Bloodstain Pattern Analysis (BPA) is a forensic discipline that uses physics, biology, and mathematics to interpret blood patterns at a scene. This analysis helps investigators reconstruct the sequence of events that led to the bloodshed. A primary goal is determining the location of the blood source in space by finding the two-dimensional Area of Convergence (AOC). The AOC is the approximate location on a surface, such as a wall or floor, from which a grouping of blood spatter originated. Determining this area provides spatial context for the actions that occurred.
The Geometry of a Single Bloodstain
The process of locating the Area of Convergence begins with the precise measurement of individual stains within the pattern. When a spherical blood droplet strikes a flat surface at an angle less than 90 degrees, it creates an elongated, elliptical stain. The degree of elongation directly relates to the angle at which the droplet impacted the surface.
Forensic analysts use the measurable dimensions of this elliptical stain to calculate the angle of impact using trigonometry. The stain’s shape allows the droplet’s trajectory to be modeled as a right-angled triangle. The Angle of Impact is calculated using the arcsine (or inverse sine) of the ratio of the stain’s width divided by its length.
A blood drop striking a surface at a steep angle, such as 80 degrees, produces a nearly circular stain because the width and length are almost equal. Conversely, a drop striking at a shallow angle, such as 15 degrees, creates a stretched, elliptical stain with a small width-to-length ratio. Analysts accurately measure the width (perpendicular to travel) and the length (along the direction of travel) to assign a precise angle of impact. Directional tails or “spines” extending from a stain are excluded from this measurement, as they can distort the calculated values. The angle of impact for each stain is necessary for determining both the AOC and the three-dimensional height of the blood source.
Mapping the Two-Dimensional Point
After determining the angle of impact for several stains, the next step is mapping the path of each droplet backward to find their common origin. This involves projecting a straight line along the long axis of each elliptical stain, following the directionality indicated by its shape. When multiple lines from different stains are drawn, they intersect in a concentrated area.
This area of overlap is the Area of Convergence (AOC). It is defined as a two-dimensional area, providing the location on the X and Y plane of the surface where the pattern was deposited. Traditionally, the AOC is determined using “stringing,” where physical strings are placed at each stain and extended along the direction of travel. The point where the strings cluster together marks the AOC on the floor or wall.
Modern forensic practice increasingly relies on specialized computer software, such as HemoSpat or FARO Zone 3D, for digital mapping. Analysts input the measurement data and stain locations, and the program uses geometry to mathematically project the trajectories back in space. This digital process, sometimes called “virtual stringing,” calculates the AOC non-invasively, providing a precise, bounded area of overlap. The resulting AOC establishes the horizontal location of the blood spatter source for crime scene reconstruction.
Area of Convergence vs. Area of Origin
The Area of Convergence (AOC) provides the two-dimensional location of the blood source on a flat plane, representing only the “footprint” of the origin. For a complete reconstruction, analysts must determine the three-dimensional location, known as the Area of Origin (AOO). The AOO calculation extends the analysis vertically from the AOC, adding the Z-coordinate (height) to the reconstruction.
The AOO is determined by combining the calculated angle of impact for each stain with the horizontal distance from that stain back to the AOC. This process uses the trigonometric function tangent to establish the vertical height. For each stain, the height of the blood source is calculated by multiplying the tangent of the stain’s angle of impact by the horizontal distance to the AOC.
By calculating and averaging the height for multiple stains, analysts establish a probable range for the AOO. This three-dimensional location is invaluable for event reconstruction, as it indicates the position of the blood source when the impact occurred (e.g., standing, kneeling, or lying). For instance, an AOO height of five feet above the floor suggests the individual was standing, while two feet suggests they were closer to the ground. The AOC serves as the necessary two-dimensional foundation upon which the full Area of Origin is built.