update

.CondaPkg/env/Lib/site-packages/skimage/draw/draw3d.py

@@ -0,0 +1,109 @@
+import numpy as np
+from scipy.special import ellipkinc as ellip_F, ellipeinc as ellip_E
+
+
+def ellipsoid(a, b, c, spacing=(1.0, 1.0, 1.0), levelset=False):
+    """
+    Generates ellipsoid with semimajor axes aligned with grid dimensions
+    on grid with specified `spacing`.
+
+    Parameters
+    ----------
+    a : float
+        Length of semimajor axis aligned with x-axis.
+    b : float
+        Length of semimajor axis aligned with y-axis.
+    c : float
+        Length of semimajor axis aligned with z-axis.
+    spacing : 3-tuple of floats
+        Spacing in three spatial dimensions.
+    levelset : bool
+        If True, returns the level set for this ellipsoid (signed level
+        set about zero, with positive denoting interior) as np.float64.
+        False returns a binarized version of said level set.
+
+    Returns
+    -------
+    ellipsoid : (M, N, P) array
+        Ellipsoid centered in a correctly sized array for given `spacing`.
+        Boolean dtype unless `levelset=True`, in which case a float array is
+        returned with the level set above 0.0 representing the ellipsoid.
+
+    """
+    if (a <= 0) or (b <= 0) or (c <= 0):
+        raise ValueError('Parameters a, b, and c must all be > 0')
+
+    offset = np.r_[1, 1, 1] * np.r_[spacing]
+
+    # Calculate limits, and ensure output volume is odd & symmetric
+    low = np.ceil(-np.r_[a, b, c] - offset)
+    high = np.floor(np.r_[a, b, c] + offset + 1)
+
+    for dim in range(3):
+        if (high[dim] - low[dim]) % 2 == 0:
+            low[dim] -= 1
+        num = np.arange(low[dim], high[dim], spacing[dim])
+        if 0 not in num:
+            low[dim] -= np.max(num[num < 0])
+
+    # Generate (anisotropic) spatial grid
+    x, y, z = np.mgrid[
+        low[0] : high[0] : spacing[0],
+        low[1] : high[1] : spacing[1],
+        low[2] : high[2] : spacing[2],
+    ]
+
+    if not levelset:
+        arr = ((x / float(a)) ** 2 + (y / float(b)) ** 2 + (z / float(c)) ** 2) <= 1
+    else:
+        arr = ((x / float(a)) ** 2 + (y / float(b)) ** 2 + (z / float(c)) ** 2) - 1
+
+    return arr
+
+
+def ellipsoid_stats(a, b, c):
+    """
+    Calculates analytical surface area and volume for ellipsoid with
+    semimajor axes aligned with grid dimensions of specified `spacing`.
+
+    Parameters
+    ----------
+    a : float
+        Length of semimajor axis aligned with x-axis.
+    b : float
+        Length of semimajor axis aligned with y-axis.
+    c : float
+        Length of semimajor axis aligned with z-axis.
+
+    Returns
+    -------
+    vol : float
+        Calculated volume of ellipsoid.
+    surf : float
+        Calculated surface area of ellipsoid.
+
+    """
+    if (a <= 0) or (b <= 0) or (c <= 0):
+        raise ValueError('Parameters a, b, and c must all be > 0')
+
+    # Calculate volume & surface area
+    # Surface calculation requires a >= b >= c and a != c.
+    abc = [a, b, c]
+    abc.sort(reverse=True)
+    a = abc[0]
+    b = abc[1]
+    c = abc[2]
+
+    # Volume
+    vol = 4 / 3.0 * np.pi * a * b * c
+
+    # Analytical ellipsoid surface area
+    phi = np.arcsin((1.0 - (c**2 / (a**2.0))) ** 0.5)
+    d = float((a**2 - c**2) ** 0.5)
+    m = a**2 * (b**2 - c**2) / float(b**2 * (a**2 - c**2))
+    F = ellip_F(phi, m)
+    E = ellip_E(phi, m)
+
+    surf = 2 * np.pi * (c**2 + b * c**2 / d * F + b * d * E)
+
+    return vol, surf