Spiderweb

It took me a suprisingly long time on a plane ride to figure a formula for the intersection point of two line segments

The general idea is to set up a system of parametric equations where t ranges from 0 (output is the first endpoint of the segment) to 1 (output is the first endpoint of the segment)

x₀ = x_0:0 * (1 - t₀) + x_0:1 * t₀ y₀ = y_0:0 * (1 - t₀) + y_0:1 * t₀ x₁ = x_1:0 * (1 - t₁) + x_1:1 * t₁ y₁ = y_1:0 * (1 - t₁) + y_1:1 * t₁

Since we are solving for an intersection point, x₀ = x₁ and y₀ = y₁. Thus we end up with two equations each with two unknowns: t₀ and t₁

x_0:0 * (1 - t₀) + x_0:1 * t₀ = x_1:0 * (1 - t₁) + x_1:1 * t₁ y_0:0 * (1 - t₀) + y_0:1 * t₀ = y_1:0 * (1 - t₁) + y_1:1 * t₁

With a bit of algebra it is straightforward to solve for both variables. If they both exist in the range [0, 1], the segments intersect. Find the intersection point by substituting their values into the original equations.