About Cross Ratio Calculator (Formula)
A Cross Ratio Calculator is a mathematical tool used in projective geometry to compute the cross ratio of four collinear points on a line. The cross ratio is a projective invariant, which means it remains the same regardless of the choice of coordinates or transformations applied to the line. The formula for calculating the cross ratio (CR) is as follows:
Cross Ratio (CR) = ((A – C) × (B – D)) / ((A – D) × (B – C))
Where:
- A, B, C, and D are the coordinates of the four collinear points on the line.
The cross ratio is a fundamental concept in projective geometry and is used to define the concept of a projective transformation, which preserves collinearity and incidence between points, lines, and conics.
Cross Ratio Calculators are used in various fields, including mathematics, computer graphics, and computer vision, where projective geometry concepts are applied to solve problems related to geometric transformations, perspective, and image analysis. They simplify the calculation of the cross ratio, a critical parameter in projective geometry and its applications.