trinterp

Interpolate SE(3) homogeneous transformations

TRINTERP(T0, T1, S) is a homogeneous transform (4×4) interpolated between T0 when S=0 and T1 when S=1. T0 and T1 are both homogeneous transforms (4×4). If S (N×1) then T (4×4× N) is a sequence of homogeneous transforms corresponding to the interpolation values in S.

TRINTERP(T1, S) as above but interpolated between the identity matrix when S=0 to T1 when S=1.

TRINTERP(T0, T1, M) as above but M is a positive integer and return a sequence (4×4× M) of homogeneous transforms linearly interpolating between T0 and T1 in M steps.

TRINTERP(T1, M) as above but return a sequence (4×4× M) of homogeneous interpolating between identity matrix and T1 in M steps.

Notes

T0 or T1 can also be an SO(3) rotation matrix (3×3) in which case the result is (3×3× N).
Rotation is interpolated using quaternion spherical linear interpolation (slerp).
To obtain smooth continuous motion S should also be smooth and continuous, such as computed by tpoly or lspb.

trinterp

Notes

See also