Graphics Reference
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Figure 35.8: Piecewise-cubic interpolation of position over time of a point on a character's
hand using a spline.
• We can't control different parts of the character independently. For exam-
ple, we might want to make the arms swing while the legs walk.
• The animation scheme doesn't provide for interaction or high-level control.
There is no notion of an arm or a leg, just a flat array of vertices.
• We still require a strategy for creating animation data, either by hand or as
measurements of real-world examples.
• We've only considered animation that is tied to a specific mesh. Creat-
ing animation proves to be time-consuming by current practices, so it is
desirable to transfer animation of one mesh to a new mesh representing a
different character—doing so means abstracting the animation away from
the vertices to higher-level primitives like limbs. (The mesh deformation
transfer described in Section 25.6.1 is one technique for this.)
Inline Exercise 35.2: Create a simple animation data format and playback pro-
gram to explore these ideas. Instead of a 3D character, limit yourself to a 2D
stick figure. Use only four frames of animation for the walk cycle, and manu-
ally enter the key pose vertex positions in a text file. Making even four frames
of animation will probably be challenging. Why? What kind of tool could you
build to simplify the process? What aspects of the linear interpolation are dis-
satisfying during playback?
35.2.2 Firing a Cannon (Simulation)
Let's render an animation of a sailing ship firing a cannon as shown in Figure 35.9.
The cannonball will be rendered as a black sphere, so we can ignore its orienta-
tion and focus only on the motion of its center of mass/local coordinate frame
origin—the root motion. Neglecting the effects of drag due to wind and the slight
variance in gravitational acceleration, the cannonball experiences only constant
acceleration due to gravity after it is fired. A physics textbook gives an equation
for the motion of an object under constant acceleration as
 
 
 
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