Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Table 2

Equations to calculate the intersection between a circle and a 2D segment.

Segment function	Circle function	Segment-Circle intersection equation on 𝑡
𝑥=𝑥1+(𝑥2−𝑥1)⋅𝑡𝑦=𝑦1+(𝑦2−𝑦1)⋅𝑡𝑡∈[0,…,1]	𝑥^2+𝑦^2=𝑅^2	(𝑥1+(𝑥2−𝑥1)⋅𝑡)^2+(𝑦1+(𝑦2−𝑦1)⋅𝑡)^2=𝑅^2