case study


Apply the following basic transformations to a  triangle with vertices  (10,20),(10,10),(20,10)
a) Translation with translation factors tx= 10 and ty= 15 
b) Rotation about origin in the anticlockwise direction through an angle 30°
c) Scaling relative to origin with scale factors  sx=2  and  sy=1.5

a)Translation applied to vertex (10,20):
x'=x+tx=10+10=20, y'=y+ty=20+15=35 ;The new vertex is (20,35)

Translation applied to vertex (10,10):
x'=x+tx=10+10=20, y'=y+ty=10+15=25 ;The new vertex is (20,25)

Translation applied to vertex (20,10):
x'=x+tx=20+10=30, y'=y+ty=10+15=25 ;The new vertex is (30,25)
The transformed triangle has vertices ( 20,35),(20,25)and (30,25)

b)Scaling applied to vertex (10,20):
x'=x*sx=10*2=20, y'=y*sy=20*1.5=30 ;The new vertex is (20,30)

Scaling applied to vertex (10,10):
x'=x*sx=10*2=20, y'=y*sy=10*1.5=15 ;The new vertex is (20,15)

Scaling applied to vertex (20,10):
x'=x*sx=20*2=40, y'=y*sy=10*1.5=15 ;The new vertex is (40,15)
The transformed triangle has vertices ( 20,30),(20,15)and (40,15) Click to view animation

c)Rotation applied to vertex (10,20):
The new vertex is (-1.34,22.32)
Rotation applied to vertex (10,10):
The new vertex is (3.66,13.66)
Rotation applied to vertex (20,10):
The new vertex is (12.32,13.66)
The transformed triangle has vertices ( -1.34,22.32),(3.66,13.66)and (12.32,13.66)

Geometric Transformations by Mrs.S.Sathya

  • Introduction

    Geometric tranformations are the trasformations used to alter or manipulate pictures in a graphics package.Changes in orientation,size … Read more »

  • Basic Transformations

    There are three basic transformations from which any other transformation can be obtained.They change the orientation,size and shape… Read more »

  • Translation

    Translation is a transformation that repositions and object along a straight line path from one coordinate location to another. … Read more »

  • Rotation

    Rotation of an object is repositioning it along a circular path in the xy plane.To rotate, we need to specify a rotation angle θ and the rotation point(xr,yr) about which the object is rotated. … Read more »

  • Scaling

    A Scaling transformation alters the size of an object.Scaling is carried out by applying scaling factors sx,sy for xand y direction … Read more »

  • Homogeneous Coordinates

    Homogeneous coordinates are coordinates used to represent the cartesian coordinate (x,y) as three - element vector.We represent each cartesian … Read more »

  • Matrix Representations

    For translation, the transformation equvations are written as … Read more »

  • Other Transformations

    Other transformations inculde Reflection and Shear. Reflections : Reflections are transformations that rotate an object 180" about a reflection axis. … Read more »