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101.

How many minimum numbers of zeros are there in ‘3 x 3’ triangular matrix?(a) 4(b) 3(c) 5(d) 6The question was asked in class test.The doubt is from Composite 2D Transformations topic in section 2D Transformation and Viewing of Computer Graphics

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Correct option is (B) 3

The explanation: In a TRIANGULAR matrix, all entries, EITHER above or below the diagonal are zero. So in case of ‘3 x 3’ matrix, there should be minimum 3 elements as 0.

102.

Which one of the following is the correct notation of a matrix with ‘m’ rows and ’n’ columns?(a) m + n(b) m – n(c) m x n(d) m/nThe question was asked in a national level competition.The question is from Composite 2D Transformations in portion 2D Transformation and Viewing of Computer Graphics

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Right choice is (c) m X n

The EXPLANATION is: m x n represents a matrix with ‘m’ number of rows and ‘n’ number of COLUMNS, while others are just arithmetic OPERATIONS which can be done on 2 matrices.

103.

Which transformation distorts the shape of an object such that the transformed shape appears as if the object were composed of internal layers that had been caused to slide over each other?(a) Rotation(b) Scaling up(c) Scaling down(d) ShearingThis question was addressed to me in an interview for job.My question comes from Composite 2D Transformations topic in chapter 2D Transformation and Viewing of Computer Graphics

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Right answer is (d) Shearing

To explain: TWO common shearing transformations are the type of transformation that shift coordinate x values coordinate y values. In SHEAR transformation, the transformed SHAPE appears as if the object were COMPOSED of internal layers that had been caused to slide over each other.

104.

Transpose of a column matrix is________________(a) Zero matrix(b) Identity matrix(c) Row matrix(d) Diagonal matrixI had been asked this question in an interview.My doubt stems from Composite 2D Transformations in portion 2D Transformation and Viewing of Computer Graphics

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Right CHOICE is (c) Row MATRIX

To explain I would say: Transpose of a matrix is a matrix which is made by interchanging the rows and COLUMNS of the original matrix. Hence the transpose of column matrix is row matrix and vice VERSA.

105.

Reversing the order in which a sequence of transformations is performed may affect the transformed position of an object.(a) True(b) FalseI had been asked this question in quiz.The query is from Composite 2D Transformations in section 2D Transformation and Viewing of Computer Graphics

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Correct OPTION is (a) True

The explanation is: As we know that, MATRIX transformations are not commutative and the ORDER of transformation matters. So it will affect the POSITION of the OBJECT.

106.

Which of the following is NOT correct? (A, B and C are matrices)(a) A.B = B.A(b) A.B.C = (A.B).C = A.(B.C)(c) C(A+B) = C.A + C.B(d) 1 A = A 1I have been asked this question in examination.The doubt is from Composite 2D Transformations topic in portion 2D Transformation and Viewing of Computer Graphics

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Correct CHOICE is (a) A.B = B.A

The best explanation: MATRIX multiplication does not commute. We cannot SWITCH the ORDER of the factors and expect to end up with the same result. Hence, A.B ≠ B.A.

107.

Reflection about the line y=0, the axis, is accomplished with the transformation matrix with how many elements as ‘0’?(a) 8(b) 9(c) 4(d) 6I had been asked this question in homework.My question is based upon Composite 2D Transformations in portion 2D Transformation and Viewing of Computer Graphics

Answer» CORRECT answer is (d) 6

Explanation: The MATRIX used for reflection about y=0 is an identity matrix with 6 ‘0’s and TWO ‘1’s and one ELEMENT as ‘-1’.
108.

General pivot point rotation can be expressed as _____________________(a) T(zr,yr).R(θ).T(-zr,-yr) = R(xr,yr,θ)(b) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,θ)(c) T(xr,yr).R(θ).T(-xr,-yr) = R(zr,yr,θ)(d) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,Q)I have been asked this question in a job interview.I would like to ask this question from Composite 2D Transformations in chapter 2D Transformation and Viewing of Computer Graphics

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The CORRECT answer is (b) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,θ)

EXPLANATION: Since the FIRST two parameters are in 2D, HENCE only ‘x’ and ‘y’ can be variable along with ‘θ’. In other options, there is one more parameter ‘z’.

