Compuer Graphics(Numericals)- 1

Computer Graphics 

Numericals Questions

Q1 Compute co-ordinate points of circle drawn with center at (0,0) and radius 5, using mid-point circle.

Q2 Draw line segment from point (2,4) to (9,9) using DDA algorithm.

Q3 Using DDA algorithm draw line segments from point (1,1) to (9,7).

Q4 What steps are required to plot a line whose slope is between 0 degree to 45 degree using Bresenham's line generation method? Draw a line joining(5,4) and (11,15) using the Bresenham's line generation algorithm.

Q5 Write a C program to implement DDA line drawing algorithm.

Q6 Using any of the line clipping algorithm obtain the visible position of the following line segment

1) P1=(0.5,0.4)  P2=(1.6,0.7)

2) P1=(0.4,-1.6) P2=(0.4,2.7)

3) P1=(0.4,-1.6) P2=(0.8,-2.7)

4) P1=(-2,-3)   P2=(3.5)

Q7 Find the new co-ordinate of a triangle A(0,0), B(1,1), C(5,2) after it has been

a) Magnified to twice its size

b) Reduced to half its size

Q8 Perform a 45 degree rotation of a triangle A(0,0), B(1,1), C(5,2) about the 

origin.

Q9 Translate a square ABCD with the coordinates A(0,0), B(5,0), C(5,5), D(0,5) by 

2 units in x-direction and 3 units in y direction.

Q10 Perform a 45 degree rotation of triangle A(0,0), B(1,1), C(5,2) about 

an arbitary point P(-1,-1)

Q11 Perform a rotation of triangle A(1,2), B(2,4), C(1,1) about P(-1,-2) in anti-clockwise direction by 60 degree.

Q12 Reflect the diamond-shaped polygon whose  vertices are A(-1,0), B(0,-2), C(0,0) and D (0,2) about

a) The horizontal line y=2

b) The vertical line x=2

c) the line y=x+2

Q13 Consider a given triangle ABC where A(1,0), B(0,1), C(1,1) and apply the following transformation as below

1) Rotate around the origin and then translate in the direction of vector(1,0) 

2) Translate first in the direction of vector (1,0) and then rotate by 45 degree.

Q14 Obtain the mirror reflection of the triangle formed by the vertices A(0,3), B(2,0) and C(3,2) about the line passing through the points (1,3) and (-1,-1)

Q15 Show that Sa,b.Sc,d=Sa,b.Sa,b=Sac,Sbd

Q16 Find the isometric view of a cuboid. The size of cuboid is 10 x 8 x 6, which is lying at the origin.

Q17 Obtain a transformation matrix for perspective projection for a given object projected onto x=4 plane as viewed from (6,0,0)

Q18 Consider the line segment AB parallel to z axis with end points A(3,2,4) and 

B(3,2,8). Perform a perspective projection onto the z=0 plane from the center of projection at E(0,0,-2). Also find out the vanishing point.

Q19 Obtain the perspective transformation onto z=-2 plane where the center of projection is at (0,0,18)

Q20 Find equation of plance which passes through point P(0,0,0) and the normal

to the plane is given by N(1,0,-1)

Q21 Calculate the equation of plane for a quadrilateral planar polygon described by the four vertices V1(1,0,1) , V2(1,1,0) , V3(0,1,1) nd V4(1,1,1)

Q22 Given P0(1,1);P1(2,3);P2(4,3);P3(3,1) as vertices of Beizer curve. Determine

three points on Bezier curve.

Q23 To prove P(u=0)=P0

Q24 To prove P(1)=Pn

Q25 Based on the Bezier curve definition derive the equation of 3 points Bezier curve defined by the following control point (-1,0),(0,2) & (1,0)

Q26 What is an image aspect ratio, if an image has a height of 2 inches and aspect ratio of 1.5, What is its width?