What is the advantage of homogeneous coordinate system over euclidean coordinate system?
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The theorems from Euclidean geometry does not provide anything regarding the coordinates, and lack the guides for calculating data while applying them to physical theorems.
This is exactly the advantage homogeneous coordinates have over euclidean coordinates. They provide all the calculation strategies which are required to solve a geometrical theorem, unlike euclidean theorems.
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The advantages of the homogeneous coordinate system are:
They help in capturing composite transformations conveniently.
They can display a point at infinity that does not exist. Capturing the concept of infinity is the main purpose of homogeneous coordinates while Euclidean coordinate system cannot does so, it is used to denote the location of the object.
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