## Dot Product to Cull Points and Establish a Gradient

Here’s another super-simple trick you can perform with the dot product of two vectors. If you create two nulls and get the vector between them, you can compare that with the vector from any point to the first null using a dot product. Any value less than zero is past the plane of the first control normal to the second. That doesn’t read well, but the result is straightforward, you are using the controls to act like a normal and cull points.

Furthermore, the distance between those two nulls acts as a handy scale factor to color points in a gradient between the two. Here for instance we’ve “cut” a sphere in half…

The structure is very simple as you can see in the network view. The wrangle is also very simple. Thanks to Tokeru for inspiration and the basic structure of this wrangle.

vector p1, p2, v1, v2; p1 = point(1,'P',0); //control null 1 p2 = point(2,'P',0); //control null 2 v1 = normalize(p2-p1); //vector between control nulls v2 = @P-p1; //vector from current eval point to control 1 f@angle = dot(v2, v1); //The dot product of the two, indicates 'perpendicularity' if (@angle <= 0){ removepoint(0,@ptnum);} //Cull out any points past p1 float dist = distance(p1,p2); @Cd = dot(v2,v1)/dist; //The distance between the two can also act as a gradient

This works, but there’s a far simpler approach to take using the matrix transforms mentioned a few posts earlier. Transform the points to the origin of a control object’s local space (you saved that wrangle as an asset, right?) and then you can use very simple logic – in this case let’s delete any point greater than zero in z.

if ( @P.z > 0) { removepoint(0,@ptnum); }

Translate the points back to their original world position (in that other wrangle you saved as an asset, right?) and bam, you have a super easy tool to cull points according to a control object. Or make a gradient, or whatever else you want.