The document discusses composite transformations, which involve performing two or more transformations in sequence. It provides examples that two successive translations can be represented as a single translation, and two successive rotations can be represented as a single rotation. It also explains that scaling an object with respect to a fixed point can be achieved through a sequence of translations, scaling around the origin, and inverse translations, as represented by a composite matrix.

1. Prof. Neeraj Bhargava
Pooja Dixit
Department of Computer Science
School of Engineering & System Sciences
MDS, University Ajmer, Rajasthan, India
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2.  A composite transformation (or composition of transformations)
is two or more transformations performed one after the other.
Sometimes, a composition of transformations is equivalent to a
single transformation. The following is an example of a
translation followed by a reflection. The original triangle is the
brown triangle and the image is the blue striped triangle. The
brown striped triangle shows the intermediate step after the
translation has taken place.
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3.  if we translate a shape with 2 successive translation
vectors: (tx1, ty1) and (tx2, ty2),it is equal to a
single translation of (tx1+ tx2, ty1+ ty2).
 This additive property can be demonstrated by
composite transformation matrix:
•This demonstrates that 2 successive translations are additive
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4.  if we rotate a shape with 2 successive rotation angles: and
about the origin, it is equal to rotating the shape once by an
angle ? + a about the origin.Similarly, this additive property
can be demonstrated by composite transformation matrix:
This demonstrates that 2 successive rotations are additive
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5.  SCALING
 The animation illustrates a transformation sequence to
produce scaling with respect to a selected fixed position (a,b)
using a scaling function that can only scale relative to the
coordinate origin.
 Translate object so that the fixed point coincides with the
coordinate origin.
 Scale the object with respect to the coordinate origin.
 Use the inverse translation of step 1 to return the object to its
original position.
 The composite matrix for this sequence is obtained as:
 where,