There are three basic transformations from which any other transformation can be obtained.They change the orientation,size and shape… Read more »
rotation contd
Rotating a point P(x,y) about any arbitrary pivot point(xr,yr)
The transformation equations for rotating a point (x,y) through an angle θ about the pivot point(xr,yr) are
x'=xr+ (x - xr) cos θ -(y - yr) sin θ
y'=yr+ (x - xr) sin θ + (y - yr)cos θ.
Rotation about pivot point can be performed by a sequence of translate - rotate - translate operations
- Translate the object so that the pivot point position is moved to the coordinate origin
- Rotate the object about the coordinate origin
- Translate the object so that the pivot point is returned to its original position.
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Geometric Transformations by Mrs.S.Sathya
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Introduction
Geometric tranformations are the trasformations used to alter or manipulate pictures in a graphics package.Changes in orientation,size … Read more »
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Basic Transformations
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 »