def test_Quadrilatere():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
p = Quadrilatere(A, B, C, D)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D).coordonnees)
def test_Glisseur_segment():
A = rand_pt()
B = rand_pt()
s = Segment(A, B)
M = Glisseur_segment(s)
assert(M in s)
M.k = 0
assertEqual(M.k, 0)
assertAlmostEqual(M.coordonnees, A.coordonnees)
P = Point(*M.coordonnees)
M.k = 1
assertEqual(M.k, 1)
assertAlmostEqual(M.coordonnees, B.coordonnees)
M.k = 2
assertEqual(M.k, 1) # 0<=k<=1 pour un segment
assert(M in s)
M.k = -1
assertEqual(M.k, 0) # 0<=k<=1 pour un segment
assert(M in s)
M.k = 1
Q = Point(*M.coordonnees)
assertAlmostEqual(Droite(P, Q).equation_reduite, s.equation_reduite)
M.k = 1.7
M(*M.coordonnees)
assertAlmostEqual(M.k, 1)
def test_Orthocentre():
A, B, C = rand_pt(), rand_pt(), rand_pt()
p = Polygone(A, B, C)
H = Orthocentre(p)
assert(Droite(A, H).perpendiculaire(Droite(B, C)))
assert(Droite(B, H).perpendiculaire(Droite(A, C)))
assert(Droite(C, H).perpendiculaire(Droite(B, A)))
def test_Carre_centre():
O = rand_pt()
M = rand_pt()
p = Carre_centre(O, M)
assert(p.centre.existe and p.centre is O)
assert(len(p.cotes) == 4)
assertAlmostEqual(p.aire, p.cotes[0].longueur**2)
def test_Glisseur_segment():
A = rand_pt()
B = rand_pt()
s = Segment(A, B)
M = Glisseur_segment(s)
assert (M in s)
M.k = 0
assertEqual(M.k, 0)
assertAlmostEqual(M.coordonnees, A.coordonnees)
P = Point(*M.coordonnees)
M.k = 1
assertEqual(M.k, 1)
assertAlmostEqual(M.coordonnees, B.coordonnees)
M.k = 2
assertEqual(M.k, 1) # 0<=k<=1 pour un segment
assert (M in s)
M.k = -1
assertEqual(M.k, 0) # 0<=k<=1 pour un segment
assert (M in s)
M.k = 1
Q = Point(*M.coordonnees)
assertAlmostEqual(Droite(P, Q).equation_reduite, s.equation_reduite)
M.k = 1.7
M(*M.coordonnees)
assertAlmostEqual(M.k, 1)
def test_Triangle():
A = rand_pt()
B = rand_pt()
C = rand_pt()
t = Triangle(A, B, C)
O = t.centre_cercle_circonscrit
assertAlmostEqual(Segment(O, A).longueur, Segment(O, C).longueur)
def test_Parallelogramme():
A = rand_pt()
B = rand_pt()
C = rand_pt()
p = Parallelogramme(A, B, C)
D = p.sommets[3]
assertEqual(Vecteur(A, B), Vecteur(D, C))
def test_Orthocentre():
A, B, C = rand_pt(), rand_pt(), rand_pt()
p = Polygone(A, B, C)
H = Orthocentre(p)
assert (Droite(A, H).perpendiculaire(Droite(B, C)))
assert (Droite(B, H).perpendiculaire(Droite(A, C)))
assert (Droite(C, H).perpendiculaire(Droite(B, A)))
def test_Point_equidistant():
A = rand_pt()
B = rand_pt()
C = rand_pt()
P = Point_equidistant(A, B, C)
assertAlmostEqual(Segment(A, P).longueur, Segment(B, P).longueur)
assertAlmostEqual(Segment(A, P).longueur, Segment(C, P).longueur)
assert(P in Mediatrice(A, B))
def test_Point_equidistant():
A = rand_pt()
B = rand_pt()
C = rand_pt()
P = Point_equidistant(A, B, C)
assertAlmostEqual(Segment(A, P).longueur, Segment(B, P).longueur)
assertAlmostEqual(Segment(A, P).longueur, Segment(C, P).longueur)
assert (P in Mediatrice(A, B))
def test_Pentagone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
p = Pentagone(A, B, C, D, E)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E).coordonnees)
def test_Glisseur_arc_cercle():
A = rand_pt()
B = rand_pt()
C = rand_pt()
a = Arc_cercle(A, B, C)
M = Glisseur_arc_cercle(a)
assert(M in a)
O = a.centre
M.coordonnees = O.coordonnees
def test_Centre_cercle_inscrit():
A, B, C = rand_pt(), rand_pt(), rand_pt()
p = Polygone(A, B, C)
I = Centre_cercle_inscrit(p)
P = Projete_segment(I, Segment(B, C))
Q = Projete_segment(I, Segment(A, C))
R = Projete_segment(I, Segment(A, B))
c = Cercle(I, P)
assert(P in c and Q in c and R in c)
def test_Centre_cercle_inscrit():
A, B, C = rand_pt(), rand_pt(), rand_pt()
p = Polygone(A, B, C)
I = Centre_cercle_inscrit(p)
P = Projete_segment(I, Segment(B, C))
Q = Projete_segment(I, Segment(A, C))
R = Projete_segment(I, Segment(A, B))
c = Cercle(I, P)
assert (P in c and Q in c and R in c)
def test_Glisseur_arc_cercle():
A = rand_pt()
B = rand_pt()
C = rand_pt()
a = Arc_cercle(A, B, C)
M = Glisseur_arc_cercle(a)
assert (M in a)
O = a.centre
M.coordonnees = O.coordonnees
def test_Label_point():
A = rand_pt()
B = rand_pt()
A.label("Position de l'hirondelle d'Afrique.")
