2.1 Axis-Angle to Rotation Matrix 问题背景:已知一个具有 J 个关节点(包含Root)的 Articulated Skeleton 在 Neutral Pose 下的节点位置 \mathbf{X}_T \in \mathbb{R}^{3\times J} 根据给定的 pose向量 \bm{\vartheta} \in \mathbb{R}^{3 J} ,如何变形得到 \mathbf{X}^{\prime}?
巧妙范例(1) 参见 RotationTransform EulerMatrix RollPitchYawMatrix Rotate Dot UnitVector Sin ReflectionMatrix ScalingMatrix PauliMatrix OrthogonalMatrix UnitaryMatrix AnglePath3D Function Repository: RotationMatrixToQuaternion QuaternionToRotationMatrix AxisAngle RandomRotationQuaternion技术...
或者D3DX函数D3DXQuaternionToAxisAngle求出旋转轴和旋转角度 得到了旋转轴axis和旋转角度angle以后就可以利用D3DXMatrixRotationAxis来求取旋转矩阵,也可以手动求解,看这篇博文。也可以一步到位,用D3DXMatrixRotationQuaternion函数直接求得旋转矩阵
This can be used to generate the matrix representation of the axis angle representation of rotation: Matrix to axis-angle Axis-angle to matrix
A rotation matrix is a matrix used to rotate an axis about a given point. The center of a Cartesian coordinate frame is typically used as that point of rotation. Rotation matrices are used for computations in aerospace, image processing, and other technical computing applications. ...
由Quaternion求Rotation Matrix 可以利用上面的公式先求出旋转轴和旋转角度 axis.x = q.x / sin(theta / 2) axis.y = q.y / sin(theta / 2) axis.z = q.z / sin(theta / 2) theta = 2 * arccos(q.w) 或者D3DX函数D3DXQuaternionToAxisAngle求出旋转轴和旋转角度 ...
Rotation matrix from a rotation axis and angle of rotationMichail Tsagris
RotationMatrix[θ] gives the 2D rotation matrix that rotates 2D vectors counterclockwise by θ radians. RotationMatrix[θ,w] gives the 3D rotation matrix for a counterclockwise rotation around the 3D vector w. RotationMatrix[{u,v}] gives the matrix that rotates the vector u to the directi...
rotm = axang2rotm(axang) converts a rotation given in axis-angle form, axang, to an orthonormal rotation matrix, rotm. When using the rotation matrix, premultiply it with the coordinates to be rotated (as opposed to postmultiplying). exampleExamples...
For an alterative we to think about using a matrix to represent rotation see basis vectors here. Rotation about the z axis is given by the following matrix: Rotation about z axis is: Rz = cos(a) -sin(a) 0 sin(a) cos(a) 0 0 0 1 For example if we choose an angle of +90 ...