## Dot Product and Edges in Vex

Getting the dot product of two vectors is infinitely useful, and easy in Vex. In this example I get a vector pointing from scattered particles to the camera and then get their dot product with the surface normal at that point. This gives you a very good idea of whether the surface is facing or perpendicular to the camera at any given point.

In this case, I simply cull any point which isn’t close to a value of zero, indicating the surface is perpendicular to the camera. If instead I culled particles that were less than zero I would be removing all back-facing (occluded) particles, which is perhaps more useful but less visually interesting. Since I am left with only particles near the edges of the geometry it’s easy to connect them with lines and get an “edge detection” kind of look.

Here’s the Vex wrangle I used. Note an earlier polyframe node gave me point normals on the scattered points to work with.

```float threshold = chf("Threshold");
//User input threshold
vector camPos = point(1, "P", 0);
//The position of the imported camera
vector toCam = normalize(camPos - @P);
//A vector from each point to the camera)
//@N = toCam;
//Use to visualize toCam as normals
f@angle = dot(toCam, @N);
//The dot product of the normal and toCam vectors.
if (@angle > threshold || @angle < -1*threshold){
removepoint(0,@ptnum);
}```

I’ve used this edge culling in production a few times, to create anime style speedlines and particle effects like rain strikes and halos. Culling particles behind geometry is of course also handy, though raycast solutions are much cleaner for that kind of thing. Next, we’ll use a simple dot product calculation to cull points and create a gradient effect.