Compute a Reference Frame from Three Non-Colinear Markers — compute_frame

Constructs a 4x4 transformation matrix representing a reference frame defined by three non-colinear 3D points. The frame is based on: - Origin: marker_2 - X-axis: from marker_2 to marker_3 - Y-axis: from marker_2 to marker_1 - Z-axis: orthogonal to the XY-plane (via cross product) Note that x is re-computed via cross product of y and z to make the frame orthogonal

Usage

compute_frame_generic(marker_1, marker_2, marker_3)

Arguments

marker_1: A numeric vector of length 3, representing a 3D point.
marker_2: A numeric vector of length 3, representing a 3D point (used as origin).
marker_3: A numeric vector of length 3, representing a 3D point.

Value

A 4x4 numeric matrix representing a homogeneous transformation matrix.

Examples

compute_frame_generic(c(1, 0, 0), c(0, 0, 0), c(0, 1, 0))
#>      x y  z o
#> [1,] 0 1  0 0
#> [2,] 1 0  0 0
#> [3,] 0 0 -1 0
#> [4,] 0 0  0 1