explain what mathematics is behind your discoveries.
  9. Create a spotlight and a sphere. Look through the spotlight and center the sphere. What mathematics are you using for these operations.
  10. Use the bilinear interpolation calculator
    1. Show that if you put in the coordinates for Q11-->(x1,y1), Q21-->(x2,y1) and by hand see what vector you get then you get the coordinates of P-->(x,y)
    2. Use the calculator to calculate an rgb vector at some point in a square given rgb values at the Q
  11. Create a sky object and put an hdri texture on it to light a simple scene.
  12. Use lights and make a stage to hold several objects that are reflective, refractive, bump mapped and have transparency. Make a render that creates shadows and caustics.
    1. Explain the difference between ray casting and ray tracing.
    2. How are they getting shadows when there is a depth map
    3. How does a bump map work?
  13. Create a graphic that shows how a line is projected from a point to the eye and hits a view plane.
    1. make a little line segment that is almost  90 degrees away from direction your eye is looking at. Can you tell that the line segment will be blown up in this position.