scaling contd

Scaling about fixed point

We can control the position of the scaled object by choosing a fixed point that remaines unchanged after scaling
If (xf,yf) is the fixed point than the transformation equations to scale the point P(x,y) is given by
x'=xf+(x-xf)sx
y'=yf+(y-yf)sy

Scaling about pivot fixed can be performed by a sequence of translate - scale about origin - translate operations
  1. Translate the object so that the fixed point position is moved to the coordinate origin
  2. Scale the object about the coordinate origin
  3. Translate the object so that the fixed point is returned to its original position.

 

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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 »