Develop Reference

Calculating Area of Irregular Curved Polygon in Python

I know the x, y coordinates of the blue dots shown in the image. How can I calculate the area of an irregular shape bounded by these points? Number of points on upper and lower surfaces are different
Image

As suggested by #Fractalism, You can use Schoelace formula.
Here is an implementation for python using Numpy. I took it from here:
import numpy as np
# x,y are arrays containing coordinates of the polygon vertices
x=np.array([3,5,12,9,5])
y=np.array([4,11,8,5,6])
i=np.arange(len(x))
#Area=np.sum(x[i-1]*y[i]-x[i]*y[i-1])*0.5 # signed area, positive if the vertex sequence is counterclockwise
Area=np.abs(np.sum(x[i-1]*y[i]-x[i]*y[i-1])*0.5) # one line of code for the shoelace formula

How to find the rotation matrix with known points

The corner points of a rectangle are given in 2D coordinates. I also know the real distance of the points and I have the camera matrix.
Now I want to find the rotation vector with respect to the camera, but without using the cv2.calibrateCamera() method with the chessboard corners.

Projecting a Texture Mask onto an existing 3D Mesh given the camera extrinsics

Given an image mask, I want to project the pixels onto a mesh in respect to the position and orientation of the camera and convert these pixels into a pointcloud. I have the intrinsic and extrinsic parameters of the camera in respect to the world, and the location of the mesh in world coordinates. I know the mapping from world coordinates to camera image is as follow:
imgpoint = Intrinsic * Extrinsic * worldpoint
So when I want to the opposite i do the inverse of the intrinsic and extrinsic matrices:
worldpoint= Intrinsic^(-1) * Extrinsic^(-1) * imgpoint
However, the idea that I had was to obtain two points from one pixel, with different depth values, to obtain a line and then look for the closest intersection for the mesh I want with the line, but I do not know how to properly generate a point away from the original camera plane. How can I find this extra point and/or am I complicating this problem?

The top equation below shows how to project a point (x,y,z) onto a pixel (u,v);
The extrinsic parameters are the 3x3 rotation matrix R and translation t.
The intrinsic parameters are the focal distances f_x, f_y and
principal point (c_x, c_y). The value alpha is the perspective foreshortening term that is divided out.
The bottom equation reverses the process by describing how to project
a ray from the camera position through through the pixel (u,v) out into the scene as the parameter alpha varies from 0 to infinity.
Now we have converted the problem into a ray casting problem.
Find the intersection of the ray with your mesh which is a
standard computer graphics problem.

Getting the projection matrix which can transform 3d points to 2d points in an image as done by cv2.projectPoints function in opencv

The opencv function cv2.projectPoints() takes 3d points, rotation vector, translation vector, camera matrix and distortion coefficients and aspect ratio and generate the 2d projection of the 3d point in the image plane. Is there some way to get the full projection matrix which does the same to any 3d point so that i can do the projection without using the projectPoints fucntion

3D quadrilateral mesh using Mayavi

I have an array of 3D coordinates of a mesh, where each four rows represent a mesh face.
Data:
X11,Y11,Z11
X12,Y12,Z12
X13,Y13,Z13
X14,Y14,Z14
...
XN1,YN1,ZN1
XN2,YN2,ZN2
XN3,YN3,ZN3
XN4,YN4,ZN4
where N is the total number of mesh faces
Does anyone know the best way to display this mesh using Mayavi/matplotlib?