def __projectm(vector, center):
"""
apply
clipping matrix
camera transformation matrix
camera rotation matrix
TODO: finally sort out vertices out of clipping area
and return tuple on 2D Coordinates
taken from : http://stackoverflow.com/questions/724219/how-to-convert-a-3d-point-into-2d-perspective-projection
"""
clipping_m = Matrix3D([[FOV * ASPECT_RATIO, 0.0, 0.0, 0.0],
[0.0, FOV, 0.0, 0.0],
[
0.0, 0.0, (far + near) / (far - near),
(2.0 * near * far) / (near - far)
], [0.0, 0.0, 1.0, 0.0]])
cam_translation_m = Matrix3D.get_shift_matrix(0, 0, -10)
cam_rot_m = Matrix3D.get_rot_y_matrix(Y_ANGLE).dot(
Matrix3D.get_rot_x_matrix(X_ANGLE))
# mind the order !!
new_vector = clipping_m.dot(
cam_translation_m.dot(cam_rot_m)).v_dot(vector)
new_x = center[0] + new_vector.x * 16.0 / (2.0 * new_vector.z) + 8.0
new_y = center[1] + new_vector.y * 9.0 / (2.0 * new_vector.z) + 4.5
return new_x, new_y
def test_inverse(self):
# for next example look at
# http://matheguru.com/lineare-algebra/207-determinante.html
mr = Matrix3D([
[5.0, 0.0, 3.0, -1.0],
[3.0, 0.0, 0.0, 4.0],
[-1.0, 2.0, 4.0, -2.0],
[1.0, 0.0, 0.0, 5.0],
])
print "inverse(mr) =\n", mr.inverse()
test_m = Matrix3D([
[0.0, 0.4545454545454546, 0.0, -0.36363636363636365],
[-0.6666666666666667, 1.7121212121212122, 0.5, -1.303030303030303],
[0.33333333333333337, -0.7878787878787878, 0.0, 0.696969696969697],
[0.0, -0.09090909090909091, 0.0, 0.2727272727272727]
])
assert mr.inverse() == test_m
def solve(self):
if self.a.is_singular():
return "infinity"
sol = []
for i in range(self.n):
t = Matrix3D(self.a)
t.set_row(self.b.get_list(), i)
sol.append(t.det() / self.a.det())
return sol
def test_matrix_dot(self):
"""test dot product identity matrix and transpose"""
mi = Matrix3D.identity()
# I dot transposed(I) = I
assert mi == mi.dot(mi.transpose())
mr = Matrix3D([
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
])
assert mr.dot(mi) == mr
test_transposed = Matrix3D([[1, 5, 9, 13], [2, 6, 10, 14],
[3, 7, 11, 15], [4, 8, 12, 16]])
assert mr.transpose() == test_transposed
test_m = Matrix3D([
[30, 70, 110, 150],
[70, 174, 278, 382],
[110, 278, 446, 614],
[150, 382, 614, 846],
])
assert mr.dot(mr.transpose()) == test_m
A = Matrix3D([[3, 0, 0, 0], [0, -1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 1]])
B = Matrix3D([[math.sqrt(3) / 2, 0, -1 / 2, 0], [0, 1, 0, 0],
[1 / 2, 0, math.sqrt(3) / 2, 0], [0, 0, 0, 1]])
C = Matrix3D([[1, 0, 0, 3], [0, 1, 0, -1], [0, 0, 1, 2], [0, 0, 0, 1]])
# testing assosiativeness (A*B)*C == A*(B*C)
assert A.dot(B).dot(C) == A.dot(B.dot(C))
def test_det(self):
m = Matrix3D.identity()
print "det(I)=", m.det()
# for next example look at
# http://matheguru.com/lineare-algebra/207-determinante.html
mr = Matrix3D([
[5, 0, 3, -1],
[3, 0, 0, 4],
[-1, 2, 4, -2],
[1, 0, 0, 5],
])
print "T(mr)=\n", mr.transpose()
print "det(mr)=", mr.det()
assert mr.det() == 66
print "det(T(mr))=", mr.transpose().det()
assert mr.det() == mr.transpose().det()
from Matrix3D import Matrix3D from Solver import Solver from Vector import Vector3D filename = 'sle3D.txt' a = Matrix3D() b = Vector3D() a.read_from_file(filename) b.read_from_file(filename) a.print() b.print() print() s = Solver(a, b) print(s.solve())