109.

Two successive translations are not commutative.(a) True(b) FalseI had been asked this question by my school teacher while I was bunking the class.My question is from Composite 2D Transformations in chapter 2D Transformation and Viewing of Computer Graphics

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Correct choice is (B) False

Best EXPLANATION: According to commutative property, the ORDER does not matter. Same as in the case of SUCCESSIVE translations. Hence we can say that two successive translations are commutative.

110.

We can combine the multiplicative and translational terms for 2D into a single matrix representation by expanding(a) 2 by 2 matrix into 4*4 matrix(b) 2 by 2 matrix into 3*3(c) 3 by 3 matrix into 2 by 2(d) Only cI had been asked this question by my school principal while I was bunking the class.The origin of the question is Matrix Representations and Homogeneous Coordinates topic in chapter 2D Transformation and Viewing of Computer Graphics

Answer» CORRECT answer is (b) 2 by 2 matrix into 3*3

For explanation I would say: We can combine the multiplicative and translational terms for 2D into a SINGLE matrix representation by expanding 2 by 2 matrix representation into 3 by 3.
111.

The general homogeneous coordinate representation can also be written as(a) (h.x, h.y, h.z)(b) (h.x, h.y, h)(c) (x, y, h.z)(d) (x,y,z)I have been asked this question in my homework.I need to ask this question from Matrix Representations and Homogeneous Coordinates in section 2D Transformation and Viewing of Computer Graphics

Answer» CORRECT CHOICE is (B) (h.x, h.y, h)

Explanation: The general HOMOGENEOUS coordinate representation can ALSO be written as (h.x, h.y, h).
112.

Two successive translations are___________________(a) Multiplicative(b) Inverse(c) Subtractive(d) AdditiveThis question was addressed to me during an interview for a job.The query is from Composite 2D Transformations topic in division 2D Transformation and Viewing of Computer Graphics

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Correct CHOICE is (d) Additive

The EXPLANATION: Successive translations are additive.

P’= T(tx1, ty1) .[T(tx2, ty2)] P

= {T(tx1, ty1). T(tx2, ty2)}.P

Or T(tx1, ty1). T(tx2, ty2) = T(tx1+tx2 , ty1 + ty2).

113.

If point are expressed inhomogeneous coordinates then the pair of (x, y) is represented as(a) (x’, y’, z’)(b) (x, y, z)(c) (x’, y’, w)(d) (x’, y’, w)I had been asked this question during a job interview.My enquiry is from Matrix Representations and Homogeneous Coordinates in chapter 2D Transformation and Viewing of Computer Graphics

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The CORRECT OPTION is (d) (x’, y’, W)

Explanation: If POINT are EXPRESSED in homogeneous coordinates then we add 3rd coordinate to the point (x, y), that is represented as (x’, y’, w).

114.

For 2D transformation the value of third coordinate i.e. w=?(a) 1(b) 0(c) -1(d) Any valueThe question was asked in quiz.I want to ask this question from Matrix Representations and Homogeneous Coordinates in section 2D Transformation and Viewing of Computer Graphics

Answer» RIGHT OPTION is (a) 1

Explanation: For 2D we have (X, y, 1) i.e. w=1.
115.

The matrix representation for rotation in homogeneous coordinates is(a) P’=T+P(b) P’=S*P(c) P’=R*P(d) P’=dx+dyThis question was posed to me in an internship interview.My doubt stems from Matrix Representations and Homogeneous Coordinates topic in chapter 2D Transformation and Viewing of Computer Graphics

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The correct choice is (C) P’=R*P

Easy explanation: The MATRIX representation for ROTATION is P’=R*P.

116.

What is the use of homogeneous coordinates and matrix representation?(a) To treat all 3 transformations in a consistent way(b) To scale(c) To rotate(d) To shear the objectThis question was addressed to me in final exam.This intriguing question originated from Matrix Representations and Homogeneous Coordinates topic in chapter 2D Transformation and Viewing of Computer Graphics

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The correct option is (a) To treat all 3 transformations in a consistent WAY

The EXPLANATION is: To treat all 3 transformations in a consistent way, we use homogeneous coordinates and MATRIX representation.

