重构后把不同功能独立出来。

Signed-off-by: facat <facat@facat.com>

.gitignore

@@ -1,2 +1,3 @@
 .idea
 __pycache__
+*.dxf

graphic.py

@@ -0,0 +1,131 @@
+import copy
+import math
+import ezdxf
+from type3d import Vector3D
+import numpy as np
+import transformation
+from typing import List, Union, Tuple
+
+
+class Line:
+    def __init__(
+        self,
+        start_p: Vector3D,
+        end_p: Vector3D,
+        tension_k: float,
+        n_point: int,
+    ):
+        self._start_p: Vector3D = start_p
+        self._end_p: Vector3D = end_p
+        self._tension_k: float = tension_k
+        self._n_point: int = n_point
+        self._span = 0
+        self._points = None
+        self._rotation = None
+
+    def curve(self):
+        if self._points:
+            return self._points
+        start_p = self._start_p
+        end_p = self._end_p
+        tension_k = self._tension_k
+        n_point = self._n_point
+        # 右手坐标系，Z朝上
+        line = Vector3D(end_p.x, end_p.y, end_p.z) - Vector3D(
+            start_p.x, start_p.y, start_p.z
+        )
+        # 计算与X轴的角度
+        xy_project = copy.deepcopy(line)  # 投影到xy平面上
+        xy_project.z = 0
+        x_abs_angel = xy_project.angle_to(Vector3D(1, 0, 0))
+        x_angel = x_abs_angel * np.sign(xy_project.y)
+        height = end_p.z - start_p.z
+        span: float = abs(xy_project)
+        self._span = span
+        span_l = np.linspace(0, span, n_point)  # 档距
+        z_points: Tuple[float] = (
+            start_p.z
+            + span_l * height / span
+            - span_l * (span - span_l) * tension_k / math.cos(math.atan(height / span))
+        )
+        p_points: List[
+            Union[List[float, float, float], Tuple[float, float, float]]
+        ] = list()  # 未旋转之前的伪坐标
+        for foo in range(len(span_l)):
+            p_points.append((span_l[foo] + start_p.x, start_p.y, z_points[foo]))
+        # 绕Z轴旋转
+        rotation = transformation.Rotation(
+            x_angel,
+            [start_p.x, start_p.y, start_p.z],
+            [start_p.x, start_p.y, start_p.z + 1],
+        )
+        self._rotation = rotation
+        points = rotation.rotate(
+            p_points,
+        )
+        self._points = points
+        return points
+
+    def sag(self):
+        # msp.add_polyline3d(
+        #     [(start_p.x, start_p.y, start_p.z), (end_p.x, end_p.y, end_p.z)]
+        # )
+        start_p = self._start_p
+        end_p = self._end_p
+        span = self._span
+        height = end_p.z - start_p.z
+        middle_span = span / 2
+        points = self._points
+        n_point = self._n_point
+        middle_z = points[int(n_point / 2)][2]
+        rotation = self._rotation
+        sag_points = rotation.rotate(
+            [
+                [start_p.x, start_p.y, start_p.z],
+                [
+                    middle_span + start_p.x,
+                    start_p.y,
+                    start_p.z + middle_span * height / span,
+                ],
+                [middle_span + start_p.x, start_p.y, middle_z],
+                [
+                    middle_span + start_p.x,
+                    start_p.y,
+                    start_p.z + middle_span * height / span,
+                ],
+                [start_p.x + span, start_p.y, end_p.z],
+            ]
+        )
+        return sag_points
+
+    def swing(self, angel):
+        points = self._points
+        start_p = self._start_p
+        end_p = self._end_p
+        swing_rotation = transformation.Rotation(
+            angel,
+            [start_p.x, start_p.y, start_p.z],
+            [end_p.x, end_p.y, end_p.z],
+        )
+        swing_point = swing_rotation.rotate(points)
+        return swing_point
+
+
+class Canvas:
+    def __init__(self):
+        self._doc = None
+        self._msp = None
+
+    def init_canvas(self):
+        doc = ezdxf.new()
+        self._doc = doc
+        msp = doc.modelspace()
+        self._msp = msp
+
+    def draw(self, points):
+        msp = self._msp
+        msp.add_polyline3d(points)
+
+    def save(self, file_path):
+        doc = self._doc
+        doc.saveas(file_path)

