Name of the University : University of Pune
Name of the College : MIT Arts Commerce & Science College
Degree : B.SC
Department : Computer Science
Subject Code/Name : MTC-221 Computational Geometry
Year : II
Semester : IV
Document Type : Question Bank
Website : mitacsc.ac.in
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/mitacsc.ac.in/3826.-Computational%20geometryQuestion%20Bank_1.pdf
Computational Geometry :
1) What will be the effect, if in combined transformation –
2) Determine whether the transformation matrix [ ] cos sinsin cos-
3) If a square with sides 2 cms is reflected through y axis, –
Related : MIT Arts Commerce & Science College CS201 Digital Image Processing M.SC Question Bank : www.pdfquestion.in/3853.html
4) Write the transformation matrix required to create bottom view of the object.
5) Write the transformation matrix to shear in x direction proportional –
5 And proportional to z coordinate by a factor 6.
6) What is the point at infinity on the y – axis in the positive direction-
7) Explain the difference between affine and perspective transformations.
8) Write the transformation matrix for rotation about y – axis through an angle2
9) Find the angle dq , to generate 5 points on the hyperbolic –
10) Mention any two applications of space curves.
11) The circle of area 10 cm2 is scaled uniformly by factor 2-
12) Explain the term : Point at infinity.
13) Write a 2D transformation matrix for overall scaling by factor s.-
14) A shadow of a person standing on ground is formed by sunlight. –
15) Write the transformation matrix-
16) Let L be a line with d.r.s 1, 1, 1. Find the angle –
17) Find the angle dq to generate 8 equidistant points on an elliptical-
18) Write the matrix for cabinet projection –
19) Write any two properties of Bezier Curve.
20) What is the transformation represented by the matrix [T]-
21) What is the effect of the transformation matrix [ ] 1 0
2 1) Generate uniformly spaced 7 points, in the 1st quadrant on an ellipse –
22) If the circle of circumference 14p is uniformly scaled by 3 units,
23) Find the angle through which the line y = -x rotated so that it is coincident
24) What is an apparent translation- How to obtain pure scaling-
25) Write the transformation matrix for shear in x coordinate by a factor of 2-
26) If z = -5 is the given plane, find the transformation matrix
27) Give two different aspects of perspective views experienced by human eye.
28) If 8 distinct uniformly spaced points on the periphery of an ellipse
29) Write the matrix equation form of a parametric equation of a Bezier curve
30) Let [x] represent n points of the circle x2 + y2 =1
31) Define foreshortening factors
32) What is the determinant of the inverse of any pure rotation matrix-
33) If line L is transformed to the line L* using a transformation matrix [ ] 1 2
34) Write the rotation matrix required to rotate the line y = 2x
35) If y = 0 is the given plane. Find the transformation matrix
36) Write the transformation matrix for orthographic projection
37) Determine the foreshortening factors fx and fy if the transformation
38) Find an angle dq to generate uniformly spaced 5 points
39) State whether the following statement is true or false.
40) Explain, what you mean by variation diminishing property of a Bezier curve.
41) Explain different possible effects due to the entries of a general
42) Show that the parallel lines AB and CDare not transformed
43) Rotate DABC about its centroid through an angle 45° ,
44) Write an algorithm for reflection through any arbitrary plane in space.
45) Find the combined transformation matrix for the following sequence
46) Consider the Bezier curve determined by the control points
47) Let [X] be a square with vertices A, B, C where A=[0 0], B=[1 0], C[1 1],
48) Prove that, if a 2 x 2 transformation matrix is applied on a pair of parallel
49) If an object [X] is reflected through the plane Z =3,
50) If the 2×2 transformation matrix transforms the point P and Q
51) Find the concatenated transformation matrix for the following transformation in order.
a) Translate in X, Y, Z direction by -2, -2, -2 units respectively.
b) Rotate about x-axis by an angle 45°.
c) Reduce to half of its size.
52) Generate uniformly spaced 3 points on the parabolic segment in first quadrant for 3 ≤ x ≤ 12 and equation of the parabola is y2 = 12x.
53) If B0 [2, 1], B1 [4, 4], B2 [5, 3], B3 [5, 1] are vertices of a Be’zier polygon, then determine the point [P (0, 7)] of the Be’zier curve. Also find the first derivative of [P (t)] corresponding to t = 0.3.
54)Write the transformation matrix for the diametric projection with fz = 1/3 and also find the foreshortening factors along x and y direction. [Take f > 0,q < 0].
55) Consider a triangle with vertices {A [3 6], B [6 9], C [3 9]}. Rotate the triangle about a point (-2, 1) through an angle 35°. Write the position vectors of the transformed triangle.
56) Derive the transformation matrix for rotation about origin through an angle θ.
57) Obtain the concatenated matrix for the following sequence of transformations. First translation in x, y and z direction by -1, 2, 1 units respectively, followed by a rotation about z-axis by 90°, followed by a reflection in z=0 plane. Apply it on the point [1 2 3].
58) Generate uniformly spaced 3 points of the parabolic segment y2 = 8x, in the first quadrant for 4 ≤ y ≤ 20.