题目内容

Consider a modified orthographic projection matrix:\( \left( \begin{array}{cccc} \frac{2}{r-l} & 0 & 0 & -\frac{r+l}{r-l}\\ 0 & \frac{2}{t-b} & 0 & -\frac{t+b}{t-b}\\ 0 & 0 & \mathbf{\frac{2}{f-n}} & -\frac{f+n}{f-n}\\ 0 & 0 & 0 & 1 \end{array} \right) \)When would we use such a matrix instead of the normal glOrtho?

A. When we wish to tilt our camera.
B. When we wish to view along a direction not aligned with an axis.
C. When the far plane is closer than the near plane.
D. When we define our coordinate system so that we are looking down a positive axis.
E. The results are unpredictable.

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Given a R2 point defined on the canonical x,y axis, i⃗ =(22), what are the coordinates in a new coordinate system with the origin at j⃗ =(11), and axes at 45 degrees? (The rotated first axis will be aligned to (11) in an unrotated coordinate system, with an origin at j⃗ ). Denote this changed vector as k⃗ Enter your answers as numbers.kx=? ky=?

The gluLookAt matrix can be summarized as:

A. Scaled followed by Translation followed by Rotation
B. Rotation followed by Scale followed by Translation
C. Translation followed by Rotation
D. Rotation followed by Translation
E. None of the above.

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Given that you are doing a 3D rotation operation, \( M=R\left(\vec{a}, \theta\right) \) ,on your vertices, what is the corresponding normal transformation,\( Q \)？

A. \( R(\vec{a},\theta) \)
B. \( R(\vec{a},-\theta) \)
C. \( -R(\vec{a},\theta)\)
D. \( -R(-\vec{a},\theta)\)
E. The result is unpredictable.
F. None of the above.

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Using the Rodrigues Rotation Formula, what effect does negating the axis of rotation have?

A. \( R(-\vec{a},\theta) = R(\vec{a},\theta) \)
B. \( R(-\vec{a},\theta) = R(\vec{a},\theta+\pi) \)
C. \( R(-\vec{a},\theta) = -R(\vec{a},\theta) \)
D. \( R(-\vec{a},\theta) = R(\vec{a},-\theta) \)
E. The result is unpredictable.
F. None of the above.

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A. When we wish to tilt our camera. B. When we wish to view along a direction not aligned with an axis. C. When the far plane is closer than the near plane. D. When we define our coordinate system so that we are looking down a positive axis. E. The results are unpredictable.

The gluLookAt matrix can be summarized as:

Given that you are doing a 3D rotation operation, \( M=R\left(\vec{a}, \theta\right) \) ,on your vertices, what is the corresponding normal transformation,\( Q \)？

Using the Rodrigues Rotation Formula, what effect does negating the axis of rotation have?

A. When we wish to tilt our camera.
B. When we wish to view along a direction not aligned with an axis.
C. When the far plane is closer than the near plane.
D. When we define our coordinate system so that we are looking down a positive axis.
E. The results are unpredictable.