B.label(u"Position de l'hirondelle européenne.")
assert(A.label() == "Position de l'hirondelle d'Afrique.")
assert(B.label() == u"Position de l'hirondelle européenne.")
A.style(legende = NOM)
assert(A.label() == "")
def test_Triangle_equilateral():
O = rand_pt()
M = rand_pt()
p = Triangle_equilateral(O, M)
assert(p.centre.existe)
assert(p.centre_cercle_circonscrit.existe)
assert(p.centre_cercle_inscrit.existe)
assert(p.orthocentre.existe)
assert(p.orthocentre == p.centre == p.centre_cercle_circonscrit == p.centre_cercle_inscrit)
def test_Triangle_equilateral_centre():
O = rand_pt()
M = rand_pt()
p = Triangle_equilateral_centre(O, M)
assert(p.centre.existe and p.centre is O)
assert(p.centre_cercle_circonscrit.existe)
assert(p.centre_cercle_inscrit.existe)
assert(p.orthocentre.existe)
assert p.orthocentre.confondu(p.centre, p.centre_cercle_circonscrit, p.centre_cercle_inscrit)
def test_Losange():
A = rand_pt()
B = rand_pt()
l = Losange(A, B)
M, N, O, P = l.sommets
diagonale1 = Droite(M, O)
diagonale2 = Droite(N, P)
assert(diagonale1.perpendiculaire(diagonale2))
cote = Droite(M, N)
cote_oppose = Droite(O, P)
assert(cote.parallele(cote_oppose))
def test_Rectangle():
A = rand_pt()
B = rand_pt()
r = Rectangle(A, B)
M, N, O, P = r.sommets
diagonale1 = Segment(M, O)
diagonale2 = Segment(N, P)
assertAlmostEqual(diagonale1.longueur, diagonale2.longueur)
cote = Droite(M, N)
cote_oppose = Droite(O, P)
assert(cote.parallele(cote_oppose))
def test_Centre_alias():
u"Centre et Centre_gravite sont interchangeables."
A = rand_pt()
B = rand_pt()
C = rand_pt()
G = Centre(Triangle(A, B, C))
assertAlmostEqual(G.x, (A.x + B.x + C.x)/3)
assertAlmostEqual(G.y, (A.y + B.y + C.y)/3)
ce = Cercle(A, 1)
G = Centre_gravite(ce)
assertAlmostEqual(G.xy, A.xy)
def test_Centre_gravite():
A = rand_pt()
B = rand_pt()
C = rand_pt()
I = Milieu(B, C)
J = Milieu(A, C)
K = Milieu(A, B)
G = Centre_gravite(Triangle(A, B, C))
assertAlmostEqual(Segment(A, G).longueur, 2*Segment(I, G).longueur)
assertAlmostEqual(Segment(B, G).longueur, 2*Segment(J, G).longueur)
assertAlmostEqual(Segment(C, G).longueur, 2*Segment(K, G).longueur)
def test_Centre_gravite():
A = rand_pt()
B = rand_pt()
C = rand_pt()
I = Milieu(B, C)
J = Milieu(A, C)
K = Milieu(A, B)
G = Centre_gravite(Triangle(A, B, C))
assertAlmostEqual(Segment(A, G).longueur, 2 * Segment(I, G).longueur)
assertAlmostEqual(Segment(B, G).longueur, 2 * Segment(J, G).longueur)
assertAlmostEqual(Segment(C, G).longueur, 2 * Segment(K, G).longueur)
def test_Triangle_isocele():
A = rand_pt()
B = rand_pt()
tri = Triangle_isocele(A, B, 2*pi/13)
C = tri.point3
a = Angle(B, A, C)
assertAlmostEqual(a.radian, 2*pi/13)
assertAlmostEqual(Segment(A, B).longueur, Segment(A, C).longueur)
