def test_transformations():
c = Cercle(('1/5', '4/5'), '1/3')
h = Homothetie(('1', '1'), '5/7')
v = Vecteur(c.centre, h.centre)
c1 = h(c)
v1 = Vecteur(c1.centre, h.centre)
assert v1.coordonnees == tuple(h.rapport * array(v.coordonnees))
assert_eq('c1.centre.coordonnees', '(3/7, 6/7)', l())
assert_eq('c1.rayon', '5/21', l())
c.rayon = '2'
assert_eq('c1.rayon', '10/7', l())
r = Rotation(('0', '1'), 'pi/3')
c2 = r(c)
t = Translation(('2/3', '-1/3'))
c3 = t(c)
m = Reflexion(Droite('y=x'))
c4 = m(c)
c.rayon = '3/7'
assert_eq('c2.rayon', '3/7', l())
assert_eq('c2.centre.coordonnees',
'(1/10 + 3**(1/2)/10, 9/10 + 3**(1/2)/10)', l())
assert_eq('c3.rayon', '3/7', l())
assert_eq('c3.centre.coordonnees', '(13/15, 7/15)', l())
assert_eq('c4.rayon', '3/7', l())
assert_eq('c4.centre.coordonnees', '(4/5, 1/5)', l())
def test_intersections():
c = Cercle(('1/2', '2/3'), 'sqrt(2)')
assert_eq('c.diametre', '2*2**(1/2)', l())
d = Droite(('0', '0'), ('1', '1'))
assert_eq('d._longueur()', '2**(1/2)', l())
e = Droite(('1', '0'), ('2/3', '1'))
assert_eq('e._longueur()', '10**(1/2)/3', l())
c1 = Cercle(('1/3', '3'), 'pi')
assert_eq('c1.diametre', '2*pi', l())
assert_eq('c1.perimetre', '2*pi**2', l())
d1 = Disque(c1)
assert_eq('d1.aire', 'pi**3', l())
# Droite/droite
M = Intersection(d, e)
assert_eq('M.coordonnees', '(3/4, 3/4)', l())
# Cercle/droite
I = Intersection(c, d)
assert_eq('I.coordonnees', '(7/12 - 143**(1/2)/12, 7/12 - 143**(1/2)/12)',
l())
assert_eq_num(I.coordonnees_approchees,
(-0.41318839525844997, -0.41318839525844997))
# Cercle/cercle
J = Intersection(c, c1)
assert_eq(
'J.coordonnees',
'(913/2364 - 98*(212563/12348 + (-913/1176 - 3*pi**2/98)**2'
'- 394*pi**2/343 - 197*(125/56 - 3*pi**2/14)**2/49)**(1/2)/197'
'+ 3*pi**2/197,'
'2671/1182 - 7*(212563/12348 + (-913/1176 - 3*pi**2/98)**2'
'- 394*pi**2/343 - 197*(125/56 - 3*pi**2/14)**2/49)**(1/2)/197'
'- 42*pi**2/197)', l())
def test_Intersection_cercles():
A = Point(-4.4375, 1.95833333333, legende=2)
B = Point(-2.10416666667, 0.875, legende=2)
c1 = Cercle(A, B)
C = Point(2.1875, 1.35416666667, legende=2)
c2 = Cercle(C, B)
D = Intersection_cercles(c2, c1, False, legende=2)
assert (D == (-1.9466976004889973, 2.6017297602107377))
assert (Intersection_cercles(c2, c1, True, legende=2) == B)
assert (Droite(A, C) == Mediatrice(B, D))
def test_Cercle():
A = Point(2.78841, -5.25)
O = Point(27.8841, -0.525)
c = Cercle(O, A)
assert (c.centre is O)
assert (c.point is A)
assertAlmostEqual(c.rayon, 25.5366262763)
# Test du typage dynamique
c = Cercle(Point(1, 1), 1)
assert (Point(1, 2) in c)
c = Cercle(Point(1, 1), Point(0, 2), Point(-1, 1))
assert (Point(0, 0) in c)
assertAlmostEqual(c.centre.coordonnees, (0, 1))
def test_eqn_formatee():
c = Cercle(('1/2', '2/3'), 'sqrt(2)')
assert c.equation_formatee == u'x\xb2 + y\xb2 - x - 4/3 y - 47/36 = 0'
d = Droite(('0', '0'), ('1', '1'))
assert d.equation_formatee == '-x + y = 0'
e = Droite(('1', '0'), ('2/3', '1'))
