PyCafe - Solara - 3D Point and Plane Algebra Visualization

app.py
requirements.txt

app.py

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136

"""
Based on https://enki.ws/ganja.js/examples/coffeeshop.html#pga3d_points_and_lines.
"""

# %%
from typing import cast
from kingdon import Algebra
import math
from timeit import default_timer

from kingdon.graph import walker, encode, GraphWidget
import solara.lab
import solara
import asyncio

alg = Algebra(3, 0, 1)
# %%

point = lambda x, y, z: alg.vector(e0=1, e1=x, e2=y, e3=z).dual()
plane = lambda a, b, c, d: alg.vector(e1=a, e2=b, e3=c, e0=d)


def dist_pp(P1, P2) -> float:  # point to point
    return (P1.normalized() & P2.normalized()).norm().e


def dist_pP(P, p) -> float:  # point to plane
    return (P.normalized() & p.normalized()).norm().e


def dist_ll(l1, l2) -> float:  # line to line
    return (l1.normalized() * l2.normalized()).dual().norm().e


def angle_pp(p1, p2):  # Angle between planes
    return math.acos((p1.normalized() | p2.normalized()).e) * 180 / math.pi


def angle_ll(l1, l2):  # Angle between lines
    return math.acos((l1.normalized() | l2.normalized()).e) * 180 / math.pi


# Create 5 points.
A = point(0, 0.8, 0)
B = point(0.8, -1, -0.8)
C = point(-0.8, -1, -0.8)
D = point(0.8, -1, 0.8)
E = point(-0.8, -1, 0.8)

# Our ground plane
a = B & C & D

# %%


def graph_func(time):
    A = point(0, math.sin(time * 4), 0)

    subjects = [
        0xD0FFE1,
        [A, B, C],  # graph on face
        0x00AA88,
        [A, B],
        [A, C],
        [A, D],
        [B, C],
        [B, D],
        [C, E],
        [A, E],
        [E, D],  # graph all edges
        0x444444,
        A,
        "A",
        B,
        "B",
        C,
        "C",
        D,
        "D",
        E,
        "E",  # graph all vertices
        0xFF8844,
        [A, E],
        f"{dist_pp(A, E):.2f}",  # distance A to E
        0x224488,
        [A, B + E],
        f"{dist_pP(A, a):.2f}",  # distance A to a
        0x44AA44,
        C + E,
        f"{dist_ll(C & E, D & B):.2f}",  # distance CE to DB
        0x44AAFF,
        [A + D + E, B + C + 5 * D + 5 * E, D + E],
        f"{angle_pp(A & E & D, a):.2f}" + "&deg;",  # angle planes.
        0x884488,
        [A, 2 * A + D, 2 * A + B],
        f"{angle_ll(A & D, B & A):.2f}" + "&deg;",
    ]

    camera = math.cos(time) + math.sin(time) * alg.blades.e13

    return camera, subjects, A


@solara.component
def Page():
    result = solara.use_reactive(cast(tuple, None))
    base_options = dict(animate=False, grid=True, lineWidth=3)

    async def worker():
        while True:
            await asyncio.sleep(0.01)
            time = default_timer() / 5
            result.set(graph_func(time))

    task = solara.lab.use_task(worker, dependencies=[])

    if task.pending and result.value is None:
        solara.Text("Loading...")
    else:
        camera, raw_subjects, point_A = result.value
        subjects = walker(encode(raw_subjects, root=True))
        with solara.Card(style={"width": "750px", "height": "100%"}):
            with solara.Column():
                solara.Text(f"Camera: {str(camera)}")
                solara.Text(f"A: {str(point_A.dual())}")
            options = dict(base_options, camera=camera)
            GraphWidget.element(
                algebra=alg,
                subjects=subjects,
                options=options,
            )

requirements.txt

1
2
3
4
solara
anywidget
kingdon

Py.Cafe

solara-kingdon-3d-algebra

3D Point and Plane Algebra Visualization