t1 = Triangle_isocele((0, 0), (1, 1), u'90°')
assertAlmostEqual(t1.point3.xy, (-1, 1))
t2 = Triangle_isocele((0, 0), (2, 0), pi/3)
assertAlmostEqual(t2.point3.xy, (2*cos(pi/3), 2*sin(pi/3)))
def test_Nuage():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
while D in (A, B, C):
D = rand_pt()
n = Nuage(A, B, C)
assert n.points == (A, B, C)
assert A in n
assert B in n
assert C in n
assert D not in n
def test_polygones_et_representants_de_vecteurs():
f = Feuille()
f.objets.A = A = rand_pt()
f.objets.B = B = rand_pt()
f.objets.C = C = rand_pt()
f.objets.p = Parallelogramme(A, B, C)
f.objets.S1.renommer("D")
s = repr(f.objets.p)
del f.objets.p
assert("D" not in f.objets)
exec("p=" + s, f.objets)
assert("D" in f.objets)
assert(f.objets.D is f.objets.p.sommets[3])
def test_polygones_et_representants_de_vecteurs():
f = Feuille()
f.objets.A = A = rand_pt()
f.objets.B = B = rand_pt()
f.objets.C = C = rand_pt()
f.objets.p = Parallelogramme(A, B, C)
f.objets.S1.renommer("D")
s = repr(f.objets.p)
del f.objets.p
assert("D" not in f.objets)
exec("p=" + s, f.objets)
assert("D" in f.objets)
assert(f.objets.D is f.objets.p.sommets[3])
def test_Polygone_regulier():
O = rand_pt()
M = rand_pt()
p = Polygone_regulier(O, M, 15)
assert(len(p.cotes) == 15)
assert(p.centre in Mediatrice(O, M))
for i in xrange(15):
assertAlmostEqual(Segment(p.sommets[i%15], p.sommets[(i+1)%15]).longueur, Segment(p.sommets[(i+2)%15], p.sommets[(i+3)%15]).longueur)
p = Polygone_regulier(O, M, 3)
assert(isinstance(p, Triangle))
p = Polygone_regulier(O, M, 4)
assert(isinstance(p, Quadrilatere))
# Test de régression :
# la taille de str(p.points) croissait exponentiellement.
assert(len(str(p.points)) < 30000)
def test_Projete_demidroite():
d = Demidroite(rand_pt(), rand_pt())
M = rand_pt()
assert(Projete_demidroite(M, d) in d)
A = Point(0, 1)
B = Point(2, 1)
s = Demidroite(A, B)
M = Point(1, 7.15)
P = Projete_demidroite(M, s)
assertAlmostEqual(Milieu(A, B).coordonnees, P.coordonnees)
M.x = .5
assertAlmostEqual(Barycentre((A, 3), (B, 1)).coordonnees, P.coordonnees)
M.x = -1
assertAlmostEqual(A.coordonnees, P.coordonnees)
M.x = 3
assertAlmostEqual(Barycentre((A, -1), (B, 3)).coordonnees, P.coordonnees)
def test_Projete_segment():
s = Segment(rand_pt(), rand_pt())
M = rand_pt()
assert (Projete_segment(M, s) in s)
A = Point(0, 1)
B = Point(2, 1)
s = Segment(A, B)
M = Point(1, 7.15)
P = Projete_segment(M, s)
assertAlmostEqual(Milieu(A, B).coordonnees, P.coordonnees)
M.x = .5
assertAlmostEqual(Barycentre((A, 3), (B, 1)).coordonnees, P.coordonnees)
M.x = -1
assertAlmostEqual(A.coordonnees, P.coordonnees)
M.x = 3
assertAlmostEqual(B.coordonnees, P.coordonnees)
def test_Projete_segment():
s = Segment(rand_pt(), rand_pt())
M = rand_pt()
