This project is dedicated to the in depth development of geometric measurement algorithms. By 16307 group from Tianjin University of Science and Technology China. You can contact us via 770896174@qq.com and i look forward to your contribution. The inspiration is derived from the vision software HALCON.

In the fields of navigation, industrial measurement, surveying and mapping .etc, we need to develop a large number of geometric measurement algorithms, and most of them is reusable. However, few of people tried to classify and arrange them. So we are trying to do something to make it easier for developers based on python.

Tools

• Solidworks 3D sketch functions
• Mermaid based on markdown

Framework

This repository can solve the following three types of problems:

Geometric measurement algorithm

Any geometric algorithm can be regarded as realized by the fusion of physical quantities and geometric elements. Geometric elements include point, line and plane and physical quantities include angle, distance, coordinate, vector and pose. Any function can be named as the form of cal[...]From[...] and any conversion can be made between them. For example as calCoordinateFrome2Lines.

The drawing tools can refer to here.

Data format

• Coordinate: $$ P=\begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} $$ →numpy.array

• Vector: $$ \vec{l}=\begin{bmatrix} a\\ b\\ c\\ \end{bmatrix} $$ →numpy.array

• Pose: $$ R=\begin{bmatrix} r11&r12&r13\\ r21&r22&r23\\ r31&r32&r33\\ \end{bmatrix}{3×3} ,T=\begin{bmatrix} t_x\\ t_y\\ t_z\\ \end{bmatrix}{3×1} $$

  →numpy.array

• Distance: $$ d $$ →float

• Angle： $$ θ $$ →float

• Plane： $$ Ax+By+Cz+D=0,[A,B,C,D] $$ →numpy.array

• Line: $$ \frac{x-x_0}{m}=\frac{y-y_0}{n}=\frac{z-z_0}{p},[m,n,n,x_0,y_0,z_0] $$

  →numpy.array

Tutorial

Take the project of shield tail clearance measurement system as an example, the calculation flow chart could be shown as below:

Reference

1. http://immersivemath.com/
2. [1]丘维声. 解析几何(第2版)[M]. 北京大学出版社, 1996.
3. 视频：三维坐标变换可视化
4. Github:spatialmath-python