小案例：4*4矩阵转换成二维平面坐标

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一、需求：基于苹果数据4*4矩阵数据，转换成二维平面坐标系

二、解决方法与步骤：

1、4*4矩阵转成二维：基于四维矩阵中心点，求两端点坐标

2、利用平面内直角坐标系中坐标旋转变换公式将平面坐标点转化

用到的方法：

1、Matrix4的转化_Catirl的博客-CSDN博客

2、平面内直角坐标系中坐标旋转变换公式_Eric_Wangyz的博客-CSDN博客_坐标旋转变换公式

苹果数据代码：

[Python] 纯文本查看 复制代码

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1、4*4矩阵转成二维：基于四维矩阵中心点，求两端点坐标

[Python] 纯文本查看 复制代码

# 墙体信息
  for wall in json_data["walls"]:
    # 墙体中心坐标
    center_p = np.array([wall["transform"][-4], wall["transform"][-2]])
    length = wall["dimensions"][0]
 
    transform01 = abs(wall["transform"][10])
    if wall["transform"][10] < 0:
        transform02 = wall["transform"][8]
    else:
        transform02 = -wall["transform"][8]
 
# 基于中心点与四维矩阵，获取起始点
    p1 = center_p + 0.5 * length * np.array([transform01, transform02])
    p2 = center_p - 0.5 * length * np.array([transform01, transform02])

2、平面坐标系转化

[Python] 纯文本查看 复制代码

cos = abs(json_data["walls"][0]["transform"][10])
sin = -abs(json_data["walls"][0]["transform"][8])
 
# # # 坐标翻转
x1 = p1[0] * cos - p1[1] * sin
y1 = p1[1] * cos + p1[0] * sin
p1 = Point2D(int(round(x1 * 1000, 0)), int(round(y1 * 1000, 0)))
 
x2 = p2[0] * cos - p2[1] * sin
y2 = p2[1] * cos + p2[0] * sin
p2 = Point2D(int(round(x2 * 1000, 0)), int(round(y2 * 1000, 0)))

3、整合代码：

[Python] 纯文本查看 复制代码

import json
from sympy.geometry import *
 
PATH = r"D:\Desktop\room74.json"
f = open(PATH, 'rb')
j = json.load(f)
f.close()
 
 
def get_start_end_point(center_p, length, transform01, transform02, cos, sin):
    # 基于中心点与四维矩阵，获取起始点
    p1 = center_p + 0.5 * length * np.array([transform01, transform02])
    p2 = center_p - 0.5 * length * np.array([transform01, transform02])
 
    # # # 坐标翻转
    x1 = p1[0] * cos - p1[1] * sin
    y1 = p1[1] * cos + p1[0] * sin
    p1 = Point2D(int(round(x1 * 1000, 0)), int(round(y1 * 1000, 0)))
 
    x2 = p2[0] * cos - p2[1] * sin
    y2 = p2[1] * cos + p2[0] * sin
    p2 = Point2D(int(round(x2 * 1000, 0)), int(round(y2 * 1000, 0)))
 
    return p1, p2
 
 
def get_wall_points(json_data):
    # 获取墙所有的坐标点
    wall_p_list = []
    # 墙体信息
    cos = abs(json_data["walls"][0]["transform"][10])
    sin = -abs(json_data["walls"][0]["transform"][8])
    for wall in json_data["walls"]:
        # 墙体中心坐标
        center_p = np.array([wall["transform"][-4], wall["transform"][-2]])
        length = wall["dimensions"][0]
 
        transform01 = abs(wall["transform"][10])
        if wall["transform"][10] < 0:
            transform02 = wall["transform"][8]
        else:
            transform02 = -wall["transform"][8]
 
        p1, p2 = get_start_end_point(center_p, length, transform01, transform02, cos, sin)
        wall_p_list.extend([p1, p2])
 
    return wall_p_list
 
 
# 获取墙所有的坐标点：
wall_points_list = get_wall_points(json_data)
 
print(wall_points_list )

4、结果：

[Python] 纯文本查看 复制代码

[[Point2D(760, -869), Point2D(-270, -869)], [Point2D(1989, -869), Point2D(937, -869)], [Point2D(-637, -869), Point2D(-1430, -869)]]