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trvec2tform

Convert translation vector to homogeneous transformation

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Syntax

tform = trvec2tform(trvec)

Description

tform = trvec2tform(trvec) converts the Cartesian representation of the translation vector trvec to the corresponding homogeneous transformation tform. When using the transformation matrix, premultiply it by the coordinates to be transformed (as opposed to postmultiplying).

example

Examples

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Open Live Script
trvec = [0.5 6 100];
tform = trvec2tform(trvec)
tform = 4×4

    1.0000         0         0    0.5000
         0    1.0000         0    6.0000
         0         0    1.0000  100.0000
         0         0         0    1.0000

Input Arguments

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Cartesian representation of a translation vector, specified as an n-by-2 matrix if tform is a 3-by-3-by-n array and an n-by-3 matrix if tform is a 4-by-4-by-n array. n is the number of translation vectors. Each vector is of the form [x y] or [x y z].

Example: [0.5 6 100]

Output Arguments

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Homogeneous transformation, returned as a 3-by-3-by-n array or 4-by-4-by-n array. n is the number of homogeneous transformations. When using the rotation matrix, premultiply it with the coordinates to be rotated (as opposed to postmultiplying).

Example: [0 0 1 0; 0 1 0 0; -1 0 0 0; 0 0 0 1]

2-D homogeneous transformation matrices are of the form:

T=[r11r12t1r21r22t2001]

3-D homogeneous transformation matrices are of the form:

T=[r11r12r13t1r21r22r23t2r31r32r33t30001]

More About

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Homogeneous Transformation Matrices

Homogeneous transformation matrices consist of both an orthogonal rotation and a translation.

2-D Transformations

2-D transformations have a rotation θ about the z-axis:

Rz(θ)=[cosθ−sinθsinθcosθ]

, and a translation along the x and y axis:

t=[xy]

, resulting in the 2-D transformation matrix of the form:

T=[Rt01×21]=[I2t01×21]·[R001×21]

3-D Transformations

3-D transformations contain information about three rotations about the x-, y-, and z-axes:

Rx(ϕ)=[1000cosϕsinϕ0−sinϕcosϕ],Ry(ψ)=[cosψ0sinψ010−sinψ0cosψ],Rz(θ)=[cosθ−sinθ0sinθcosθ0001]

and after multiplying become the rotation about the xyz-axes:

Rxyz=Rx(ϕ)Ry(ψ)Rz(θ)=[cosϕcosψcosθ−sinϕsinθ−cosϕcosψsinθ−sinϕcosθcosϕsinψsinϕcosψcosθ+cosϕsinθ−sinϕcosψsinθ+cosϕcosθsinϕsinψ−sinψcosθsinψsinθcosψ]

and a translation along the x-, y-, and z-axis:

t=[xyz]

, resulting in the 3-D transformation matrix of the form:

T=[Rt01x31]=[I3t01x31]·[R001x31]

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2015a

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See Also

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