117.

The matrix representation for scaling in homogeneous coordinates is(a) P’=S*P(b) P’=R*P(c) P’=dx+dy(d) P’=S*SThe question was asked by my college director while I was bunking the class.I want to ask this question from Matrix Representations and Homogeneous Coordinates topic in portion 2D Transformation and Viewing of Computer Graphics

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The correct answer is (a) P’=S*P

To explain I would SAY: The matrix REPRESENTATION for scaling is P’=S*P.

118.

We control the location of a scaled object by choosing the position is known as(a) Pivot point(b) Fixed point(c) Differential scaling(d) Uniform scalingThis question was posed to me in examination.My question is taken from 2D Scaling topic in division 2D Transformation and Viewing of Computer Graphics

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Correct ANSWER is (B) Fixed point

Easiest EXPLANATION: None.

119.

The objects transformed using the equationP’=S*P should be(a) Scaled(b) Repositioned(c) Both a and b(d) Neither a nor bThe question was posed to me in a job interview.This interesting question is from 2D Scaling in chapter 2D Transformation and Viewing of Computer Graphics

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The CORRECT option is (c) Both a and b

The explanation: The OBJECTS transformed using the equation P’=S*P should be SCALED and repositioned.

120.

If the value of sx=1and sy=1 then(a) Reduce the size of object(b) Distort the picture(c) Produce an enlargement(d) No change in the size of an objectI have been asked this question in an interview for job.My doubt stems from 2D Scaling topic in division 2D Transformation and Viewing of Computer Graphics

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The CORRECT answer is (d) No CHANGE in the size of an OBJECT

Easiest explanation: sx=sx=1 does not change the size of the object.

121.

The polygons are scaled by applying the following transformation.(a) X’=x * Sx + Xf(1-Sx) and Y’=y * Sy + Yf(1-Sy)(b) X’=x * Sx + Xf(1+Sx) and Y’=y * Sy + Yf(1+Sy)(c) X’=x * Sx + Xf(1-Sx) and Y’=y * Sy – Yf(1-Sy)(d) X’=x * Sx * Xf(1-Sx) and Y’=y * Sy * Yf(1-Sy)The question was asked in exam.My question is from 2D Scaling topic in chapter 2D Transformation and Viewing of Computer Graphics

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Correct choice is (a) X’=x * Sx + Xf(1-Sx) and Y’=y * SY + YF(1-Sy)

The explanation is: The POLYGONS are scaled by applying the TRANSFORMATION X’=x * Sx + Xf(1-Sx) and Y’=y * Sy + Yf(1-Sy).

122.

If the scaling factors values sx and sy are assigned to unequal values then(a) Uniform rotation is produced(b) Uniform scaling is produced(c) Differential scaling is produced(d) Scaling cannot be doneI had been asked this question during an online exam.My question is taken from 2D Scaling topic in section 2D Transformation and Viewing of Computer Graphics

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The correct answer is (c) Differential SCALING is produced

The best I can EXPLAIN: Unequal VALUES for SX and sy results in differential scaling that is often used in design APPLICATIONS.

123.

Scaling of a polygon is done by computing(a) The product of (x, y) of each vertex(b) (x, y) of end points(c) Center coordinates(d) Only aThe question was asked in an interview for internship.My question comes from 2D Scaling in chapter 2D Transformation and Viewing of Computer Graphics

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Right answer is (d) Only a

Explanation: SCALING of a polygon is done by COMPUTING the product of (x, y) of each vertex with scaling FACTOR sx and SY to produce the transformation coordinates ( Xnew, Ynew).

124.

The two-dimensional scaling equation in the matrix form is(a) P’=P+T(b) P’=S*P(c) P’=P*R(d) P’=R+SI had been asked this question during an interview.Question is from 2D Scaling topic in section 2D Transformation and Viewing of Computer Graphics

Answer» RIGHT OPTION is (b) P’=S*P

Explanation: The 2D SCALING equation is P’=S*P.
125.

