Central projection problem

Intuitively speaking, on the Euclidean plane we usually contact, two intersecting straight lines may become parallel lines (with the original intersection as the projection point) or intersecting lines, but of course they cannot become straight lines; After the central projection, the isosceles triangle may no longer be an isosceles triangle or even a triangle (for example, there is a line between two parallel lines), but it may still be an isosceles triangle.

In projective geometry, projective mapping does not change the combination relationship between points and lines (combination relationship in projective geometry), that is, common points, collinear lines, etc. Some quantities (such as cross ratio) will not change. According to these unchangeable things, we can determine the properties of the graph after projective mapping.

Therefore, in projective geometry, whether two intersecting lines pass through central projection (perspective transformation) or two intersecting lines (the combination relationship is unchanged);

After the center projection of an isosceles triangle (not strictly a triangle, it can be called trilinear), the corresponding figure is still trilinear. Because the angle is no longer constant in projective geometry, this trilinear is very different from the commonly understood triangle.