Question: Implementing a $2$D Pathfinding System in Panda$3$D with Mouse Interaction

You are tasked with creating a $2$D pathfinding system in the Panda$3$D game engine, using Python, where:

$1.$ Three box objects are initialized on a flat plane.

$2.$ When you click on any box:

$-$ It should start moving toward a randomly generated goal position.

$3.$ If the box is already moving when clicked, it should pause at its current position. Clicking again will resume movement.

$4.$ Additionally, implement a way to draw a rectangle using the mouse in the $2$ D environment, and all objects inside this rectangle should start moving toward their respective goal positions.

To achieve this, consider the following requirements:

$-$ Top$-$down camera view: Set the camera to a $2$D $($top$-$down$)$ perspective.

$-$ Random goal generation: Each box should have a unique goal position within the environment bounds.

$-$ Collision and selection: Use Panda$3$D$\text{'}$s collision detection system to detect clicks and area selection.

$-$ Pathfinding algorithm: Implement a basic RRT $($Rapidly$-$Exploring Random Tree$)$ algorithm to find a path for each box from its starting position to its goal position.

$-$ Movement control: Each box should follow its path, and it should be possible to pause$/$resume the movement.

Instructions

$1.$ Write Python code to implement this $2$D environment in Panda$3$D$.$

$2.$ Ensure the code meets the requirements listed above.

$3.$ Describe how your pathfinding algorithm $($RRT$)$ operates in the $2$D space.

$4.$ Explain how you set up the mouse interactions for both object selection and drawing a rectangle.

Expected Solution

Provide a complete, functional Python code for the Panda$3$D engine that includes:

$-$ Initialization of the environment and boxes.

$-$ RRT pathfinding logic.

$-$ Mouse interactions for single object selection and area selection.

$-$ Movement toggling for each box.

Hints:

$-$ Review Panda$3$D$\text{'}$s collision system for setting up raycasting with the mouse.

$-$ For rectangle drawing, consider using screen space coordinates to capture mouse$-$drag events and determine which objects lie within the selected area.

Utilize the Vec$3$ and Point$3$ classes in Panda$3$D to handle $2$D coordinates effectively within the $3$D engine.