Problem 1
Which of the following are applications of \(2 \mathrm{D}\) graphics and which are applications of 3D graphics? a. Designing the layout of magazine pages b. Drawing an image using Microsoft Paint c. Producing images from a virtual world for video game
Problem 2
In the context of \(3 \mathrm{D}\) graphics, what corresponds to each of the following items from traditional photography? Explain your answers. a. Film b. Rectangle in viewfinder c. Scene being photographed
Problem 3
When using a perspective projection, under what conditions will a sphere in the scene not produce a circle on the projection plane?
Problem 4
When using a perspective projection, can the image of a straight line segment ever be a curved line segment on the projection plane? Justify your answer.
Problem 5
Suppose one end of an eight-foot straight pole is four feet from the center of projection. Moreover, suppose that a straight line from the center of projection to one end of the pole intersects the projection plane at a point that is one foot from the center of projection. If the pole is parallel to the projection plane, how long is the image of the pole in the projection plane?
Problem 6
Explain the concepts of kinematics and dynamics as used in 3D animation.
Problem 8
What is a significant difference between applying \(3 \mathrm{D}\) graphics to produce a motion picture and applying \(3 \mathrm{D}\) graphics to produce the animation for an interactive video game? Explain your answer.
Problem 9
Identify some properties of an object that might be incorporated in a model of that object for use in a \(3 \mathrm{D}\) graphics scene. Identify some properties that would probably not be represented in the model. Explain your answer.
Problem 10
Identify some physical properties of an object that are not captured by a model containing only a polygonal mesh. (Thus, a polygonal mesh alone does not constitute a complete model of the object.) Explain how one of those properties could be added to the object's model.
Problem 12
Each collection that follows represents the vertices (using the traditional rectangular coordinate system) of a patch in a polygonal mesh. Describe the shape of the mesh. Patch 1: \((0,0,0)(0,2,0)(2,2,0)\) Patch 2: \((0,0,0)(1,1,1)(2,0,0)\) Patch 3: \((2,0,0)(1,1,1)(2,2,0)\) Patch 4: \((2,2,0)(1,1,1)(0,2,0)\) Patch 5: \((0,2,0)(1,1,1)(0,0,0)\)
