def question_22_17(query):
VertexB = Point(Fraction(1), Fraction(-2), "B")
VertexC = Point(Fraction(-2), Fraction(-1), "C")
EdgeA = Line.get_line_contains_points(VertexB, VertexC)
p1 = Point(Fraction(2), Fraction(0), "p1")
p2 = Point(Fraction(2), Fraction(1), "p2")
EdgeC = Line.get_line_contains_points(VertexB, p1)
EdgeB = Line.get_line_contains_points(VertexC, p2)
del p1, p2
BisectorAngleA = Line.get_bisectors_for_2lines(EdgeB, EdgeC)[0]
VertexOfTargetRhombusInsideEdgeA = EdgeA.get_cross_point(BisectorAngleA)
EageOfTargetRhombusParallelsToEdgeC = Line.get_line_parallel_to(EdgeC, VertexOfTargetRhombusInsideEdgeA)
EageOfTargetRhombusParallelsToEdgeB = Line.get_line_parallel_to(EdgeB, VertexOfTargetRhombusInsideEdgeA)
VertexOfTargetRhombusInsideEdgeB = Line.get_cross_point(EageOfTargetRhombusParallelsToEdgeC, EdgeB)
VertexOfTargetRhombusInsideEdgeC = Line.get_cross_point(EageOfTargetRhombusParallelsToEdgeB, EdgeC)
TriangleEdges = {(EdgeA.a, EdgeA.b, EdgeA.c), (EdgeB.a, EdgeB.b, EdgeB.c), (EdgeC.a, EdgeC.b, EdgeC.c)}
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
init_figure.extend(TriangleEdges)
resolution_vertex_in_edge_a = query.query_point_by_symmetry(VertexOfTargetRhombusInsideEdgeA, init_figure)
resolution_vertex_in_edge_b = query.query_point_by_symmetry(VertexOfTargetRhombusInsideEdgeB, init_figure)
resolution_vertex_in_edge_c = query.query_point_by_symmetry(VertexOfTargetRhombusInsideEdgeC, init_figure)
resolution_product = itertools.product(resolution_vertex_in_edge_a,
resolution_vertex_in_edge_b,
resolution_vertex_in_edge_c)
solution_for_all = [frozenset((set(r[0]) | set(r[1]) | set(r[2]))) for r in resolution_product]
solution_for_all.sort()
targets = (VertexOfTargetRhombusInsideEdgeA, VertexOfTargetRhombusInsideEdgeB, VertexOfTargetRhombusInsideEdgeC)
for r in solution_for_all:
draw_resolution(r, targets, init_figure, grid_size)
def question_27_14(query):
total = []
total.append(centroid_of_2x2_grid(-2, +2, (True, True, True, False)))
total.append(centroid_of_2x2_grid(+2, +2, (True, True, False, True)))
total.append(centroid_of_2x2_grid(-2, -2, (True, False, True, True)))
total.append(centroid_of_2x2_grid(+2, -2, (True, True, True, False)))
x, y, w = centroid_of_iter(total)
point_target = Point(x, y, "Target")
solution = query.query_point_by_symmetry(point_target)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
for r in solution:
draw_resolution(r, [point_target], init_figure, grid_size)
def question_27_15(query):
total = []
total.append((Fraction(-1.5), Fraction(1.5), 4)) # top-left
total.append((2, Fraction(1.5), 4)) # top-right
total.append((centroid_of_2x2_grid(-2, -2, (False, True, True, True)))) # bottom-left -very left
total.append((centroid_of_2x2_grid(0, -2, (False, False, True, False)))) # bottom-left -right part
total.append((2, -2, 4)) # bottom-right
x, y, w = centroid_of_iter(total)
point_target = Point(x, y, "Target")
solution = query.query_point_by_symmetry(point_target)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
for r in solution:
draw_resolution(r, [point_target], init_figure, grid_size)
def question_16_15(query):
line1 = Line.get_line_contains_points(Point(-2, 0), Point(0, 1))
line2 = Line.get_line_contains_points(Point(0, -1), Point(1, 1))
line = Line.get_bisectors_for_2lines(line1, line2)[0]
