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Experimental Feature

Cast-off trajectories are currently a beta feature and should be used with caution. While this model provides a useful approximation of swing dynamics, it is still under development, and further scientific research is pending to validate and improve its accuracy. Please consider this when interpreting results based on cast-off trajectory analysis

Cast-off Patterns: Calculation and Interpretation

Cast-off patterns arise from bloody objects being swung, causing blood droplets to be cast off along the swing trajectory. Understanding these trajectories helps in analyzing the dynamics of the swing. Each cast-off trajectory is modeled using a set of parameters, allowing the creation of a visual representation that includes a 3D swing trajectory and associated uncertainty.

Calculation of the Cast-off Trajectory

We assume that a cast-off trajectory follows a circular path in 3D space, allowing us to simplify the complex swing motion that caused the cast-off. This assumption enables us to define the trajectory through a set of parameters that describe its shape, orientation, and associated uncertainty.

Swing Plane

The swing trajectory lies along a swing plane. This plane is defined by:

  • Plane Center: The 3D center point of the plane, located at the center of the sphere that defines the swing trajectory.
  • Plane Normal: A vector perpendicular to the plane, which describes the orientation of the plane in space.

The width and height of the plane can be adjusted for visual clarity, ensuring the plane better aligns with the scene structure in the visual representation.

Swing Plane

Trajectory Data

The trajectory data is represented as a list of 3D points. These points trace the path of the swing, approximating a circular trajectory on the surface of a sphere. The sphere and circular path provide a model of how the object (e.g., a weapon) was swung.

Cast-off Trajectory Data

Uncertainty Region

Every trajectory contains some level of uncertainty, represented by a radius around the trajectory points. This uncertainty is derived from statistical analysis of the data and defines a region within which the true swing path likely falls.

The uncertainty radius creates a 3D tube around the swing path, providing insight into the precision of the trajectory model. The size of this tube indicates how confidently the trajectory can be placed in space, with larger tubes signifying more uncertainty.

Cast-off Trajectory Uncertainty