Calculate surface area of triangles in 2D or 3D

Compute the unsigned surface area of triangles defined by vertex coordinates. Works with both 2D (xy) and 3D (xyz) input. For 2D input, z coordinates are assumed to be zero.

triangle_surface_area(x)

Arguments

x

A matrix with 2 or 3 columns (x, y) or (x, y, z). Each set of 3 consecutive rows defines one triangle.

Value

A numeric vector of surface areas, one per triangle.

Details

The area is calculated using the cross product method: Area = 0.5 * ||(v1 - v0) x (v2 - v0)||

For 2D input, this reduces to the absolute value of the shoelace formula.

Examples

# 2D triangle (unit right triangle)
tri_2d <- matrix(c(0, 0,
                   1, 0,
                   0, 1), ncol = 2, byrow = TRUE)
triangle_surface_area(tri_2d)  # 0.5
#> [1] 0.5

# 3D triangle
tri_3d <- matrix(c(0, 0, 0,
                   1, 0, 0,
                   0, 1, 1), ncol = 3, byrow = TRUE)
triangle_surface_area(tri_3d)
#> [1] 0.7071068