def distance_from_point(l0: Point, l1: Point, p: Point):
'''
source: http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
condition: distance l0, l1 can't be zero
:param l0:
:param l1:
:param p:
:return:
'''
vec0 = Vector.create_from_points(l0, p)
print("vec0", vec0)
vec1 = Vector.create_from_points(l1, p)
print("vec1", vec1)
vec2 = Vector.create_from_points(l0, l1)
print("vec2", vec2)
vec_cx = vec0.cross(vec1)
print("vec_cx", vec_cx)
num_sq = vec_cx.dot(vec_cx)
den_sq = vec2.dot(vec2)
print("N:", num_sq)
print("D:", den_sq)
dist_sq = mpmath.fdiv(num_sq, den_sq)
return mpmath.sqrt(dist_sq)
def create_from_point_vector(normal_vector: Vector, point: Point):
d = normal_vector.dot(Vector.convert_point(point))
plane_params = [
normal_vector.x, normal_vector.y, normal_vector.z,
mpmath.fneg(d)
]
return Plane(plane_params)
def test_vector_dot(self):
v0 = Vector.from_float(-14.7, 26.4, 18.2)
v1 = Vector.from_float(26.47, 76.42, 108.2)
vec_dot = v0.dot(v1)
print(vec_dot)
self.assertAlmostEqual(3597.619, float(vec_dot), 12)
def create_from_3points(points):
vec_a = Vector.create_from_points(points[0], points[1])
vec_b = Vector.create_from_points(points[0], points[2])
normal_vector = vec_a.cross(vec_b)
d = normal_vector.dot(Vector.convert_point(points[2]))
plane_params = [
normal_vector.a, normal_vector.b, normal_vector.c,
mpmath.fneg(d)
]
return Plane(plane_params)
def distance_from_point3(l0: Point, l1: Point, p: Point):
'''
http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
:param l0:
:param l1:
:param p:
:return:
'''
vec_v = Vector.create_from_points(l0, p)
vec_w = Vector.create_from_points(l1, p)
vec_x = Vector.create_from_points(l0, l1)
c = vec_v.cross(vec_w)
nom_sq = c.dot(c)
den_sq = vec_x.dot(vec_x)
dist = mpmath.sqrt(mpmath.fdiv(nom_sq, den_sq))
return dist
def test_vector_magnitude(self):
p0 = Point.from_float(-14.7, 26.4, 18.2)
p1 = Point.from_float(26.47, 76.42, 108.2)
vec = Vector.create_from_points(p0, p1)
print(vec)
self.assertAlmostEqual(41.17, float(vec.a), 2)
self.assertAlmostEqual(50.02, float(vec.b), 2)
self.assertAlmostEqual(90.00, float(vec.c), 2)
mag = vec.magnitude()
print(mag)
self.assertAlmostEqual(110.891700771519, float(mag), 12)
vec = Vector.from_float(0.0027, 10705, 90.00004)
mag = vec.magnitude()
self.assertAlmostEqual(10705.378321535736, float(mag), 12)
def test_cross_product(self):
v0 = Vector.from_float(-14.7, 26.4, 18.2)
v1 = Vector.from_float(26.47, 76.42, 108.2)
vec_cross = v0.cross(v1)
# print(vec_cross)
self.assertAlmostEqual(1465.636, vec_cross.a)
self.assertAlmostEqual(2072.294, vec_cross.b)
self.assertAlmostEqual(-1822.182, vec_cross.c)
v0 = Vector.from_float(-1, -2, 3)
v1 = Vector.from_float(4, 0, -8)
vec_cross = v0.cross(v1)
# print(vec_cross)
self.assertAlmostEqual(16, vec_cross.a)
self.assertAlmostEqual(4, vec_cross.b)
self.assertAlmostEqual(8, vec_cross.c)
def distance_from_point4(l0: Point, l1: Point, p: Point):
'''
:param l0:
:param l1:
:param p:
:return:
'''
vec_nv = Vector.create_from_points(l0, l1)
plane0 = Plane.create_from_point_vector(vec_nv, p)
plane1 = Plane.create_from_3points([l0, l1, p])
vec_nv2 = plane1.nv.cross(plane0.nv)
plane2 = Plane.create_from_point_vector(vec_nv2, l0)
dist = plane2.point_plane_distance(p)
return dist
def create_from_points(p0: Point, p1: Point):
a_vec = Vector.create_from_points(p0, p1)
return Line(p0, a_vec)
def nv(self):
return Vector(self._params[:3])