Angel ad Shreiner: Interactive Computer Graphics; Seventh
Edition
Chapter 9 Odd Solutions
9.1 If the upper arm is longer than the lower arm then, as a first
approximation, the robot can reach all points within a sphere centered at
the joint on the base. However, this answer is only approximate because
the lower arm cannot move below the level of the base, so a second
approximation is a hemisphere above the base. This approximation has to
9.3 For this simple example, there are three values of the joint angles and
three coordinates in space, so there are a couple of simple approaches that
can work. One is to use the result of the previous problem to solve for the
joint angles in terms of the given x,y, and zvalues, using a numerical
method. We could then simply move the joint angles from their initial to
final positions linearly.
9.11 The trick here is to store the average value of the four trees below at
each node. Thus, if we have an 2n×2nimage, the nodes at level nhas the
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9.13 Yes. For instance, we can save the state at nodes so that changes in
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