Transforming the Point using list

[psbasha]

Hi,

I have a Point and Transfoirmation matrix.How to translate the Point from one Coordinate system to other using list .

Point1 = [1,2,3]

#Transformation Matrix
T =
[ [1,0,0],
[0,1,0],
[0,0,1]]

I have to get the

TransPoint = Point1 * T

Other than list,is there any other approach is possible to get the transformation of point

Thanks
PSB

[bvdet]

Hi,

I have a Point and Transfoirmation matrix.How to translate the Point from one Coordinate system to other using list .

Point1 = [1,2,3]

#Transformation Matrix
T =
[ [1,0,0],
[0,1,0],
[0,0,1]]

I have to get the

TransPoint = Point1 * T

Other than list,is there any other approach is possible to get the transformation of point

Thanks
PSB

The transformation matrix you have defined (T) is the standard orthonormal basis for R3. What is the basis for Point 1? Given an orthonormal basis in R3, a point relative to that basis can be translated to the standard basis :

from macrolib.PointPlane3D import Point
 
def determinant3(a,b,c,m,n,k,u,v,w):
        return a*n*w + b*k*u + m*v*c - c*n*u - b*m*w - a*k*v
 
def translate(A, B, N, pt):
 
    X,Y,Z = tuple(pt)    
 
    '''
    Normalize pt
    '''
    M = (X*X + Y*Y + Z*Z)**0.5
    try:
        X1, Y1, Z1 = X/M, Y/M, Z/M
    except:
        X1, Y1, Z1 = 0.0, 0.0, 0.0
 
    D = determinant3(A.x, A.y, A.z, N.x, N.y, N.z, B.x, B.y, B.z)
    Dx = determinant3(X1, A.y, A.z, Z1, N.y, N.z, Y1, B.y, B.z)
    Dy = determinant3(A.x, X1, A.z, N.x, Z1, N.z, B.x, Y1, B.z)
    Dz = determinant3(A.x, A.y, X1, N.x, N.y, Z1, B.x, B.y, Y1)
 
    '''        
    Calculate the resultant unit vector 'R1'
    '''
    R1 = Point(Dx/D, Dy/D, Dz/D)
 
    '''
    Return the global coordinate vector
    '''
    return R1*M
 
# local basis 'X'
a = Point(0.462352, 0.850215, 0.251725)
# local basis 'Y'
b = Point(0.791086, -0.267295, -0.550215)
# local basis 'Z'
n = Point(-0.400516, 0.453529, -0.796177)
 
print repr(translate(a, b, n, Point(12,12,12)))
 
'''
>>> Point(10.235071, 12.437392, -13.136013)
'''

Please, check my math!

Given three non-collinear points in R3, you can define an orthonormal basis. Let's say point1 is the basis origin, point2 defines the X axis with respect to the origin, and point 3, in combination with p1 and p2, defines the plane:

>>> c.p1
Point(144.000000, 256.000000, 300.000000)
>>> c.p2
Point(324.000000, 587.000000, 398.000000)
>>> c.p3
Point(645.000000, 400.000000, 130.000000)
>>> a = BasisTransToGlobal(c.p1, c.p2, c.p3, Point(12,12,12))
>>> a.R
Point(154.235075, 268.437392, 286.863999)
>>> a.R-c.p1
Point(10.235075, 12.437392, -13.136001)
>>> 

BTW - This should have been posted to Python Forum instead of Python Articles.

[bartonc]

Moved from Python Articles

Please be careful not to post questions in the Articles section.

Thanks you for your co-operation in this matter.

[Motoma]

Jinkies bvdet! That was amazing!

[bvdet]

Jinkies bvdet! That was amazing!

Nuthin' to it Motoma. I've been working on this module for about a year (in my spare time of course).

[bvdet]

Here's the return trip:

def transToLocal(pt, m):
    '''
    pt - point object in the standard R3 orthonormal basis
    vA - local 'X' unit vector
    vB - local 'Y' unit vector
    vN - local 'Z' unit vector
 
    'dot()' is a Point object method that returns the dot product    
 
    Return the local coordinate
    Vector projection of: pt along vA, pt along vB, pt along vN
    '''
    return Point(pt.dot(Point(*m[0])), \
                 pt.dot(Point(*m[1])), \
                 pt.dot(Point(*m[2])))
 
# Local basis translation matrix
m = [(0.462352, 0.850215, 0.251725), \
     (0.791086, -0.267295, -0.550215), \
     (-0.400516, 0.453529, -0.796177)]
# Point object in standard orthonormal basis
pt = Point(10.235071, 12.437392, -13.136013)
 
print repr(transToLocal(pt, m))
# Point(12.000000, 12.000000, 12.000000)