Which are just convenient mechanism for accom-plishing certain goals
ROTATION MATRIX METHODS SUMMARY
| projections | and | in | common | use. | Typically | a | ||||||
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help | in | various | rotation | tasks. | Matrix | methods | |||||
IX.2 TRANSFORMING AXES
IX.2
Sometimes an interactive 3D application needs to know roughly which way a set of transformed coordinate axes are pointing on the screen. For example, the application may want to know if the x-axis of a given modeling space is pointing into or out of the screen after the axis undergoes a sequence of modeling and viewing transforms; this could help the application understand the orientation of an object on the screen. Even if the application knows only the net transform for the object, it can still calculate the approximate orientation of the object’s axes quite efficiently.
Solution
| [ | yin | zin | 1 ] | a12 | a13 | a14 |
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= α [ | β | γ |
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(1) | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a22 | a23 | a24 | |||||||||||||
| a32 | a33 | a34 | |||||||||||||
| (2) | |||||||||||||||
| a42 | a43 | a44 | |||||||||||||
| xout=α ω, yout=β ω, zout=γ ω. | |||||||||||||||
| 456 | |||||||||||||||
