What this helper works out
This helper finds the point where two straight lines intersect, given two points on each. In bloodstain work those lines are the directions of travel projected back from individual stains.
It is two-dimensional. Convergence gives a point on the surface; establishing the three-dimensional area of origin requires the impact angles as well, and carries considerably more uncertainty. This is a teaching aid, not a casework tool.
Two lines
Each line is defined by two points: (x1,y1) to (x2,y2).
| x1 | y1 | x2 | y2 | |
|---|---|---|---|---|
| Line A | ||||
| Line B |
Before you use it
- Directions are determined from the long axis of each stain, running back from the tail towards the origin.
- Coordinates must share a consistent origin and axis orientation across all stains.
- Two lines always intersect unless they are parallel. Two stains alone therefore produce a point regardless of whether it means anything.
- Real analysis uses many stains and looks for a cluster, not a single intersection.
The area of convergence is a two-dimensional point on the impact surface. The area of origin adds the third dimension, using each stain's impact angle and the tangent method to project back in space. That step is where systematic error enters, because the tangent method assumes straight-line flight and ignores gravity and drag, which curve the actual path.
How this calculator works
The standard two-line intersection formula:
d = (x₁ − x₂)(y₃ − y₄) − (y₁ − y₂)(x₃ − x₄)
If d is zero the lines are parallel or coincident
Otherwise the intersection is found from the determinant form of the two line equationsThe guard against a near-zero determinant matters. Two nearly parallel lines intersect at a point that moves enormously for a tiny change in either direction, so an intersection from two shallow-angled stains is far less meaningful than one from lines meeting closer to perpendicular.
With many stains, the intersections form a scatter rather than a single point, and the size of that scatter is itself the useful information.
Worked example: two crossing lines
Using the default figures — line A from (0, 0) to (10, 10), line B from (0, 10) to (10, 0):
- Intersection: (5.000, 5.000)
These lines cross at 90 degrees, which is the best case: shift either endpoint by one unit and the intersection moves by roughly half a unit. Now imagine two lines meeting at 5 degrees. The same one-unit shift moves the intersection by more than ten units. This is why analysts select stains with well-separated directions, and why a convergence derived from stains all pointing much the same way is weak evidence however precisely it is calculated.
Common mistakes
- Using only two stains. They will always produce a point; a cluster from many is the real result.
- Choosing stains with similar directions. Near-parallel lines give an unstable intersection.
- Mixing coordinate origins between stains. All measurements must share one frame.
- Treating convergence as origin. The third dimension is a separate and less certain step.
- Reporting more decimal places than the measurements support.
Frequently asked questions
How is the area of origin found?
By combining convergence with the impact angle of each stain. The tangent method projects a line back from each stain at its measured angle and looks for where those lines converge in three dimensions. It is known to overestimate the height of origin, because it assumes straight-line flight while real droplets follow a ballistic arc.
How many stains are needed?
More than two, and ideally a well-distributed set with a range of directions. Published guidance and practice vary, but the principle is consistent: the reliability comes from agreement across many stains, not from the precision of any single calculation.
Why does gravity matter?
A droplet in flight falls as it travels, so its path is a curve rather than a straight line. Projecting straight back from the stain therefore traces above the true origin, and the error grows with the distance travelled. Methods that account for the ballistic path exist but need more information about droplet size and velocity.
Can this be used for anything other than bloodstains?
The arithmetic is a general two-line intersection and applies to any pair of straight lines. It appears in surveying, navigation and computer graphics. The forensic application is simply one use of a standard geometric result.
Is what I enter stored?
No. Coordinates are processed entirely in your browser and never transmitted or retained.
Related tools
References
- GOV.UK — Forensic Science Regulator codes of practice for pattern interpretation
- Met Office — environmental data occasionally relevant to outdoor scene reconstruction
Sources are checked at publication and can change — how I choose and check references.