Virtual Reality Toolbox™

Rotation Matrix to VRML Rotation - Convert rotation matrix into representation used in VRML

Library

Virtual Reality Toolbox

Description

Takes an input of a rotation matrix and outputs the axis/angle rotation representation used for defining rotations in VRML. The rotation matrix can be either a 9-element column vector or a 3-by-3 matrix defined columnwise.

Block Parameters Dialog Box

Maximum value to treat input value as zero — The input is considered to be zero if it is equal to or lower than this value.

Rotation Matrix

A representation of a three-dimensional spherical rotation as a 3-by-3 real, orthogonal matrix R: R^TR = RR^T = I, where I is the 3-by-3 identity and R^T is the transpose of R.

In general, R requires three independent angles to specify the rotation fully. There are many ways to represent the three independent angles. Here are two:

• You can form three independent rotation matrices R₁, R₂, R₃, each representing a single independent rotation. Then compose the full rotation matrix R with respect to fixed coordinate axes as a product of these three: R = R₃*R₂*R₁. The three angles are Euler angles.

• You can represent R in terms of an axis-angle rotation n = (n_x,n_y,n_z) and θ with n*n = 1. The three independent angles are θ and the two needed to orient n. Form the antisymmetric matrix:

  

  Then Rodrigues' formula simplifies R:

  

Rotation Between 2 Vectors

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