assert(Projete_segment(M, s) in s)
A = Point(0, 1)
B = Point(2, 1)
s = Segment(A, B)
M = Point(1, 7.15)
P = Projete_segment(M, s)
assertAlmostEqual(Milieu(A, B).coordonnees, P.coordonnees)
M.x = .5
assertAlmostEqual(Barycentre((A, 3), (B, 1)).coordonnees, P.coordonnees)
M.x = -1
assertAlmostEqual(A.coordonnees, P.coordonnees)
M.x = 3
assertAlmostEqual(B.coordonnees, P.coordonnees)
def test_Projete_demidroite():
d = Demidroite(rand_pt(), rand_pt())
M = rand_pt()
assert (Projete_demidroite(M, d) in d)
A = Point(0, 1)
B = Point(2, 1)
s = Demidroite(A, B)
M = Point(1, 7.15)
P = Projete_demidroite(M, s)
assertAlmostEqual(Milieu(A, B).coordonnees, P.coordonnees)
M.x = .5
assertAlmostEqual(Barycentre((A, 3), (B, 1)).coordonnees, P.coordonnees)
M.x = -1
assertAlmostEqual(A.coordonnees, P.coordonnees)
M.x = 3
assertAlmostEqual(Barycentre((A, -1), (B, 3)).coordonnees, P.coordonnees)
def test_Carre():
O = rand_pt()
M = rand_pt()
p = Carre(O, M)
A, B, C, D = p.sommets
assert(p.centre == Milieu(A, C) == Milieu(B, D))
assert(A == O and B == M)
assert(len(p.cotes) == 4)
assertAlmostEqual(p.aire, p.cotes[0].longueur**2)
# Test redéfinition d'un sommet
c = Carre((3, 2), (7, 2))
M = Point(0, 2)
c.point1 = M
assert(c.point1 is M)
assert(c.regulier)
assertAlmostEqual(c.aire, 49)
assertAlmostEqual(c.point4.coordonnees, (0, 9))
def test_Polygone_regulier_centre():
O = rand_pt()
M = rand_pt()
p = Polygone_regulier_centre(O, M, 15)
assert(len(p.cotes) == 15)
assert(p.centre is O)
for Mi in p.sommets:
assertAlmostEqual(Segment(O, Mi).longueur, Segment(O, M).longueur)
for i in xrange(10):
coeffs = tuple(random() for i in xrange(15))
G = Barycentre(*zip(p.sommets, coeffs))
assert(G in p)
# cas particuliers :
p = Polygone_regulier_centre(O, M, 3)
assert(isinstance(p, Triangle))
p = Polygone_regulier_centre(O, M, 4)
assert(isinstance(p, Quadrilatere))
assert(len(str(p.points)) < 30000)
def test_Droite_vectorielle():
v = Vecteur_libre(1, 7)
A = Point(-2, 3)
d = Droite_vectorielle(A, v)
assert (d.vecteur is v and d.point is A)
assertAlmostEqual(v.y / v.x, -d.equation[0] / d.equation[1])
B = rand_pt()
d1 = Droite_vectorielle(B, v)
assert (d.parallele(d1))
def test_Droite_vectorielle():
v = Vecteur_libre(1, 7)
A = Point(-2, 3)
d = Droite_vectorielle(A, v)
assert(d.vecteur is v and d.point is A)
assertAlmostEqual(v.y/v.x, -d.equation[0]/d.equation[1])
B = rand_pt()
d1 = Droite_vectorielle(B, v)
assert(d.parallele(d1))
def test_Octogone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
G = rand_pt()
H = rand_pt()
p = Octogone(A, B, C, D, E, F, G, H)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E, F, G, H).coordonnees)
def test_latex_incorrect():
u"On teste le comportement en cas de code LaTeX incorrect."
