Space Curves Beizer curves

Space Curves Beizer curves MCQ &amp Answers

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Q.1. Parametric equation of a circle with center at origin and radius r are ------.

A. (- 𝑟 cos 𝜃 , 𝑟 sin 𝜃)
B. (𝑟 cos 𝜃 , 𝑟 sin 𝜃)
C. (𝑟 cos 𝜃 , - 𝑟 sin 𝜃)
D. (- 𝑟 cos 𝜃 , - 𝑟 sin 𝜃)

Q.2. Parametric equation of a circle with center at (h, k ) and radius r are -------.

A. (- 𝑟 cos 𝜃 + ℎ , 𝑟 sin 𝜃 − 𝑘)
B. (𝑟 cos 𝜃 + ℎ , 𝑟 sin 𝜃 + 𝑘)
C. (𝑟 cos 𝜃 + ℎ , 𝑟 sin 𝜃 - 𝑘)
D. (𝑟 cos 𝜃 − ℎ , 𝑟 sin 𝜃 + 𝑘)

Q.3. The angle 𝛿𝜃 to generate uniformly spaced 5 points on the circumference of a circle in the 2^nd and 3^rd quadrant is -----------

A. -45°
B. 45°
C. 60°
D. -60°

Q.4. The angle 𝛿𝜃 to generate 36 points on the circle (𝑥 − 2)² + (𝑦 + 2)² = 25 is……..

$A. \:\: \frac{\pi}{18}$

$B. \:\: \frac{\pi}{8}$

$C. \:\: \frac{\pi}{11}$

$D. \:\: \frac{\pi}{36}$

Q.5. If we generate 4 points in the first quadrant of the unit circle with center at origin then first point is ----------.

A. (0.9239, 0.3827) B. ( 0, 1)
C. ( 1, 0) performance D. (-0.9239, 0.3827)

Q.6. Let [x] represents n points of the origin centered circle of radius 2 then matrix representing circle of radius 2 with center located at ( 2, 2) is --------.

$A.\:\:\: \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0\\ 2 & 2 & 1 \\ \end{bmatrix} \quad$

$B.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0\\ 1 & 1 & 1 \\ \end{bmatrix} \quad$

$C.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0\\ 2 & 2 & 1 \\ \end{bmatrix} \quad$

$D.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0\\ -2 & -2 & 1 \\ \end{bmatrix} \quad$

Q.7. If we generate 8 uniformly spaced points on the circle 𝑥² + 𝑦² = 1 the second point is -------.

$A.\:\:\: \left(\frac{1}{\sqrt{2}}\:\:,\frac{-1}{\sqrt{2}} \right)$

$B.\:\:\: \left(\frac{1}{\sqrt{2}}\:\:,\frac{1}{\sqrt{2}} \right)$

C. (0, 1)
D. (1, 0)

Q.8. The parametric curve representation of straight line segment between two position vectors 𝑃₁ and 𝑃₂ is --------.

A. 𝑃(𝑡) = 𝑃₁ + (𝑃₂ − 𝑃₁)t
B. 𝑃(𝑡) = 𝑃₁ - (𝑃₂ − 𝑃₁)t
C. 𝑃(𝑡) = 𝑃₁ + 𝑃₂t
D. 𝑃(𝑡) = 𝑃₂ + 𝑃₁t

Q.9. Let [x] represent n points of the circle 𝑥² + 𝑦² = 1 and [𝑋^∗] = [X] [ 𝑇₁] [𝑇₂] represent n points of circle (𝑥 − 5)² + (𝑦 + 3)² = 4. The transformation matrix is -----

$A.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0\\ -5 & -3 & 1 \\ \end{bmatrix} \quad$

$B.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0\\ 5 & -3 & 1 \\ \end{bmatrix} \quad$

$C.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0\\ 5 & 3 & 1 \\ \end{bmatrix} \quad$

$D.\:\:\: \begin{bmatrix} 2 & 0 & 0 \\ 0 & -2 & 0\\ -5 & -3 & 1 \\ \end{bmatrix} \quad$

Q.10. To generate n points on a are of a circle the parameter range is-------.

$A.\:\:\: \delta \theta = \frac{\theta_n -\theta_1 }{n}$

$B.\:\:\: \delta \theta = \frac{\theta_n -\theta_1 }{n-1}$

$C.\:\:\: \delta \theta = \frac{\theta_n +\theta_1 }{n}$

$D.\:\:\: \delta \theta = \frac{\theta_n +\theta_1 }{n+1}$

Computational Geometry : Space Curves Beizer curves

Space Curves Beizer curves