If the scaling factors values sx and sy < 1 then(a) It reduces the size of object(b) It increases the size of object(c) It stunts the shape of an object(d) NoneThe question was posed to me in an interview for internship.This interesting question is from 2D Scaling topic in portion 2D Transformation and Viewing of Computer Graphics

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Correct ANSWER is (a) It reduces the size of object

The explanation is: If the scaling factors VALUES sx and SY < 1 then it reduces the size of object.

126.

An ellipse can also be rotated about its center coordinates by rotating(a) End points(b) Major and minor axes(c) Only a(d) NoneI have been asked this question in a job interview.This intriguing question originated from 2D Rotation in division 2D Transformation and Viewing of Computer Graphics

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The correct OPTION is (b) MAJOR and MINOR axes

To ELABORATE: None.

127.

If the scaling factors values sx and sy are assigned to the same value then(a) Uniform rotation is produced(b) Uniform scaling is produced(c) Scaling cannot be done(d) Scaling can be done or cannot be doneThe question was posed to me during an online interview.Asked question is from 2D Scaling topic in section 2D Transformation and Viewing of Computer Graphics

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The CORRECT choice is (b) Uniform scaling is produced

The BEST explanation: When sx and sy are assigned the same value then uniform scaling is produced that maintains relative OBJECT PROPORTIONS.

128.

The original coordinates of the point in polor coordinates are(a) X’=r cos (Ф +ϴ) and Y’=r cos (Ф +ϴ)(b) X’=r cos (Ф +ϴ) and Y’=r sin (Ф +ϴ)(c) X’=r cos (Ф -ϴ) and Y’=r cos (Ф -ϴ)(d) X’=r cos (Ф +ϴ) and Y’=r sin (Ф -ϴ)This question was addressed to me during an online exam.I would like to ask this question from 2D Rotation in chapter 2D Transformation and Viewing of Computer Graphics

Answer» CORRECT ANSWER is (b) X’=r COS (Ф +ϴ) and Y’=r SIN (Ф +ϴ)

To EXPLAIN: The original coordinates of the point in polor coordinates are X’=r cos (Ф +ϴ) and Y’=r sin (Ф +ϴ).
129.

________ is the rigid body transformation that moves object without deformation.(a) Translation(b) Scaling(c) Rotation(d) ShearingI have been asked this question in my homework.I'd like to ask this question from 2D Rotation topic in chapter 2D Transformation and Viewing of Computer Graphics

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The correct option is (c) Rotation

For EXPLANATION: Rotation is the RIGID body transformation that MOVES object without DEFORMATION.

130.

The two-dimensional rotation equation in the matrix form is(a) P’=P+T(b) P’=R*P(c) P’=P*P(d) P’=R+PI got this question in a national level competition.This intriguing question comes from 2D Rotation topic in portion 2D Transformation and Viewing of Computer Graphics

Answer» CORRECT CHOICE is (B) P’=R*P

Easy explanation: The 2D TRANSLATION equation is P’=R*P.
131.

The rotation axis that is perpendicular to the xy plane and passes through the pivot point is known as(a) Rotation(b) Translation(c) Scaling(d) ShearingThe question was asked in final exam.This intriguing question comes from 2D Rotation in division 2D Transformation and Viewing of Computer Graphics

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Correct OPTION is (a) Rotation

To elaborate: The rotation TRANSFORMATION is also described as a rotation about a rotation axis that is perpendicular to the XY PLANE and passes through the PIVOT point.

132.

Positive values for the rotation angle ϴ defines(a) Counterclockwise rotations about the end points(b) Counterclockwise translation about the pivot point(c) Counterclockwise rotations about the pivot point(d) Negative directionI got this question during an internship interview.My query is from 2D Rotation in portion 2D Transformation and Viewing of Computer Graphics

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Correct ANSWER is (C) Counterclockwise rotations about the PIVOT point

Easiest explanation: A positive VALUE for the rotation ANGLE ϴ defines counterclockwise rotations about the pivot point.

133.

To generate a rotation , we must specify(a) Rotation angle ϴ(b) Distances dx and dy(c) Rotation distance(d) All of the mentionedThe question was asked by my college director while I was bunking the class.The above asked question is from 2D Rotation in division 2D Transformation and Viewing of Computer Graphics

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Right answer is (a) ROTATION angle ϴ

Explanation: GENERATE a rotation, we MUST specify rotation angle ϴ of the rotation point or PIVOT point which the object is to be ROTATED.

