Module sverchok.utils.modules.geom_utils

Functions

def add_v3_v3v3(a, b)

add a to b.

inputs: two 3-element-vector-like-iterables, a and b output: one 3-element-vector-like tuple

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def add_v3_v3v3(a, b):
    """
    add a to b.

    inputs: two 3-element-vector-like-iterables, a and b
    output: one 3-element-vector-like tuple
    """
    return a[0]+b[0], a[1]+b[1], a[2]+b[2]

def ccw_angle(v1, v2, normal)

you want to know the counter-clockwise angle between 3 vertices. v1 / / v0
v2 input: # all must be numpy arrays input: v1, v2 # are vectors positioned in respect to an origin (v0) input: normal # this determines the direction of ccw. (relative to which axis) output: angle in radians

https://uk.mathworks.com/matlabcentral/answers/461410 'how-to-get-direction-for-3d-angles-between-2-vectors'

if v0 is not already at [0, 0, 0] then you must translate the v1 and v2 locations first.

ccw_angle(v1-v0, v2-v0, normal)

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def ccw_angle(v1, v2, normal):
    """
    you want to know the counter-clockwise angle between 3 vertices.
           v1
         / 
       / 
    v0         
       \
         \
           v2
    input:          # all must be numpy arrays
    input: v1, v2   # are vectors positioned in respect to an origin (v0)
    input: normal   # this determines the direction of ccw. (relative to which axis)
    output: angle in radians

    https://uk.mathworks.com/matlabcentral/answers/461410
    'how-to-get-direction-for-3d-angles-between-2-vectors'

    if v0 is not already at [0, 0, 0] then you must translate the v1 and v2 locations first.

        ccw_angle(v1-v0, v2-v0, normal)

    """
    ang = np.arctan2(np.linalg.norm(np.cross(v1, v2)), np.dot(v1, v2))
    if np.dot(np.cross(v1, v2), normal) < 0:
        ang = 2*np.pi - ang
    return ang

def dot_v3v3(a, b)

the sum of the elementwise multiplication of a and b.

inputs: two 3-element-vector-like-iterables, a and b output: one scalar value

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def dot_v3v3(a, b):
    """
    the sum of the elementwise multiplication of a and b.

    inputs: two 3-element-vector-like-iterables, a and b
    output: one scalar value
    """
    return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]

def interp_v3_v3v3(a, b, t=0.5)

linearly interpolate between two 3-element-vector-like values

inputs: a and b must be 3-element iteratibles like: [0,0,0] or (0,0,0) t should be a float, usually (not not limited to) values between 0 and 1 outputs: single 3-element vector

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def interp_v3_v3v3(a, b, t=0.5):
    """
    linearly interpolate between two 3-element-vector-like values
    
    inputs: 
        a and b must be 3-element iteratibles like: [0,0,0] or (0,0,0)
        t should be a float, usually (not not limited to) values between 0 and 1
    outputs:
        single 3-element vector
    """
    if t == 0.0: return a
    elif t == 1.0: return b
    else:
        s = 1.0 - t
        return (s * a[0] + t * b[0], s * a[1] + t * b[1], s * a[2] + t * b[2])

def is_reasonably_opposite(n, normal_one)

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def is_reasonably_opposite(n, normal_one):
    return dot_v3v3(normalize(n), normalize(normal_one)) < 0.0

def isect_line_plane(l1, l2, plane_co, plane_no)

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def isect_line_plane(l1, l2, plane_co, plane_no):
    u = l2[0]-l1[0], l2[1]-l1[1], l2[2]-l1[2]
    h = l1[0]-plane_co[0], l1[1]-plane_co[1], l1[2]-plane_co[2]
    dot = plane_no[0]*u[0] + plane_no[1]*u[1] + plane_no[2]*u[2]

    if abs(dot) > 1.0e-5:
        f = -(plane_no[0]*h[0] + plane_no[1]*h[1] + plane_no[2]*h[2]) / dot
        return l1[0]+u[0]*f, l1[1]+u[1]*f, l1[2]+u[2]*f
    else:
        # parallel to plane
        return False

def length(v)

gives you the length of the 3-element-vector

input: vector-like output: scalar length

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def length(v):
    """
    gives you the length of the 3-element-vector
    
    input: vector-like
    output: scalar length
    """
    return math.sqrt((v[0] * v[0]) + (v[1] * v[1]) + (v[2] * v[2]))

def length_v2(v)

gives you the length of the 2-element-vector

input: vector-like output: scalar length

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def length_v2(v):
    """
    gives you the length of the 2-element-vector
    
    input: vector-like
    output: scalar length
    """    
    return math.sqrt((v[0] * v[0]) + (v[1] * v[1]))

def madd_v3_v3v3fl(a, b, f=1.0)

multiply b by f, and add the result to a

inputs: - two 3-element-vector-like-iterables, a and b - f : a scalar "amplifier" factor output: one 3-element-vector-like tuple

