# Multiple-View Geometry ### Chapter 1: Introduction #### Projective Geometry * preserve straightness * Projective in homogeneous coordinates: both$$(x, y, 1)$$and$$(x, y, 0)$$are defined #### Affine Geometry * In Projective Space, we single out a particular line and call it the line at infinity. * With this line at infinity, we are able to define parallelism, and equal length of two intervals. #### Euclidean Geometry * In Affine Geometry, we further single out two circular points in the line at infinity. * Two circular points: $$(1, ±i, 0)^\mathrm{T}$$which satisfy a pair of real equations: $$x^2 + y^2 = 0; w = 0$$. * With two circular points, we are able to define angle and length ratios. * Representation: $$(x, y)$$ --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://wiki.hanzheteng.com/algorithm/cv/multiple-view-geometry.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.