Create a program to analyze and interpret simulator data

For this project we would like to generate a program to calculate the area of a 2D shape contained within a 3D shape. We would like this program to be a freestanding graphic user interface that can run on Mac and PC or we can use Matlab or Mathematica to run the programs (Matlab preferable) We are working with an ultrasound simulator that records x, y, z coordinates; pitch and roll; and angle of the ultrasound crystals within the probe as CSV or Excel files. Attached is a sample of what our data look like. We also have depth and angle of the pie-slice-shaped image. The simulator stores “Target cut planes” that represent the ideal ultrasound image. The coordinates and rotation parameters for the target cut plane are visible at the top of the output metrics CSV file. The 3D shape would be defined by the target cut plane plus and minus 1cm on the y-axis. The line of data in the excel spreadsheet represents the final image and is the 2D shape we are interested in. The columns represent the movement of the probe over time, both absolute position (X pos, Y pos, Z pos) and position relative to the target cut plane (X Distance [Target], Y Distance [Target], Z distance [Target]). Additionally, measures of rotation such as pitch, roll, and cumulated angle are recorded. The TEE angle represents the rotation of the ultrasound crystals in the probe and is important for determining the position of the 2D shape in space. We would like to be able to manually input or import the target cut plane coordinates into the program and have the program create a 3D volume in space using ± 1cm on the y-axis. Then we will input the X pos, Y pos, Z pos or X Distance [Target], Y Distance [Target], Z distance [Target] coordinates, and pitch, roll, TEE angle, image angle, and image depth into the program to generate the 2D shape. The output of the program would be the area of intersection of the plane within the 3D shape. A conceptualized drawing of how we see this working is attached. Ideally we would be able to save and store the sets of target cut plane coordinates in the program so they do not need to be re-entered each time we analyze a data set. Before being hired we require an extensive description of your strategy in solving this problem. However, we are free and open to other methods; If you have an alternative plan, please feel free to share it with us. Attached are a set of sample metrics so you can see what our outputs look like. Below is the conceptualized drawing of how we envision the two shapes intersecting. In summary, we would like 1. To create a 3D shape in space given x,y,z coordinates and other metrics representing the location and shape of the target cut plane 2. To calculate the area of intersection of the 3D shape with a 2D shape given a set of x,y,z coordinates, angle metrics, and depth 3. To generate a script or program to do these calculations and to provide us with the source code 4. The script/program should be able to store target cut plane metrics