use cinema 4d and take snapshots for emphasis:
- Draw a Bezier curve with endpoints at (0,0) and (2,2) and a
horizontal tangent at (0,0) and a vertical 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?
- Draw a Bezier curve in the front window and use the Lathe
object to make a bowl. Explain how the lathe object works to
create the curves and points necessary to triangulate a surface.
- Create a plane. Move the plane to (0,0,1). Select all the
vertices. Scale the vertices by 2. What happens to the plane.
From our math theory why does this happen?
- Create a pyramid and move a point. Is this still a good
polygon. Why does arbitrarily moving a point on a
cube sometimes give unsatisfactory results.
- Create a sphere with 8 segments and make it a polygon. Extrude
a face. How do you think cinema 4d does this? Delete the new
face you created. How far in does the hole go.
- 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?
- 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.
- Create a spotlight and a sphere. Look through the spotlight
and center the sphere. What mathematics are you using for these
operations.
- Use the
bilinear interpolation calculator
- 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)
- Use the calculator to calculate an rgb vector at some point
in a square given rgb values at the Q
- Create a sky object and put an hdri texture on it to light a
simple scene.
- 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.
- Explain the difference between ray casting and ray tracing.
- How are they getting shadows when there is a depth map
- How does a bump map work?
- Create a graphic that shows how a line is projected from a
point to the eye and hits a view plane.