Create coordinate system with vector components

Jimmy He

If I know the vector components of the principal coordinate axes, how should I go about creating a coordinate system using Mechanical scripting?

Jimmy He

Below is a code snippet to achieve this:
`

import math

##########################################################
# Created by P. Thieffry
# Last update: 2021/04/07
def dotProduct(v1,v2):
    return v2[0]*v1[0]+v2[1]*v1[1]+v2[2]*v1[2]

def TransformationMatrix(origCS,targCS):
    # compute transformation matrix to align origCS to targCS
    # All coordinates are expressed in the global CS
    #
    tMat=[[dotProduct(origCS[0],targCS[0]),dotProduct(origCS[0],targCS[1]),dotProduct(origCS[0],targCS[2])],
    [dotProduct(origCS[1],targCS[0]),dotProduct(origCS[1],targCS[1]),dotProduct(origCS[1],targCS[2])],
    [dotProduct(origCS[2],targCS[0]),dotProduct(origCS[2],targCS[1]),dotProduct(origCS[2],targCS[2])]]
    return tMat
##########################################################

##########################################################
# Modified from: https://learnopencv.com/rotation-matrix-to-euler-angles/
def rotationMatrixToEulerAngles_ZYX( R ) :
    sy = math.sqrt(R[0][0] * R[0][0] +  R[1][0] * R[1][0])
    singular = sy < 1e-6
    factor = 180./math.pi
    if  not singular :
        x = math.atan2(R[2][1] , R[2][2])*factor
        y = math.atan2(-R[2][0], sy)*factor
        z = math.atan2(R[1][0], R[0][0])*factor
    else :
        x = math.atan2(-R[1][2], R[1][1])*factor
        y = math.atan2(-R[2][0], sy)*factor
        z = 0
    return [z, y, x]
##########################################################

def norm( v ):
    return ( v[0]**2 + v[1]**2 + v[2]**2 )**0.5

def unit_vec( v ):
    n = norm( v )
    return [ _/n for _ in v ]

def CreateCS( origin , xyz , name , unit='mm' ):
    # Create coordinate
    testCS = ExtAPI.DataModel.Project.Model.CoordinateSystems.AddCoordinateSystem()
    testCS.OriginDefineBy= CoordinateSystemAlignmentType.Fixed
    testCS.OriginX = Quantity(origin[0],unit)
    testCS.OriginY = Quantity(origin[1],unit)
    testCS.OriginZ = Quantity(origin[2],unit)

    # Get rotations
    origCS = [[1,0,0],[0,1,0],[0,0,1]]
    tMat = TransformationMatrix(origCS,xyz)
    angs = rotationMatrixToEulerAngles_ZYX(tMat)

    ##########################################################
    # Created by M.H. Pernelle
    # Last update: 2021/06
    # Perform transformation
    testCS.PrimaryAxisDefineBy = CoordinateSystemAlignmentType.GlobalX
    # Rotation Z
    testCS.RotateZ()
    testCS.SetTransformationValue(1,angs[0])
    # Rotation Y
    testCS.RotateY()
    testCS.SetTransformationValue(2,angs[1])
    # Rotation X
    testCS.RotateX()
    testCS.SetTransformationValue(3,angs[2])
    ##########################################################

    # Set name
    testCS.Name = name

# Example
xyz = [[0.5,0.5,-0.70711],[-0.14645,0.85355,0.5],[0.85355,-0.14645,0.5]]
CreateCS( [1,2,3] , xyz , 'my_cs' , unit='m' )

`

Mike.Thompson

@Jimmy He ,
If you have any time/desire I am hoping to expand this solution to have a function that creates a CS with inputs of XYZ origin and a Z vector definition. X and Y can be arbitrary, but the Z direction should be from a unit vector.

Thanks for any help with this.

