Find perpendicular to given vector (Velocity) in 3D <python>

Question

I have a object A move with Velocity (v1, v2, v3) in 3D space.
Object position is (px,py,pz)
Now i want to add certain particles around object A (in radius dis) on plane which perpendicular to its Velocity direction.

I find something call “cross product” but seen that no use in this case.

Anyone can help?
I’m new to python and don’t really know how to crack it.

Asked By: kaworuonline

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Source

Answer 1

The plane perpendicular to a vector ⟨A, B, C⟩ has the general equation Ax + By + Cz + K = 0.

Answered By: Ignacio Vazquez-Abrams

Answer 2

The equation of the plane is:

v1*(x-px) + v2*(y-py) + v3*(z-pz) = 0

When you know (x,y) you can find z and so on.

Example:

z = pz – (v1*(x-px) + v2*(y-py))/v3

Answered By: Igor Chubin

Answer 3

Lets say we have a point p1, and we want to build a circle of points around it with radius r so that all points on the circle are orthogonal to a vector n.. here is a working example

p1 = np.array([-21.03181359,   4.54876345,  19.26943601])
n = np.array([-0.06592715,  0.00713031, -0.26809672])
n = n / np.linalg.norm(n) # normalise n
r = 0.5


x = np.array([1,0,0]).astype(np.float64) # take a random vector of magnitude 1
x -= x.dot(n) * n / np.linalg.norm(n)**2  # make it orthogonal to n
x /= np.linalg.norm(x)  # normalize

# find first point on circle (x1). 
# currently it has magnitude of 1, so we multiply it by the r
x1 = p1 + (x*r)

# vector from lumen centre to first circle point
p1x1 = x1 - p1

def rotation_matrix(axis, theta):
    """
    Return the rotation matrix associated with counterclockwise rotation about
    the given axis by theta radians.
    """
    axis = np.asarray(axis)
    axis = axis / math.sqrt(np.dot(axis, axis))
    a = math.cos(theta / 2.0)
    b, c, d = -axis * math.sin(theta / 2.0)
    aa, bb, cc, dd = a * a, b * b, c * c, d * d
    bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
    return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],
                     [2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
                     [2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])


# rotate the vector p1x1 around the axis n with angle theta
circle = []
for theta in range(0,360,6):
    circle_i = np.dot(rotation_matrix(n, np.deg2rad(theta)), p1x1)
    circle.append(circle_i+p1)

ax = axes3d.Axes3D(plt.figure(figsize=(10,10)))
ax.scatter3D(*np.array(circle).T, s=10, c='red')
ax.scatter3D(*p1.T, s=10, c='black')
ax.set_xlabel('X', size=40)
ax.set_ylabel('Y', size=40)
ax.set_zlabel('Z', size=40)

ax.set_xlim(-19,-22)
ax.set_ylim(2,5)
ax.set_zlim(18,21)

Answered By: noble_kazoo

Find perpendicular to given vector (Velocity) in 3D <python>

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