main.py

@@ -1,9 +1,13 @@
 import math
-from transformation import rotation
-import numpy as np
+
+from graphic import Canvas, Line
+from type3d import Vector3D
 
 if __name__ == "__main__":
-    t = rotation(
-        45 / 180 * math.pi, np.array([0, 0, 1]), np.array([[1, 1, 0], [2, 3, 4]])
-    )
-    print(t)
+    canvas = Canvas()
+    canvas.init_canvas()
+    line = Line(Vector3D(20, 30, 0), Vector3D(400, 100, 1), 0.3 * 1e-3, 400)
+    canvas.draw(line.curve())
+    canvas.draw(line.sag())
+    canvas.draw(line.swing(80/180*math.pi))
+    canvas.save("lwpolyline1.dxf")

transformation.py

@@ -1,5 +1,6 @@
 import numpy as np
 from math import cos, sin
+from typing import List, Union, Tuple
 
 
 def create_rx(unit_axis: np.ndarray) -> np.ndarray:
@@ -32,16 +33,41 @@ def create_t(axis: np.ndarray) -> np.ndarray:
     return np.array([[1, 0, 0, -x1], [0, 1, 0, -y1], [0, 0, 1, -z1], [0, 0, 0, 1]])
 
 
-def rotation(angel: float, axis: np.ndarray, points: np.ndarray):
+def rotation_matrix(
+    angel: float, axis_start: np.ndarray, axis_end: np.ndarray
+) -> np.ndarray:
     # 依据《计算机图形学》第4版 9.28公式
+    axis = axis_end - axis_start
     unit_axis = axis / np.linalg.norm(axis)
     rz = create_rz(angel)
     rx = create_rx(unit_axis)
     ry = create_ry(unit_axis)
-    t = create_t(axis)
+    t = create_t(axis_start)
     t_i = np.linalg.inv(t)
     rx_i = np.linalg.inv(rx)
     ry_i = np.linalg.inv(ry)
-    r_transform = t_i.dot(rx_i.dot(ry_i.dot(rz.dot(ry.dot(rx.dot(t))))))
-    expand_point = np.concatenate((points, np.ones((points.shape[0], 1))), axis=1)
-    return r_transform.dot(expand_point.T)
+    r_transform = t_i @ rx_i @ ry_i @ rz @ ry @ rx @ t
+    return r_transform
+
+
+def rotation(
+    angel: float, axis_start: np.ndarray, axis_end: np.ndarray, points: np.ndarray
+) -> np.ndarray:
+    _rotation = Rotation(angel, axis_start.tolist(), axis_end.tolist())
+    return _rotation.rotate(points.tolist())
+
+
+class Rotation:
+    def __init__(self, angel: float, axis_start: List[float], axis_end: List[float]):
+        self._r_transform = rotation_matrix(
+            angel, np.array(axis_start), np.array(axis_end)
+        )
+
+    def rotate(self, points: List[Union[List[float], Tuple[float]]])->List:
+        np_points = np.array(points)
+        r_transform = self._r_transform
+        expand_point = np.concatenate(
+            (np_points, np.ones((np_points.shape[0], 1))), axis=1
+        )
+        transformed_points = r_transform @ expand_point.T
+        return transformed_points[:-1, :].T.tolist()

type3d.py

@@ -1,5 +1,22 @@
+import math
+
+
 class Vector3D:
     def __init__(self, x, y, z):
-        self.x = x
-        self.y = y
-        self.z = z
+        self.x:float = x
+        self.y:float = y
+        self.z:float = z
+
+    def __sub__(self, other):
+        return Vector3D(self.x - other.x, self.y - other.y, self.z - other.z)
+
+    def __abs__(self) -> float:
+        return (self.x ** 2 + self.y ** 2 + self.z ** 2) ** 0.5
+
+    # 计算两向量间夹角
+    def angle_to(self, other):
+        return math.acos(
+            abs(self.x * other.x + self.y * other.y + self.z * other.z)
+            / abs(self)
+            / abs(other)
+        )