Precision 3D Shape Fitting

I'm working on a project that involves finding the best fit among a cone, cylinder, plane, sphere, and line for a given set of 3D points. This task is crucial for my work with coordinate measurement machines, where accuracy significantly impacts our ability to analyze data patterns and optimize shape fitting for various applications.

### Key Requirements:
- **High Precision**: The algorithm must offer results with better than 0.01mm error margin. Accuracy is paramount.
- **Output Format**: The final output should be in the form of coordinate data points. These points will be further analyzed and used in our measurement systems.
- **3D Points Analysis**: The solution should efficiently analyze a set of 3D points to determine the best fit shape from the options given (cone, cylinder, plane, sphere, line).

### Ideal Skills and Experience:
- **Expertise in 3D Mathematics**: Proficiency in 3D geometry and understanding the nuances of different shapes and how they interact with sets of points.
- **Programming Skills**: Strong C programming skills are necessary, given the complexity and precision requirements of the task.
- **Experience in Precision Modeling**: Previous experience or knowledge in working with coordinate measurement machines or similar precision-dependent technologies is highly beneficial.
- **Problem-Solving Ability**: Capacity to develop innovative solutions that can significantly reduce errors and improve the accuracy of the fitting process.

In summary, this project demands a freelancer with a strong background in mathematics, excellent programming capabilities in C, and a keen eye for detail to achieve the high level of precision required. Your contribution will play a vital role in enhancing our ability to accurately interpret and utilize 3D point data for various applications.