klampt.math.so3 module
Operations for rigid rotations in Klampt. All rotations are represented by a 9-list specifying the entries of the rotation matrix in column major form.
In other words, given a 3x3 matrix:
[a11,a12,a13]
[a21,a22,a23]
[a31,a32,a33],
Klamp’t represents the matrix as a list [a11,a21,a31,a12,a22,a32,a13,a23,a33].
The reasons for this representation are 1) simplicity, and 2) a more convenient interface with C code.
- klampt.math.so3.apply(R, point)[source]
Applies the rotation to a point.
- Return type:
Sequence[float]
- klampt.math.so3.matrix(R)[source]
Returns the 3x3 rotation matrix corresponding to R.
- Return type:
Sequence[Sequence[float]]
- klampt.math.so3.from_matrix(mat)[source]
Returns a rotation R corresponding to the 3x3 rotation matrix mat.
- Return type:
Sequence[float]
- klampt.math.so3.ndarray(R)[source]
Returns the 3x3 numpy rotation matrix corresponding to R.
- Return type:
- klampt.math.so3.from_ndarray(mat)[source]
Returns a rotation R corresponding to the 3x3 rotation matrix mat.
- Return type:
Sequence[float]
- klampt.math.so3.rpy(R)[source]
Converts a rotation matrix to a roll,pitch,yaw angle triple. The result is given in radians.
- Return type:
Sequence[float]
- klampt.math.so3.from_rpy(rollpitchyaw)[source]
Converts from roll,pitch,yaw angle triple to a rotation matrix. The triple is given in radians. The x axis is “roll”, y is “pitch”, and z is “yaw”.
- Return type:
Sequence[float]
- klampt.math.so3.rotation_vector(R)[source]
Returns the rotation vector w (exponential map) representation of R such that e^[w] = R. Equivalent to axis-angle representation with w/||w||=axis, ||w||=angle.
- Return type:
Sequence[float]
- klampt.math.so3.axis_angle(R)[source]
Returns the (axis,angle) pair representing R
- Return type:
Tuple
- klampt.math.so3.from_axis_angle(aa)[source]
Converts an axis-angle representation (axis,angle) to a 3D rotation matrix.
- Return type:
Sequence[float]
- klampt.math.so3.from_rotation_vector(w)[source]
Converts a rotation vector representation w to a 3D rotation matrix.
- Return type:
Sequence[float]
- klampt.math.so3.moment(R)
Returns the rotation vector w (exponential map) representation of R such that e^[w] = R. Equivalent to axis-angle representation with w/||w||=axis, ||w||=angle.
- Return type:
Sequence[float]
- klampt.math.so3.from_moment(w)
Converts a rotation vector representation w to a 3D rotation matrix.
- Return type:
Sequence[float]
- klampt.math.so3.from_quaternion(q)[source]
Given a unit quaternion (w,x,y,z), produce the corresponding rotation matrix.
- Return type:
Sequence[float]
- klampt.math.so3.quaternion(R)[source]
Given a Klamp’t rotation representation, produces the corresponding unit quaternion (w,x,y,z).
- Return type:
Tuple
- klampt.math.so3.distance(R1, R2)[source]
Returns the absolute angle one would need to rotate in order to get from R1 to R2
- Return type:
float
- klampt.math.so3.error(R1, R2)[source]
Returns a 3D “difference vector” that describes how far R1 is from R2. More precisely, this is the (local) Lie derivative, which is the rotation vector representation of R1*R2^T.
Fun fact: the error w=error(R1,R2) is related to the derivative of interpolate(R2,R1,u) at u=0 by d/du interpolate(R2,R1,0) = mul(cross_product(w),R2).
You can also recover R1 from w via R1 = mul(from_moment(w),R2).
- Return type:
float
- klampt.math.so3.cross_product(w)[source]
Returns the cross product matrix associated with w.
The matrix [w]R is the derivative of the matrix R as it rotates about the axis w/||w|| with angular velocity ||w||.
- Return type:
Sequence[float]
- klampt.math.so3.diag(R)[source]
Returns the diagonal of the 3x3 matrix reprsenting the so3 element R.
- Return type:
Sequence[float]
- klampt.math.so3.deskew(R)[source]
If R is a (flattened) cross-product matrix of the 3-vector w, this will return w. Otherwise, it will return a representation w of (R-R^T)/2 (off diagonals of R) such that (R-R^T)/2 = cross_product(w).
- Return type:
Sequence[float]
- klampt.math.so3.rotation(axis, angle)[source]
Given a unit axis and an angle in radians, returns the rotation matrix.
- Return type:
Sequence[float]
- klampt.math.so3.canonical(v)[source]
Given a unit vector v, finds R that defines a basis [x,y,z] such that x = v and y and z are orthogonal
- Return type:
Sequence[float]
- klampt.math.so3.align(a, b)[source]
Returns a minimal-angle rotation that aligns the vector a to align with the vector b. Both a and b must be nonzero.
- Return type:
Sequence[float]
- klampt.math.so3.interpolate(R1, R2, u)[source]
Interpolate linearly between the two rotations R1 and R2.
- Return type:
Sequence[float]
- klampt.math.so3.interpolator(R1, R2)[source]
Returns a function of one parameter u that interpolates linearly between the two rotations R1 and R2. After f(u) is constructed, calling f(u) is about 2x faster than calling interpolate(R1,R2,u).
- Return type:
Callable