A = line1.get_cross_point(line2)
# query and show it(them)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
init_figure.extend(((line1.a, line1.b, line1.c), (line2.a, line2.b, line2.c)))
solution = query.query_line_by_symmetry(line, (A,), init_figure)
points = set([s[0] for s in solution])
for r in solution[:4]:
p, fig = r
draw_resolution(fig, points, init_figure, grid_size)
def question_24_6(query):
A = Point(1, -2)
B = Point(0, 1)
line1 = Line.get_line_contains_points(A, B)
line2 = Line.get_line_by_point_slope(A, Fraction(4))
tan_alpha = Fraction(1, 4)
tan_beta = Fraction(1, 3)
tan_theta = tan_of_add(tan_of_double(tan_beta), tan_alpha)
slope = tan_of_neg(tan_of_complementary(tan_theta))
line = Line.get_line_by_point_slope(A, slope)
# query and show it(them)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
init_figure.extend(((line1.a, line1.b, line1.c), (line2.a, line2.b, line2.c)))
solution = query.query_line_by_symmetry(line, (A,), init_figure)
points = set([s[0] for s in solution])
for r in solution[:4]:
p, fig = r
draw_resolution(fig, points, init_figure, grid_size)
def question_14_8(query):
# get Point B
line1 = Line.get_line_contains_points(Point(-3, -1), Point(3, -3))
line_tmp = Line(1, 0, -2)
B = line1.get_cross_point(line_tmp)
# get Point A
line2 = Line.get_line_contains_points(Point(-3, 1), Point(2, 2))
line_tmp = Line(1, 0, 1)
A = line2.get_cross_point(line_tmp)
line = Line.get_line_contains_points(A, B)
point_target = A.middle(B)
# query and show it(them)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
for ll in (line, line1, line2):
init_figure.append((ll.a, ll.b, ll.c))
solution = query.query_point_by_symmetry(point_target, init_figure)
for r in solution[:4]:
draw_resolution(r, [point_target], init_figure, grid_size)
def question_14_9(query):
# get Point B
line1 = Line.get_line_contains_points(Point(-3, 1), Point(3, 3))
line2 = Line(1, 0, -2)
B = line1.get_cross_point(line2)
# get Point A
line1 = Line.get_line_contains_points(Point(2, -3), Point(3, 0))
line2 = Line(0, 1, -1)
A = line1.get_cross_point(line2)
del line1, line2
# get the midpoint
target_point_x = (A.x + B.x) / 2
target_point_y = (A.y + B.y) / 2
point_target = Point(target_point_x, target_point_y, "Target")
# query and show it(them)
solution = query.query_point_by_symmetry(point_target)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
for r in solution:
draw_resolution(r, [point_target], init_figure, grid_size)
def question_24_7(query):
A = Point(2, -1)
B = Point(-2, 0)
line1 = Line.get_line_contains_points(A, B)
line2 = Line.get_line_by_point_slope(A, Fraction(-1))
tan_alpha = Fraction(1, 4)
tan_beta = tan_of_sub(Fraction(1), tan_alpha)
tan_theta = tan_of_sub(tan_beta, tan_alpha)
slope = tan_theta
line = Line.get_line_by_point_slope(A, slope)
# query and show it(them)
init_figure, grid_size = common.INIT_FIGURE(), common.GRID_SIZE()
init_figure.extend(((line1.a, line1.b, line1.c), (line2.a, line2.b, line2.c)))
solution = query.query_line_by_symmetry(line, (A,), init_figure)
points = set([s[0] for s in solution])
for r in solution[:4]:
p, fig = r
draw_resolution(fig, points, init_figure, grid_size)
def get_pythagorea_graph():
point_tab = bfs_dump_for_pythagorea(common.INIT_FIGURE(),
common.GRID_SIZE(), 3)
return point_tab