Random selection of points distributed on curved surfaces.

Area of Science:

• Medical Physics
• Computational Physics
• Radiation Dosimetry

Background:

• Monte Carlo simulations are crucial for modeling radiation transport in complex medical geometries.
• Accurate simulation requires precise selection of initial particle origins.
• Particle sources are often distributed on curved surfaces.

Purpose of the Study:

• To develop general sampling techniques for selecting particle trajectory origins on arbitrary smooth surfaces.
• To enhance the realism and accuracy of Monte Carlo simulations in medical physics.
• To provide straightforward implementation for common convex volumes.

Main Methods:

• Parametric representation of smooth surfaces using two variables.
• Development of general random sampling techniques for these surfaces.
• Application to surfaces enclosing convex volumes like spheres and ellipsoids.

Main Results:

• Generalizable methods for sampling particle origins on parametrically defined smooth surfaces.
• Demonstrated straightforward implementation for spheres and ellipsoids.
• Applicable to non-uniform source distributions.

Conclusions:

• The presented sampling techniques offer a robust solution for accurate particle origin selection in Monte Carlo simulations.
• These methods are particularly beneficial for complex geometries encountered in medical physics.
• Improved simulation accuracy leads to more reliable radiation transport solutions.