bezierVisualize.py

import cairo
import numpy as np
import math


def cb(x1, y1, x4, y4, xc, yc):
    ax = x1 - xc
    ay = y1 - yc
    bx = x4 - xc
    by = y4 - yc
    q1 = ax * ax + ay * ay
    q2 = q1 + ax * bx + ay * by
    k2 = (4 / 3) * ((2 * q1 * q2) ** 0.5 - q2) / (ax * by - ay * bx)

    x2 = xc + ax - k2 * ay
    y2 = yc + ay + k2 * ax
    x3 = xc + bx + k2 * by
    y3 = yc + by - k2 * bx

    return x2, y2, x3, y3


def bezier_circle_center(p0, p1, p2):
    """
    计算二阶贝塞尔曲线的圆心坐标
    :param P0: 起点
    :param P1: 控制点
    :param P2: 终点
    :return: 圆心坐标
    """
    p0 = np.asarray(p0)
    p1 = np.asarray(p1)
    p2 = np.asarray(p2)
    v1, v2 = p0 - p1, p2 - p1
    l1, l2 = np.linalg.norm(v1), np.linalg.norm(v2)
    # assert is_close(l1, l2) and not is_close(l1, 0)

    theta = np.arccos(np.dot(v1 / l1, v2 / l2))
    tan_half_theta = np.tan(theta / 2)
    r = l1 * tan_half_theta
    o2control_distance = np.sqrt(r**2 + l1**2)

    control2target_distance = o2control_distance - r
    control2target_dir = (v1 + v2) / np.linalg.norm(v1 + v2)
    target_point = control2target_dir * control2target_distance + p1

    o = control2target_dir * o2control_distance + p1

    return (target_point, o)


# creating a SVG surface
# here geek95 is file name & 700, 700 is dimension
with cairo.SVGSurface("geek95.svg", 2000, 2000) as surface:
    # creating a cairo context object for SVG surface
    # using Context method
    context = cairo.Context(surface)

    x1, y1 = 0, 0
    control = np.asarray((500, 400))
    x4, y4 = control[0] * 2, 0

    # 二阶
    # https://blog.csdn.net/sl8023dxf/article/details/112624927
    context.move_to(x1, y1)
    C1 = np.asarray([x1, y1])
    C4 = np.asarray([x4, y4])
    C2 = C1 + 2 / 3 * (control - C1)
    C3 = C4 + 2 / 3 * (control - C4)
    context.curve_to(C2[0], C2[1], C3[0], C3[1], x4, y4)
    context.set_source_rgb(1, 0, 0)
    context.set_line_width(10)
    context.stroke()

    # 三阶
    _, (xc, yc) = bezier_circle_center((x1, y1), (control[0], control[1]), (x4, y4))
    x2, y2, x3, y3 = cb(x1, y1, x4, y4, xc, yc)
    context.move_to(x1, y1)
    context.curve_to(x2, y2, x3, y3, x4, y4)
    context.set_source_rgb(0, 1, 0)
    context.set_line_width(10)
    context.stroke()

    # 圆弧
    # context.move_to(x1, y1)
    # context.arc(control[0], 0, control[0], 0, 0.5 * math.pi)
    radian = math.atan((y4 - yc) / (x4 - xc))
    context.arc(
        xc, yc, ((xc - x1) ** 2 + (yc - y1) ** 2) ** 0.5, radian, math.pi - radian
    )
    context.set_source_rgb(0, 0, 1)
    context.set_line_width(5)
    context.stroke()