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Explain Homogeneous Coordinates with example.

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**Solution:**

In 3-D space, a physical point is located and if we want to change from one coordinate to another frame then we need to use a 4 X 4 homogenous transformation matrix.

As mentioned earlier, in regard to 3D computer graphics, homogeneous coordinates are useful in certain situations. We will look at some of those situations here.

**It consists of 4 sub-matrices as given below:**

$3 \mathrm{X} 3$ sub - matrix $\mathrm{R}$ is a rotation matrix

$3 \mathrm{X} 1$ column vector $\mathrm{p}$ is a translation matrix

$1 \mathrm{X} 3 \eta^{\mathrm{T}}$ is a perspective vector

Scalar $\sigma$ is a non-zero scale factor set to unity.

$ \mathrm{T}=\left[\begin{array}{ll} R & P \\ \eta & \sigma \end{array}\right]\\ $

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