A = rand_pt()
A.label('2$')
assertEqual(A.label(), r'2\$')
A.label('US$2.50')
assertEqual(A.label(), r'US\$2.50')
A.label('$M__i$')
assertEqual(A.label(), r'\$M__i\$')
A.label('2$')
def test_Polygone_regulier_centre():
O = rand_pt()
M = rand_pt()
p = Polygone_regulier_centre(O, M, 15)
assert(len(p.cotes) == 15)
assert(p.centre is O)
for Mi in p.sommets:
assertAlmostEqual(Segment(O, Mi).longueur, Segment(O, M).longueur)
for i in xrange(10):
coeffs = tuple(random() for i in xrange(15))
G = Barycentre(*zip(p.sommets, coeffs))
assert(G in p)
G.points_ponderes[randint(11)].coefficient = -5
assert(G not in p)
# cas particuliers :
p = Polygone_regulier_centre(O, M, 3)
assert(isinstance(p, Triangle))
p = Polygone_regulier_centre(O, M, 4)
assert(isinstance(p, Quadrilatere))
assert(len(str(p.points)) < 30000)
def test_Heptagone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
G = rand_pt()
p = Heptagone(A, B, C, D, E, F, G)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E, F, G).coordonnees)
def test_Point():
A = Point(1, 2)
assert (isinstance(A.etiquette, Label_point))
assertEqual(A.x, 1)
assertEqual(A.y, 2)
assertEqual(type(A.coordonnees), tuple)
A.x = 5
A.y = 7
assertEqual(A.coordonnees, (5, 7))
assert (A.style("legende") == NOM)
# Test du typage dynamique
d = Droite(rand_pt(), rand_pt())
B = Point(d)
assert (isinstance(B, Glisseur_droite))
c = Cercle(A, 3)
C = Point(c)
assert (isinstance(C, Glisseur_cercle))
d = Demidroite(rand_pt(), rand_pt())
B = Point(d)
assert (isinstance(B, Glisseur_demidroite))
s = Segment(rand_pt(), rand_pt())
B = Point(s)
assert (isinstance(B, Glisseur_segment))
a = Arc_points(Point(), Point(1, 1), Point(1, 2))
B = Point(a)
assert (isinstance(B, Glisseur_arc_cercle))
def test_Point():
A = Point(1, 2)
assert(isinstance(A.etiquette, Label_point))
assertEqual(A.x, 1)
assertEqual(A.y, 2)
assertEqual(type(A.coordonnees), tuple)
A.x = 5
A.y = 7
assertEqual(A.coordonnees, (5, 7))
assert(A.mode_affichage == NOM)
# Test du typage dynamique
d = Droite(rand_pt(), rand_pt())
B = Point(d)
assert(isinstance(B, Glisseur_droite))
c = Cercle(A, 3)
C = Point(c)
assert(isinstance(C, Glisseur_cercle))
d = Demidroite(rand_pt(), rand_pt())
B = Point(d)
assert(isinstance(B, Glisseur_demidroite))
s = Segment(rand_pt(), rand_pt())
B = Point(s)
assert(isinstance(B, Glisseur_segment))
a = Arc_points(Point(), Point(1, 1), Point(1, 2))
B = Point(a)
assert(isinstance(B, Glisseur_arc_cercle))
def test_Glisseur_droite():
A = rand_pt()
B = rand_pt()
d = Droite(A, B)
M = Glisseur_droite(d)
assert (M in d)
M.k = 0
assertEqual(M.k, 0)
assertAlmostEqual(M.coordonnees, A.coordonnees)
P = Point(*M.coordonnees)
M.k = 1
assertEqual(M.k, 1)
assertAlmostEqual(M.coordonnees, B.coordonnees)
M.k = 2
assertEqual(M.k, 2)
M.k = -1
assertEqual(M.k, -1)
Q = Point(*M.coordonnees)
assertAlmostEqual(Droite(P, Q).equation_reduite, d.equation_reduite)
M.k = 1.7
M(*M.coordonnees)
assertAlmostEqual(M.k, 1.7)
def test_Projete_arc_cercle():
O = Point(23.15, -12.75)
A = Point(-12.5, 7.14)
B = Point(7.15, 8.64)
a = Arc_cercle(O, A, B)
M = rand_pt()
P = Projete_arc_cercle(M, a)
assert (P in a)
M.coordonnees = a.centre.coordonnees
assert (not P.existe)
M.coordonnees = -17.826266675199999, 11.760911186
assert (type(P.coordonnees) is tuple)
assertAlmostEqual(A.coordonnees, P.coordonnees)
assertEqual(A, P)
def test_Intersection_droites():
d1 = rand_dte()
d2 = rand_dte()
A = Intersection_droites(d1, d2)
if not d1.parallele(d2):
assert (A in d1 and A in d2)
d3 = Parallele(d1, rand_pt())
assert (not Intersection_droites(d1, d3).existe)
D = Point(-14.201335283549275, 1.5093204196583834)
U = Point(-14.201335283549273, 17.644024286752096)
d = Droite(U, D)
s = Segment(U, D)
V = Point(1.933368583544437, 7.5065025053891166)
W = Point(7.1347038670937115, 8.3895493390615954)
d2 = Droite(W, V)
M1 = Intersection_droites(s, d2)
M2 = Intersection_droites(d, d2)
assert (M1.existe)
assert (M2.existe)
def test_Triangle_rectangle():
t = Triangle_rectangle(rand_pt(), rand_pt(), pi/7)
a = Angle(t.point1, t.point3, t.point2)
assertAlmostEqual(a.degre, 90)
def test_Centre_cercle_circonscrit():
A, B, C = rand_pt(), rand_pt(), rand_pt()
p = Polygone(A, B, C)
O = Centre_cercle_circonscrit(p)
assert (O == Point_equidistant(A, B, C))
