Point-to-segment distance (vectorized)

Computes the Euclidean distance from one or more points `(px, py)` to the line segment defined by endpoints `A(ax, ay)` and `B(bx, by)`. The projection is clamped to the segment (i.e., `pos_on_seg` is restricted to `[0, 1]`).

Usage

point_segment_distance_vec(px, py, ax, ay, bx, by)

Arguments

px, py

Numeric vectors (or scalars) giving the x/y coordinates of the query point(s).

ax, ay

Numeric scalars giving the x/y coordinates of endpoint A.

bx, by

Numeric scalars giving the x/y coordinates of endpoint B.

Value

A numeric vector of distances, with length equal to `max(length(px), length(py))` (after R's usual vector recycling rules).

Details

Let `v = B - A` and `pos_on_seg = ((P - A) · v) / ||v||^2`. The closest point on the infinite line is `A + pos_on_seg v`; clamping `pos_on_seg` to `[0, 1]` yields the closest point on the segment.

If `A` and `B` are identical (`||v||^2 == 0`), the function returns the distance from `P` to `A`.

Examples

# Single point to a horizontal segment
point_segment_distance_vec(px = 1, py = 2, ax = 0, ay = 0, bx = 3, by = 0)
#> [1] 2

# Multiple points (vectorized)
px <- c(0, 1, 2, 3)
py <- c(1, 1, 1, 1)
point_segment_distance_vec(px, py, ax = 0, ay = 0, bx = 3, by = 0)
#> [1] 1 1 1 1

# Degenerate segment (A == B)
point_segment_distance_vec(px = c(0, 1), py = c(0, 1), ax = 0, ay = 0, bx =
0, by = 0)
#> [1] 0.000000 1.414214