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def madd_v3_v3v3fl(a, b, f=1.0):
    """
    multiply b by f, and add the result to a

    inputs:
        - two 3-element-vector-like-iterables, a and b
        - f : a scalar "amplifier" factor
    output: one 3-element-vector-like tuple
    """    
    return a[0]+b[0]*f, a[1]+b[1]*f, a[2]+b[2]*f

def mean(verts)

get the average 3d location of all inputs.

input: expects a list of 3-element-vector like iterables output: a single 3-element-vector like tuple

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def mean(verts):
    """
    get the average 3d location of all inputs.

    input: expects a list of 3-element-vector like iterables
    output: a single 3-element-vector like tuple
    """

    vx, vy, vz = 0, 0, 0
    for v in verts:
        vx += v[0]
        vy += v[1]
        vz += v[2]
    numverts = len(verts)
    return vx/numverts, vy/numverts, vz/numverts

def mul_v3_f1v3(a, v)

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def mul_v3_f1v3(a, v):
    return a*v[0], a*v[1], a*v[2]

def normalize(v)

rescales the input (3-element-vector), so that the length of the vector "extents" is One. this doesn't change the direction of the vector, only the magnitude.

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def normalize(v):
    """
    rescales the input (3-element-vector), so that the length of the vector "extents" is One.
    this doesn't change the direction of the vector, only the magnitude.
    """
    l = math.sqrt((v[0] * v[0]) + (v[1] * v[1]) + (v[2] * v[2]))
    return [v[0]/l, v[1]/l, v[2]/l]

def obtain_normal3(p1, p2, p3)

http://stackoverflow.com/a/8135330/1243487 finds the normal of a triangle defined by passing 3 vectors

input: three 3-element-iterables (tuples or lists) output: one 3-element tuple representing the direction of the face (not normalized)

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def obtain_normal3(p1, p2, p3):
    """
    http://stackoverflow.com/a/8135330/1243487
    finds the normal of a triangle defined by passing 3 vectors

    input: three 3-element-iterables (tuples or lists)
    output: one 3-element tuple representing the direction of the face (not normalized)
    """
    return [
        ((p2[1]-p1[1])*(p3[2]-p1[2]))-((p2[2]-p1[2])*(p3[1]-p1[1])),
        ((p2[2]-p1[2])*(p3[0]-p1[0]))-((p2[0]-p1[0])*(p3[2]-p1[2])),
        ((p2[0]-p1[0])*(p3[1]-p1[1]))-((p2[1]-p1[1])*(p3[0]-p1[0]))
    ]

def pt_in_triangle(p_test, p0, p1, p2)

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def pt_in_triangle(p_test, p0, p1, p2):
    # Function taken from Ramiro R.C https://stackoverflow.com/a/46409704
    dX = p_test[0] - p0[0]
    dY = p_test[1] - p0[1]
    dX20 = p2[0] - p0[0]
    dY20 = p2[1] - p0[1]
    dX10 = p1[0] - p0[0]
    dY10 = p1[1] - p0[1]

    s_p = (dY20*dX) - (dX20*dY)
    t_p = (dX10*dY) - (dY10*dX)
    D = (dX10*dY20) - (dY10*dX20)

    if D > 0:
        return (  (s_p >= 0) and (t_p >= 0) and (s_p + t_p) <= D  )
    else:
        return (  (s_p <= 0) and (t_p <= 0) and (s_p + t_p) >= D  )

def random_pt_between(v1, v2, v3)

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def random_pt_between(v1, v2, v3):
    a = random.random()
    b = random.random()
    # x = v1 + a(v2 - v1) + b(v3 - v1)
    A = sub_v3_v3v3(v2, v1)
    B = sub_v3_v3v3(v3, v1)
    A = mul_v3_f1v3(a, A)
    B = mul_v3_f1v3(b, B)
    return sum_v3_v3l([v1, A, B])

def sub_v3_v3v3(a, b)

subtract b from a.

inputs: two 3-element-vector-like-iterables, a and b output: one 3-element-vector-like tuple

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def sub_v3_v3v3(a, b):
    """
    subtract b from a.

    inputs: two 3-element-vector-like-iterables, a and b
    output: one 3-element-vector-like tuple
    """
    return a[0]-b[0], a[1]-b[1], a[2]-b[2]

def sum_v3_v3l(lvtx)

sum all input "vectors"

input : list of iterables of 3 element output : a new 3-tuple

usage :

new_v = sum_v3_v3l([v1, v2, v3, v4, v5,....])

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def sum_v3_v3l(lvtx):
    """ sum all input "vectors"

    input  : list of iterables of 3 element
    output : a new 3-tuple

    usage  :

        new_v = sum_v3_v3l([v1, v2, v3, v4, v5,....]) 

    """
    vx, vy, vz = 0, 0, 0
    for v in lvtx:
        vx += v[0]
        vy += v[1]
        vz += v[2]
    return vx, vy, vz