def _matrix_loaded():
try:
x = a5.Matrix(1.0, 0.0, 0.0, 1.0)
return True
except:
pass
return False
def test_matrix_constructor():
"""Tests the constructor for matrices"""
#Test default values for matrices:
m = a5.Matrix()
cunittest.assert_floats_equal(1.0, m.a)
cunittest.assert_floats_equal(0.0, m.b)
cunittest.assert_floats_equal(0.0, m.c)
cunittest.assert_floats_equal(1.0, m.d)
#Test matrix constructor with float arguments:
m = a5.Matrix(1.23, 2.34, 3.45, 4.56)
cunittest.assert_floats_equal(1.23, m.a)
cunittest.assert_floats_equal(2.34, m.b)
cunittest.assert_floats_equal(3.45, m.c)
cunittest.assert_floats_equal(4.56, m.d)
#Test matrix constructor with int arguments
# (ints should be converted to floats)
m = a5.Matrix(1, 2, 3, 4)
cunittest.assert_floats_equal(1.0, m.a)
cunittest.assert_floats_equal(2.0, m.b)
cunittest.assert_floats_equal(3.0, m.c)
cunittest.assert_floats_equal(4.0, m.d)
def test_matrix_vector_multiplication():
"""Tests multiplication between matrices and vectors"""
#Test x-component of resulting vector
m = a5.Matrix(5, 7, 0, 0)
v = a5.Vector(3, 2)
result = m * v
cunittest.assert_floats_equal(29.0, result.x)
cunittest.assert_floats_equal(0.0, result.y)
#Test y-component of resulting vector:
m = a5.Matrix(0, 0, 2, 3)
v = a5.Vector(1, 1)
result = m * v
cunittest.assert_floats_equal(0.0, result.x)
cunittest.assert_floats_equal(5.0, result.y)
#Identity Matrix Test Case:
m = a5.Matrix(1, 0, 0, 1)
v = a5.Vector(426.317, 9921.33)
result = m * v
cunittest.assert_floats_equal(426.317, result.x)
cunittest.assert_floats_equal(9921.33, result.y)
#General Test Case:
m = a5.Matrix(0, 1, 2, 3)
v = a5.Vector(1, 0)
result = m * v
cunittest.assert_floats_equal(0.0, result.x)
cunittest.assert_floats_equal(2.0, result.y)
#Identity Matrix Test Case:
m = a5.Matrix(1, 0, 0, 1)
v = a5.Vector(426.317, 9921.33)
result = m * v
cunittest.assert_floats_equal(426.317, result.x)
cunittest.assert_floats_equal(9921.33, result.y)
def ShearY(cls, k):
"""**Constructor** (alternate): Returns a Shear transform along the y-axis.
:param k: the shear amount
**Precondition**: a number (float or int).
The matrix is a shear Matrix, while the vector component is None. The
method ``transform`` will use the default value of translation.
Should this constructor fail (because of an incomplement implementation
in module ``a5``, it will return an Identity transform."""
try:
matrix = a5.Matrix(1, 0, k, 1)
self = cls(matrix)
return self
except:
pass
return cls.Identity()
def Rotation(cls, angle):
"""**Constructor** (alternate): Returns a Rotation transform for the given angle.
:param angle: the angle of rotation
**Precondition**: a number (float or int).
The matrix is a rotation Matrix, while the vector component is None. The
method ``transform`` will use the default value of translation.
Should this constructor fail (because of an incomplement implementation
in module ``a5``, it will return an Identity transform."""
try:
matrix = a5.Matrix(math.cos(angle), -math.sin(angle),
math.sin(angle), math.cos(angle))
self = cls(matrix)
return self
except:
pass
return cls.Identity()
def Scale(cls, sx, sy=None):
"""**Constructor** (alternate): Returns a Scale transform for the given magnification.
:param x: the magnification in the x direction
**Precondition**: a number (float or int).
:param y: the magnification in the y direction
**Precondition**: a number (float or int).
The matrix is a scaling Matrix, while the vector component is None. The
method ``transform`` will use the default value of translation.
Should this constructor fail (because of an incomplement implementation
in module ``a5``, it will return an Identity transform."""
try:
sy = sx if sy is None else sy
matrix = a5.Matrix(sx, 0, 0, sy)
self = cls(matrix)
return self
except:
pass
return cls.Identity()
def Projection(cls, x=1, y=0):
"""**Constructor** (alternate): Returns a Projection transform on to the given vector.
:param x: the x coordinate of the vector to project on
**Precondition**: a number (float or int).
:param y: the y coordinate of the vector to project on
**Precondition**: a number (float or int).
The matrix is a projection Matrix, while the vector component is None. The
method ``transform`` will use the default value of translation.
Should this constructor fail (because of an incomplement implementation
in module ``a5``, it will return an Identity transform."""
try:
norm = x * x + y * y # dot product
matrix = a5.Matrix(x * x / norm, x * y / norm, x * y / norm,
y * y / norm)
self = cls(matrix)
return self
except:
pass
return cls.Identity()
def test_matrix_matrix_multiplication():
"""Tests multiplication between matrices"""
#Test element a of the resulting matrix:
m1 = a5.Matrix(3, 5, 0, 0)
m2 = a5.Matrix(1, 0, 1, 0)
result = m1 * m2
cunittest.assert_floats_equal(8.0, result.a)
cunittest.assert_floats_equal(0.0, result.b)
cunittest.assert_floats_equal(0.0, result.c)
cunittest.assert_floats_equal(0.0, result.d)
#Test element b of the resulting matrix:
m1 = a5.Matrix(3, 5, 0, 0)
m2 = a5.Matrix(0, 2, 0, 7)
result = m1 * m2
cunittest.assert_floats_equal(0.0, result.a)
cunittest.assert_floats_equal(41.0, result.b)
cunittest.assert_floats_equal(0.0, result.c)
cunittest.assert_floats_equal(0.0, result.d)
#Test element c of the resulting matrix:
m1 = a5.Matrix(0, 0, 1, 7)
m2 = a5.Matrix(3, 0, 2, 0)
result = m1 * m2
cunittest.assert_floats_equal(0.0, result.a)
cunittest.assert_floats_equal(0.0, result.b)
cunittest.assert_floats_equal(17.0, result.c)
cunittest.assert_floats_equal(0.0, result.d)
#Test element d of the resulting matrix:
m1 = a5.Matrix(0, 0, 2, 3)
m2 = a5.Matrix(0, 9, 0, 1)
result = m1 * m2
cunittest.assert_floats_equal(0.0, result.a)
cunittest.assert_floats_equal(0.0, result.b)
cunittest.assert_floats_equal(0.0, result.c)
cunittest.assert_floats_equal(21.0, result.d)
#General Test Case:
m1 = a5.Matrix(1, 2, 3, 4)
m2 = a5.Matrix(4, 3, 2, 1)
result = m1 * m2
cunittest.assert_floats_equal(8.0, result.a)
cunittest.assert_floats_equal(5.0, result.b)
cunittest.assert_floats_equal(20.0, result.c)
cunittest.assert_floats_equal(13.0, result.d)
#Identity Matrix Test Case:
m1 = a5.Matrix(1, 0, 0, 1)
m2 = a5.Matrix(1, 4, 9, 16)
result = m1 * m2
cunittest.assert_floats_equal(1.0, result.a)
cunittest.assert_floats_equal(4.0, result.b)
cunittest.assert_floats_equal(9.0, result.c)
cunittest.assert_floats_equal(16.0, result.d)