Chapter 3
1) Draw a nested space hierarchy tree for the sheep described in Section 3.3, assuming
that its head, ears, upper legs, lower legs, and body move indemendently.
2) Suppose our object axes are transformed to world axes by rotating them
counterclockwise around the y-axis by 42º and then translating six units along the z-
axis and 12 units along the x-axis. Describe this transformation from the
perspective of the object.
Imagine a point on the object, in object space. As the axes are rotating
counterclockwise, the point is actually rotating counterclockwise relative to the axes.
Then, as the axes translate by [12, 0, 6], the point translates [-12, 0, -6] relative to the
axes.
3) Which coordinate space is the most appropriate in which to ask the following
questions?
a) Is my computer in front of or behind me? Object space. If we know the
position of the computer within our object space, this question is a trivial
matter of checking for a positive z value. (Assuming the conventions from
Section 2.3.4)
b) Is the book east or west of me? Inertial space is the easiest space to make this
test. Again, assuming the conventions from Section 2.3.4, the book is east of
us if the x-coordinate of the book’s position in our inertial space is positive,
and west if this value is negative. Alternatively, we could answer the
question in world space, by comparing the x-coordinate of the book in world
space, with our own world space x-coordinate.
c) How do I get from one room to the other? Pathfinding-type querries are
usually made in world space.
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