assert e.equation_formatee == '-x - 1/3 y + 1 = 0'
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_Cercle_diametre():
A = Point(2.78841, -5.25)
B = Point(27.8841, -0.525)
c = Cercle_diametre(A, B)
c1 = Cercle(A, B)
assertAlmostEqual(c.diametre, c1.rayon)
assertAlmostEqual(c.diametre, Segment(A, B).longueur)
assertAlmostEqual(c.centre.coordonnees, Milieu(A, B).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_aire_diametre_perimetre():
p = Triangle(('0', '0'), ('0', '1/3'), ('1/3', '0'))
assert_eq('p.aire', '1/18', l())
c = Cercle(('0', '0'), '5/3')
assert_eq('c.rayon', '5/3', l())
assert_eq('c.diametre', '10/3', l())
assert_eq('c.perimetre', '10/3*pi', l())
D = Disque(c)
assert_eq('D.aire', 'pi*25/9', l())
def test_nommage_automatique():
f = Feuille()
M1 = f.objets._ = Point()
assert("M1" in f.objets)
M2 = f.objets._ = Point(1, 3)
assert("M2" in f.objets)
f.objets._ = Droite(M1, M2)
assert("d1" in f.objets)
f.objets._ = Cercle(M1, M2)
assert("c1" in f.objets)
f.objets._ = Segment(M1, M2)
assert("s1" in f.objets)
def test_Tangente():
A = Point(4.75, -2.56887)
O = Point(2.56874, -85.2541)
M = Point(7.854, -552.444)
c = Cercle(O, A)
d = Tangente(c, A)
assert (A in d)
assert (M not in d)
d1 = Tangente(c, M)
assert (M in d1)
assert (A not in d1)
assert (not Tangente(c, O).existe)
def test_Intersection_droite_cercle():
A = Point(-3.075, 2.0, legende=2)
B = Point(0.0, 1.625, legende=2)
c1 = Cercle(A, B)
C = Point(-0.375, 4.425, legende=2)
D = Point(3.25, 0.125, legende=2)
d1 = Droite(C, D)
assert (not Intersection_droite_cercle(d1, c1).existe)
C(-5.675, 4.95)
I = Intersection_droite_cercle(d1, c1, True)
assert (I == (-4.87791007862, 4.51908023858))
J = Intersection_droite_cercle(d1, c1, False)
assert (J == (0.0201000262814, 1.87113640036))
def test_intersection_et_feuille():
u"""On teste que par défaut, le deuxième d'intersection soit différent du premier."""
f = Feuille()
f.objets._ = Point(-5.11060948081, 0.144469525959)
f.objets._ = Point(-3.97291196388, 0.794582392777)
f.objets._ = Cercle(f.objets.M1, f.objets.M2)
f.objets._ = Point(-3.26862302483, -1.10158013544)
f.objets._ = Point(-5.79683972912, 2.41986455982)
f.objets._ = Droite(f.objets.M3, f.objets.M4)
f.objets._ = Intersection_droite_cercle(f.objets.d1, f.objets.c1, True)
f.objets._ = Intersection_droite_cercle(f.objets.d1, f.objets.c1)
# On vérifie qu'on a bien obtenu le 2e point d'intersection (et non deux fois de suite le même)
assert (f.objets.M6.premier_point == False)
def test_transformations():
c = Cercle(('1/5', '4/5'), '1/3')
h = Homothetie(('1', '1'), '5/7')
v = Vecteur(c.centre, h.centre)
c1 = h(c)
v1 = Vecteur(c1.centre, h.centre)
assert v1.coordonnees == tuple(h.rapport*array(v.coordonnees))
assert_eq('c1.centre.coordonnees', '(3/7, 6/7)', l())
assert_eq('c1.rayon', '5/21', l())
c.rayon = '2'
assert_eq('c1.rayon', '10/7', l())
r = Rotation(('0', '1'), 'pi/3')
c2 = r(c)
t = Translation(('2/3', '-1/3'))
c3 = t(c)
m = Reflexion(Droite('y=x'))
c4 = m(c)
