Maya script to extrude along a curve.

ExtrudeAlongCurve.py

import maya.cmds as cmds
import math
import numpy

def basisToEuler(tangent, bitangent, normal):
#Adapted from http://www.staff.city.ac.uk/~sbbh653/publications/euler.pdf
    m = [tangent, bitangent, normal]

    if abs(m[2][0]) != 1:
        theta = -math.asin(m[2][0])
        invCosTheta = 1.0 / math.cos(theta)
        psi = math.atan2(m[2][1] * invCosTheta, m[2][2] * invCosTheta)
        phi = math.atan2(m[1][0] * invCosTheta, m[0][0] * invCosTheta)
    else:
        phi = 0
        if m[2][0] == -1:
            theta = math.pi * 0.5
            psi = theta + math.atan2(m[0][1], m[0][2])
        else:
            theta = -math.pi * 0.5
            psi = math.atan2(-m[0][1], -m[0][2])
    return (psi, theta, phi)

def degrees(radians):
    return radians * 180.0 / math.pi

curve = cmds.ls(selection=True)[0]
startPoint = cmds.pointOnCurve(curve, parameter=0.0) 

tangent = cmds.pointOnCurve(curve, normalizedTangent=True)
normal = cmds.pointOnCurve(curve, normalizedNormal=True)
bitangent = numpy.cross(normal, tangent)

rotation = basisToEuler(tangent, bitangent, normal)

(cubeTransform, polyCubeNode) = cmds.polyCube()
cmds.setAttr(cubeTransform + '.translate', startPoint[0], startPoint[1], startPoint[2])

cmds.setAttr(cubeTransform + '.rotate', degrees(rotation[0]), degrees(rotation[1]), degrees(rotation[2]) )

cubeShape = cmds.listRelatives(cubeTransform, children=True)[0]

cmds.polyExtrudeFacet(cubeShape + '.f[4]', inputCurve=curve, divisions=20)