Different Color for region of intersection Is there a simple way to make a region or new object in order to change the material properties at the intersection of two or more objects?
For example:


Or this, where the intersection area of interest is shown in orange and is the intersection between 3 different objects

I have read a little about using the Boolean tool for Union, Intersection, and Difference between two objects, but when applied, it does not create a new region or object. It destroys part of the objects that are present and replaces it with the union, or whichever is chosen.
In addition, if the intersection is chosen, the resulting object is not the type of intersection shown below. The intersection given would be the plane with the bottom part of the cone sticking down for some reason.
Is there a better way to achieve the question above?
The "Boolean Modifier" doesn´t work as expected with non-manifold meshes. When you add a plane use the "Solidify Modifier" first, to give it a slight thickness (e.g. 0.0001).

Give the plane a "Boolean Modifier" afterwards and set the target to the cone. Set "Operation" to "Difference". Copy the plane with ShiftD and press Esc to avoid moving the copy. For the copy set the "Operation" of the "Boolean Modifier" to "Intersect".

Edit: The pictures show the Modifier Tab in the Properties Panel (click the wrench icon). Note that the order of the modifiers in the modifier stack is important.





You could also parent the two planes so they can be moved around together. Hold Shift and select both plane objects with RMB. Press CtrlP and select "Object".

Afterwards materials can be assigned on every object separatly.
You can then use Freestyle for line rendering.

The advantage of using modifiers is fast editing and your objects are easy to animate.