c.rayon = '3/7'
assert_eq('c2.rayon', '3/7', l())
assert_eq('c2.centre.coordonnees', '(1/10 + 3**(1/2)/10, 9/10 + 3**(1/2)/10)', l())
assert_eq('c3.rayon', '3/7', l())
assert_eq('c3.centre.coordonnees', '(13/15, 7/15)', l())
assert_eq('c4.rayon', '3/7', l())
assert_eq('c4.centre.coordonnees', '(4/5, 1/5)', l())
def test_noms_latex():
f = Feuille()
f.objets.A = Point()
assert(f.objets.A.nom == "A")
assert(f.objets.A.nom_latex == "$A$")
f.objets.B1 = Point()
assert(f.objets.B1.nom == "B1")
assert(f.objets.B1.nom_latex == "$B_{1}$")
f.objets.C17 = Point()
assert(f.objets.C17.nom == "C17")
assert(f.objets.C17.nom_latex == "$C_{17}$")
f.objets.objet5 = Point()
assert(f.objets.objet5.nom == "objet5")
assert(f.objets.objet5.nom_latex == "$objet_{5}$")
f.objets.Delta = Point()
assert(f.objets.Delta.nom == "Delta")
assert(f.objets.Delta.nom_latex == "$\\Delta$")
f.objets.delta = Point()
assert(f.objets.delta.nom == "delta")
assert(f.objets.delta.nom_latex == "$\\delta$")
f.objets.phi15 = Point()
assert(f.objets.phi15.nom == "phi15")
assert(f.objets.phi15.nom_latex == "$\\phi_{15}$")
f.objets.A_prime_prime = Point()
assert(f.objets.A_prime_prime.nom == "A_prime_prime")
assert(f.objets.A_prime_prime.nom_latex == "$A''$")
f.objets["A'B'"] = Point()
assert(f.objets.A_primeB_prime.nom == "A_primeB_prime")
assert(f.objets.A_primeB_prime.nom_latex == "$A'B'$")
f.objets.A_prime71 = Point()
assert(f.objets.A_prime71.nom == "A_prime71")
assert(f.objets.A_prime71.nom_latex == "$A'_{71}$")
f.objets.A17B22 = Point()
assert(f.objets.A17B22.nom == "A17B22")
assert(f.objets.A17B22.nom_latex == "$A_{17}B_{22}$")
f.objets.C_prime = Cercle()
assert(f.objets.C_prime.nom_latex == "$\\mathscr{C}'$")
f.objets.u = Vecteur()
assert(f.objets.u.nom_latex == "$\\vec u$")
f.objets.u_prime = Vecteur()
assert(f.objets.u_prime.nom_latex == "$\\overrightarrow{u'}$")
def test_info():
f = Feuille()
o = f.objets
with contexte(decimales = 2):
A = o.A = Point(5, 7)
assert(A.info == u"Point A de coordonnées (5, 7)")
B = o.B = Point(6.5, 9.3)
assert(B.info == u"Point B de coordonnées (6.5, 9.3)")
s = o.s = Segment(A, B)
assert(s.info == u"Segment s de longueur 2.75")
c = o.c = Cercle(s)
assert(c.info == u"Cercle c de rayon 1.37")
d = o.d = Droite(A, B)
assert(d.info == u"Droite d d'équation -2.3 x + 1.5 y + 1 = 0")
C = o.C = Point(-1.5, 2.7)
a = o.a = Arc_cercle(A, B, C)
assert(a.info == u'Arc a de longueur 7.5')
alpha = o.alpha = Angle(A, B, C)
assert(alpha.info == u'Angle alpha de valeur 0.3')
with contexte(decimales = 3):
assert(a.info == u'Arc a de longueur 7.505')
def test_equation_formatee():
assert Cercle((10, 0),
(1, 5)).equation_formatee == u'x\xb2 + y\xb2 - 20 x - 6 = 0'
def test_cercle_defini_par_equation():
c = Cercle("x^2+y^2-2x+y-3=0")
assertAlmostEqual(c.centre.xy, (1, -.5))
assertAlmostEqual(c.rayon, sqrt(4.25))
def test_Rayon():
c = Cercle((1, 1), (4, 5))
r = Rayon(c)
assertAlmostEqual(r.val, 5)
c.point.x = 1
assertAlmostEqual(r.val, 4)