使用 python 的第三方繪圖庫 mayavi 繪制不同尺寸的球
“萬惡”的 mayavi 庫，琢磨了老半天，才弄清楚怎么根據球心坐標和半徑繪制出一個球。
解決方案
mayavi 的 mlab 類似 matplotlib 的 pyplot, 其中points3d函數用來繪制一些三維空間的離散點，在實際情況中，一個點必然需要一種“表示方式”，在points3d函數中，提供了"sphere", "point", "cylinder", "cone", "cube", "2darrow", "2dcircle"等很多模式，即用“球、點、圓柱、圓錐、方塊、二維箭頭、二維圓”等來表示一個點，當選擇"point"時，往往可能由於點的可視感太低而顯示出來的結果“啥都沒有”，所以此函數默認的圖例模式為"sphere"。由此引發感想，若可控制每個球的大小，那么不就可以用這些球來表示出自己想畫的一些球了嘛。
於是通過研究mlab.points3d()函數發現，可以傳入若干球的球心坐標對應的x,y,z，以及相應的半徑r，然后設置好scale_factor、resolution、mode參數即可。這三個參數和r參數的說明如下：
scale_factor：縮放因子，mayavi 的官方文檔說得很含糊，其到底怎么發揮作用的完全沒有說清楚，這里經過多次試驗總結為：將其設置為scale_factor=1的話，即會按傳入的“大小參數”r進行一比一縮放，這個參數可視為不存在。resolution：每一個點（球）的解析度/分辨率，為整數，默認值為 8，默認值為 8 時可明顯看出用球表示點時球有“棱角”，這里將其設置為 30。
觀察這里的坐標，顯然，resolution參數還會一定程度上影響計算的精度吧，畢竟表面是計算后渲染出來的！咳，這點以后再說吧，目前只是需要繪制圖形效果。
mode：其實可以不設置，默認情況即是用 sphere 作為點的的圖例，這里拿出來只是作為強調，應該設置為mode="sphere"。r：按照官方文檔，嚴格來說這不是r參數，其形參名為s，但不管叫什么，它就是表示points3d函數繪制出來的點的大小的一個參數。這里經過多次試驗，發現它的數值表示的“大小含義”，對於mode="sphere"來說就是球的直徑，對於mode="cube"來說就是立方體的邊長，對於mode="cone"來說就是圓錐的高，對於mode="cylinder"來說就是圓柱的高。概括而言，在內部實現中，這種對應關系是否有統一理論指導其代碼實現尚不得而知。
於是，這樣繪制你的球：mlab.points3d(x, y, z, r*2, scale_factor=1, resolution=30)。
示例
設置一個位於原點的單位球，然后在其上、下、左、右、前、后再各放置 1 個球，檢驗他們的相切情況。
import numpy as np
from mayavi import mlab
points = np.array([[0, 0, 0, 1],
[4, 0, 0, 3],
[-4, 0, 0, 3],
[0, 2, 0, 1],
[0, -2, 0, 1],
[0, 0, 2, 0.5],
[0, 0, -2, 0.5]])
x, y, z, r = points[:, 0], points[:, 1], points[:, 2], points[:, 3]
mlab.points3d(x, y, z, r*2, scale_factor=1, resolution=30, mode="sphere")
mlab.outline()
mlab.axes()
mlab.show()
附1：我本來想要畫的球堆積顆粒模型：
附2：原本我采用的繪球函數：
若要在一張圖上繪制很多球的話，這種方式只能使用for循環一個球一個球地進行繪制，效率比較低，硬件成本也比較高。也是為此一直在研究points3d函數的。
import random
import numpy as np
class Plotter:
random.seed(3.14)
@classmethod
def randomColor(cls):
color = (random.random(), random.random(), random.random())
return color
@classmethod
def sphere(cls, center, radius, nPoints=100, opacity=1.0, color=None):
"""Draw a sphere according to given center and radius.
Parameters:
-----------
center(tuple): (x, y, z) coordinate
radius(float): radius of the sphere
"""
u = np.linspace(0, 2 * np.pi, nPoints)
v = np.linspace(0, np.pi, nPoints)
x = radius * np.outer(np.cos(u), np.sin(v)) + center[0]
y = radius * np.outer(np.sin(u), np.sin(v)) + center[1]
z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) + center[2]
from mayavi import mlab
color = cls.randomColor() if color is None else color
scene = mlab.mesh(x, y, z, color=color, opacity=opacity)
return scene
附3：mlab.points3d函數的官方文檔：
mayavi.mlab.points3d(*args, **kwargs)¶
Plots glyphs (like points) at the position of the supplied data.
Function signatures:
points3d(x, y, z...)
points3d(x, y, z, s, ...)
points3d(x, y, z, f, ...)
x, y and z are numpy arrays, or lists, all of the same shape, giving the positions of the points.
If only 3 arrays x, y, z are given, all the points are drawn with the same size and color.
In addition, you can pass a fourth array s of the same shape as x, y, and z giving an associated scalar value for each point, or a function f(x, y, z) returning the scalar value. This scalar value can be used to modulate the color and the size of the points.
Keyword arguments:
color: the color of the vtk object. Overides the colormap, if any, when specified. This is specified as a triplet of float ranging from 0 to 1, eg (1, 1, 1) for white. colormap: type of colormap to use. extent: [xmin, xmax, ymin, ymax, zmin, zmax] Default is the x, y, z arrays extent. Use this to change the extent of the object created. figure: Figure to populate. line_width: The width of the lines, if any used. Must be a float. Default: 2.0 mask_points: If supplied, only one out of ‘mask_points’ data point is displayed. This option is useful to reduce the number of points displayed on large datasets Must be an integer or None. mode: the mode of the glyphs. Must be ‘2darrow’ or ‘2dcircle’ or ‘2dcross’ or ‘2ddash’ or ‘2ddiamond’ or ‘2dhooked_arrow’ or ‘2dsquare’ or ‘2dthick_arrow’ or ‘2dthick_cross’ or ‘2dtriangle’ or ‘2dvertex’ or ‘arrow’ or ‘axes’ or ‘cone’ or ‘cube’ or ‘cylinder’ or ‘point’ or ‘sphere’. Default: sphere name: the name of the vtk object created. opacity: The overall opacity of the vtk object. Must be a float. Default: 1.0 reset_zoom: Reset the zoom to accomodate the data newly added to the scene. Defaults to True. resolution: The resolution of the glyph created. For spheres, for instance, this is the number of divisions along theta and phi. Must be an integer. Default: 8 scale_factor: The scaling applied to the glyphs. the size of the glyph is by default calculated from the inter-glyph spacing. Specify a float to give the maximum glyph size in drawing units scale_mode: the scaling mode for the glyphs (‘vector’, ‘scalar’, or ‘none’). transparent: make the opacity of the actor depend on the scalar. vmax: vmax is used to scale the colormap. If None, the max of the data will be used vmin: vmin is used to scale the colormap. If None, the min of the data will be used