# cross ratio - how to calculate values with it?

I have this scenario here. It is a projective image.

1. What would be the cross-ratio formula for these points?: $$v,c_{r},r_{2},r_{1}$$

2.And let be $$dst(r_{2},r_{1})=30cm$$ in the real world. How can I calculate the other values (distances) between the points given in 1.?

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## 1 Answer

I found it out myself:
Look at this picture.

a is the real world and b is the projective image of it. The interesting thing is that the cross ratio of the points v,cr,r2,r1 in picture a is the same as the cross ratio in picture b. That´s called invariance. So the following relationship can be written in a formula:
THIS explaines the rest.

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