134.

The basic geometric transformations are(a) Translation(b) Rotation(c) Scaling(d) All of the mentionedThe question was asked in final exam.The doubt is from 2D Translation topic in section 2D Transformation and Viewing of Computer Graphics

Answer» RIGHT OPTION is (d) All of the mentioned

To elaborate: These are the BASIC GEOMETRIC transformations and other transformations are REFLECTION and shear.
135.

To change the position of a circle or ellipse we translate(a) Center coordinates(b) Center coordinates and redraw the figure in new location(c) Outline coordinates(d) All of the mentionedThis question was addressed to me in quiz.The above asked question is from 2D Translation in chapter 2D Transformation and Viewing of Computer Graphics

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The correct option is (b) CENTER coordinates and REDRAW the figure in new location

The EXPLANATION: By TRANSLATING the center coordinates and redraw the figure in new location we can change the position of a CIRCLE or ellipse.

136.

Polygons are translated by adding __________ to the coordinate position of each vertex and the current attribute setting.(a) Straight line path(b) Translation vector(c) Differences(d) Only bThe question was posed to me in an international level competition.My doubt stems from 2D Translation in portion 2D Transformation and Viewing of Computer Graphics

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The CORRECT CHOICE is (d) Only b

The BEST EXPLANATION: NONE.

137.

A straight line segment is translated by applying the transformation equation(a) P’=P+T(b) Dx and Dy(c) P’=P+P(d) Only cI had been asked this question by my college professor while I was bunking the class.The question is from 2D Translation in portion 2D Transformation and Viewing of Computer Graphics

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Right answer is (a) P’=P+T

The explanation is: A straight line SEGMENT is translated by APPLYING the TRANSFORMATION EQUATION P’=P+T to each of line endpoints.

138.

In 2D-translation, a point (x, y) canmove to the new position (x’, y’) by using the equation(a) x’=x+dx and y’=y+dx(b) x’=x+dx and y’=y+dy(c) X’=x+dy and Y’=y+dx(d) X’=x-dx and y’=y-dyThis question was posed to me during an internship interview.Asked question is from 2D Translation topic in section 2D Transformation and Viewing of Computer Graphics

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Right answer is (b) x’=x+DX and y’=y+DY

For EXPLANATION I WOULD say: By ADDING translation distance dx and dy to its originsl position (x, y) we can obtain a new position (x’, y’).

139.

_________ is a rigid body transformation that moves objects without deformation.(a) Rotation(b) Scaling(c) Translation(d) All of the mentionedI got this question in quiz.Enquiry is from 2D Translation topic in portion 2D Transformation and Viewing of Computer Graphics

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Correct choice is (c) Translation

To elaborate: Translation a rigid BODY transformation that MOVES objects WITHOUT DEFORMATION.

140.

The two-dimensional translation equation in the matrix form is(a) P’=P+T(b) P’=P-T(c) P’=P*T(d) P’=pI got this question in an interview for internship.I would like to ask this question from 2D Translation in chapter 2D Transformation and Viewing of Computer Graphics

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The CORRECT CHOICE is (a) P’=P+T

Explanation: The 2D TRANSLATION EQUATION is P’=P+T.

141.

The translation distances (dx, dy) is called as(a) Translation vector(b) Shift vector(c) Both a and b(d) Neither a nor bThis question was posed to me during a job interview.My question is based upon 2D Translation in chapter 2D Transformation and Viewing of Computer Graphics

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The correct choice is (C) Both a and b

To elaborate: The TRANSLATION distances (dx, dy) from its original POSITION is called as translation VECTOR or shift vector.

142.

We translate a two-dimensional point by adding(a) Translation distances(b) Translation difference(c) X and Y(d) Only aThe question was posed to me in exam.The above asked question is from 2D Translation in section 2D Transformation and Viewing of Computer Graphics

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Right choice is (d) Only a

To explain: We can translate 2D POINT by adding translation DISTANCES dx and dy.