A ridiculously low cost sensor to compute the x-coordinate of right index fingertip on a water surface.
Project tutorial by Sumit Aich
A ridiculously low cost water-based 3D sensor for real-time tracking of precise coordinates of the tip of a stylus in confined 3D space.
If you face any issues while reconstructing this water-based 3D sensor, feel free to ask here.
Many people are confused regarding the use of slant electrodes instead of perpendicular electrodes in my 3D sensor.
Well, here's the deal.
In case of cuboid, the normal vector to the 3 planes will be parallel to the horizontal base. So the angle between normal vector and z-axis equals pi/2 radians. So the 'n' direction cosine of normal vector equals 0. So the 3rd column of the matrix of direction cosines of the 3 planes is a column of 0s . The determinant of a matrix is 0 if any of its rows or columns are 0. So matrix 'A' is a singular matrix. For a non-homogeneous system of 3 unknowns, if matrix 'A' is singular, it implies that the system of equations will have either no solution or infinity number of solutions. Since, 3rd column of matrix is 0, so its matrix of co-factors is a null matrix. Transpose of a null matrix is a null matrix. So adj(A) is a null matrix. So (adj(A)).B is also a null matrix. This will prove that the system of equations is consistent and has infinity number of solutions.
This issue is not present in case of slant electrodes.
the reason is that the current density vector must be normal to the end planes at all points on the plane. This can be made possible only if the ENTIRE end plane is an equipotential surface. Since aluminum has negligible resistivity compared to water, it acts as an equipotential surface and must cover the entire end planes.
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