因为固体物理书上的球面投影图太难看，就自学 javascipt 用 echarts 做了个可交互的，效果如下：
上面为立方晶系主要晶面（晶向）的球面投影，具体计算代码如下：
import math
import numpy as np
def c_scale(A):
A = np.array(A)
n_dim = A.shape[1]; n_size = A.shape[0]
scale2 = np.zeros(n_size)
for j in range(n_dim):
for i in range(n_size):
scale2[i] += A[i,j]**2
scale = scale2 ** 0.5
return scale
def normalize(A): # 二维数组归一化
A = np.array(A)
scale = c_scale(A)
A = np.divide(A.T,scale).T
return A
def cal_point_dict(input_str_list):
points = []; points_dicts = []
for input_str in input_str_list:
input_str=input_str.replace('[',''); input_str=input_str.replace(']','')
try:
data = input_str.split(' ')
point = [] # 求解投影点
for j in range(len(data)):
point.append(int(data[j]))
points.append(point)
except:
data = input_str.split(',')
point = [] # 求解投影点
for j in range(len(data)):
point.append(int(data[j]))
points.append(point)
points_p = normalize(points)
for i in range(len(points_p)):
points_dict={}
points_dict['name']=input_str_list[i]
points_dict['value']=points_p[i].tolist()
points_dicts.append(points_dict)
return points_dicts
# 各晶面指数
input_str_list = ['[0 0 1]','[1 0 0]','[0 1 0]','[0 0 -1]','[-1 0 0]','[0 -1 0]',
'[1 0 1]','[0 1 1]','[1 1 0]','[-1 0 -1]','[0 -1 -1]','[-1 -1 0]',
'[1 0 -1]','[0 1 -1]','[1 -1 0]','[-1 0 1]','[0 -1 1]','[-1 1 0]',
'[1 1 1]','[-1 1 1]','[1 -1 1]','[1 1 -1]',
'[-1 -1 -1]','[1 -1 -1]','[-1 1 -1]','[-1 -1 1]']
points_dicts = cal_point_dict(input_str_list)
points_dicts # 将该数据复制到 球坐标.html 下
绘图 html 源码：
<!DOCTYPE html>
<html style="height: 100%">
<head>
<meta charset="utf-8">
</head>
<body style="height: 100%; margin: 0">
<div id="container" style="height: 100%"></div>
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/echarts/dist/echarts.min.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/echarts-gl/dist/echarts-gl.min.js"></script>
<script type="text/javascript">
var dom = document.getElementById("container");
var myChart = echarts.init(dom);
var app = {};
option = null;
//var data = [{name:'[1 0 0]',value:[1,0,0]},{name:'[0 1 1]',value:[0,1,1]}];
var data1 =
[{'name': '[0 0 1]', 'value': [0.0, 0.0, 1.0]},
{'name': '[1 0 0]', 'value': [1.0, 0.0, 0.0]},
{'name': '[0 1 0]', 'value': [0.0, 1.0, 0.0]},
{'name': '[0 0 -1]', 'value': [0.0, 0.0, -1.0]},
{'name': '[-1 0 0]', 'value': [-1.0, 0.0, 0.0]},
{'name': '[0 -1 0]', 'value': [0.0, -1.0, 0.0]},
{'name': '[1 0 1]', 'value': [0.7071067811865475, 0.0, 0.7071067811865475]},
{'name': '[0 1 1]', 'value': [0.0, 0.7071067811865475, 0.7071067811865475]},
{'name': '[1 1 0]', 'value': [0.7071067811865475, 0.7071067811865475, 0.0]},
{'name': '[-1 0 -1]',
'value': [-0.7071067811865475, 0.0, -0.7071067811865475]},
{'name': '[0 -1 -1]',
'value': [0.0, -0.7071067811865475, -0.7071067811865475]},
{'name': '[-1 -1 0]',
'value': [-0.7071067811865475, -0.7071067811865475, 0.0]},
{'name': '[1 0 -1]', 'value': [0.7071067811865475, 0.0, -0.7071067811865475]},
{'name': '[0 1 -1]', 'value': [0.0, 0.7071067811865475, -0.7071067811865475]},
{'name': '[1 -1 0]', 'value': [0.7071067811865475, -0.7071067811865475, 0.0]},
{'name': '[-1 0 1]', 'value': [-0.7071067811865475, 0.0, 0.7071067811865475]},
{'name': '[0 -1 1]', 'value': [0.0, -0.7071067811865475, 0.7071067811865475]},
{'name': '[-1 1 0]', 'value': [-0.7071067811865475, 0.7071067811865475, 0.0]},
{'name': '[1 1 1]',
'value': [0.5773502691896258, 0.5773502691896258, 0.5773502691896258]},
{'name': '[-1 1 1]',
'value': [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258]},
{'name': '[1 -1 1]',
'value': [0.5773502691896258, -0.5773502691896258, 0.5773502691896258]},
{'name': '[1 1 -1]',
'value': [0.5773502691896258, 0.5773502691896258, -0.5773502691896258]},
{'name': '[-1 -1 -1]',
'value': [-0.5773502691896258, -0.5773502691896258, -0.5773502691896258]},
{'name': '[1 -1 -1]',
'value': [0.5773502691896258, -0.5773502691896258, -0.5773502691896258]},
{'name': '[-1 1 -1]',
'value': [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258]},
{'name': '[-1 -1 1]',
'value': [-0.5773502691896258, -0.5773502691896258, 0.5773502691896258]}]
;
var radius = 1;
option = {
tooltip: {},
xAxis3D: {},
yAxis3D: {},
zAxis3D: {},
grid3D: {},
animation: true,
series: [{
name: '参考球',
type: 'surface',
parametric: true,
// shading: 'albedo',
wireframe: {
show: true
},
shading: 'color',
itemStyle: {
color: [1, 1, 1, 1],
opacity: 0.8
},
parametricEquation: {
u: {
min: -Math.PI,
max: Math.PI,
step: Math.PI / 20
},
v: {
min: 0,
max: Math.PI,
step: Math.PI / 20
},
x: function (u, v) {
return radius * Math.sin(v) * Math.sin(u);
},
y: function (u, v) {
return radius * Math.sin(v) * Math.cos(u);
},
z: function (u, v) {
return radius * Math.cos(v);
}
}
},
{
name: '球面投影点',
type: 'scatter3D',
blendMode: 'darken',
showEffectOn: 'render',
zlevel: 2,
symbol : 'circle',
label: {
show: true,
position: 'top',
formatter: '{b}'},
symbolSize: 10,
data: data1
}
]
};;
if (option && typeof option === "object") {
myChart.setOption(option, true);
}
</script>
</body>
</html>
然而这样画出的图形还不能实现 3D 空间中的遮挡关系，要进一步实现可能还要借助 echarts 的地理坐标功能。
总结
