Homogenous coördinates

Homogenous coördinates are a system of coördinates used to label (not uniquely) points in a Projective space $P 𝑛 𝕂$ . A projective point is labelled by $𝑛 + 1$ scalars that are not all zero, written as

𝑝 = (𝑝 1 : 𝑝 2 : \dots : 𝑝 𝑛 + 1)

where any nonzero multiple of the coördinates denotes the same point. Viewing $P 𝑛 𝕂$ as the quotient $𝕂 𝑛 ∖ {0} / 𝕂 \times$ , the point $(𝑝 1 : \dots : 𝑝 𝑛 + 1)$ denotes the equivalence class of $(𝑝 1, \dots, 𝑝 𝑛 + 1)$ .

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Homogenous coördinates

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