Houdini VEX allows you to do some pretty amazing things. If it’s not in Houdini, you can simply create it.

how to generate lines that follow a surface towards a target point

Here, 3D Artist Stefan Sietzen walks through using VEX to build a system that will generate lines on the surface of an object. The line will also be attracted to a target int he scene. This way you can control where the lines are traveling by moving the target in the scene.

If you are not familiar, VEX is a low level language in Houdini that allows you to create custom nodes. The nodes are really fast too, as it is similar to create code with C or C++. You can basically create custom operators for geometry, volumes, audio, or images, without having to actually write the code.

Stefan provides the scene file for download, which you can find here.