Jimmy He

Hi @Mike.Thompson

Please see the updated solution here. The user can specify the unit of the origin XYZ. Angle unit is detected in the code and appropriate conversion is performed.

import math

##########################################################
# Created by P. Thieffry
# Last update: 2021/04/07
def dotProduct(v1,v2):
    return v2[0]*v1[0]+v2[1]*v1[1]+v2[2]*v1[2]

def TransformationMatrix(origCS,targCS):
    # compute transformation matrix to align origCS to targCS
    # All coordinates are expressed in the global CS
    #
    tMat=[[dotProduct(origCS[0],targCS[0]),dotProduct(origCS[0],targCS[1]),dotProduct(origCS[0],targCS[2])],
    [dotProduct(origCS[1],targCS[0]),dotProduct(origCS[1],targCS[1]),dotProduct(origCS[1],targCS[2])],
    [dotProduct(origCS[2],targCS[0]),dotProduct(origCS[2],targCS[1]),dotProduct(origCS[2],targCS[2])]]
    return tMat
##########################################################

##########################################################
# Modified from: https://learnopencv.com/rotation-matrix-to-euler-angles/
def rotationMatrixToEulerAngles_ZYX( R ) :
    sy = math.sqrt(R[0][0] * R[0][0] +  R[1][0] * R[1][0])
    singular = sy < 1e-6
    if  not singular :
        x = math.atan2(R[2][1] , R[2][2])
        y = math.atan2(-R[2][0], sy)
        z = math.atan2(R[1][0], R[0][0])
    else :
        x = math.atan2(-R[1][2], R[1][1])
        y = math.atan2(-R[2][0], sy)
        z = 0
    return [z, y, x]
##########################################################

def norm( v ):
    return ( v[0]**2 + v[1]**2 + v[2]**2 )**0.5

def unit_vec( v ):
    n = norm( v )
    return [ _/n for _ in v ]

def cross(a, b):
    result = [a[1]*b[2] - a[2]*b[1],
            a[2]*b[0] - a[0]*b[2],
            a[0]*b[1] - a[1]*b[0]]
    return result

def CreateCS( origin , z , name , unit='mm' ):
    angle_unit = DataModel.CurrentUnitFromQuantityName("Angle")
    convert_factor = Quantity(1,'rad').ConvertUnit( angle_unit ).Value

    # Create coordinate
    testCS = ExtAPI.DataModel.Project.Model.CoordinateSystems.AddCoordinateSystem()
    testCS.OriginDefineBy= CoordinateSystemAlignmentType.Fixed
    testCS.OriginX = Quantity(origin[0],unit)
    testCS.OriginY = Quantity(origin[1],unit)
    testCS.OriginZ = Quantity(origin[2],unit)

    z_unit = unit_vec(z)
    x_unit = unit_vec([ z_unit[1] , -z_unit[0] , 0 ])
    y_unit = unit_vec(cross(z_unit, x_unit))
    xyz = [ x_unit , y_unit , z_unit ]

    # Get rotations
    origCS = [[1,0,0],[0,1,0],[0,0,1]]
    tMat = TransformationMatrix(origCS,xyz)
    angs = rotationMatrixToEulerAngles_ZYX(tMat)

    ##########################################################
    # Created by M.H. Pernelle
    # Last update: 2021/06
    # Perform transformation
    testCS.PrimaryAxisDefineBy = CoordinateSystemAlignmentType.GlobalX
    # Rotation Z
    testCS.RotateZ()
    testCS.SetTransformationValue(1,angs[0]*convert_factor)
    # Rotation Y
    testCS.RotateY()
    testCS.SetTransformationValue(2,angs[1]*convert_factor)
    # Rotation X
    testCS.RotateX()
    testCS.SetTransformationValue(3,angs[2]*convert_factor)
    ##########################################################

    # Set name
    testCS.Name = name

# Example
z = [1.,1.,0.]
CreateCS( [0,0,0] , z , 'my_cs' , unit='m' )