Shape-Based Optimization in JavaScript

This challenge focuses on implementing a simple shape-based optimization algorithm in JavaScript. Imagine you're designing a robotic arm that needs to move objects around a workspace, avoiding obstacles. This problem asks you to find the shortest path for a rectangular "gripper" to move between two points, considering the presence of other rectangular obstacles.

Problem Description

You are tasked with creating a function optimizePath(start, end, obstacles) that calculates the optimal path for a rectangular gripper to move from a start position to an end position, avoiding a set of obstacles. The gripper is also rectangular. The "optimal path" in this simplified scenario is defined as the shortest Euclidean distance between the start and end points, adjusted to account for the gripper's size and the obstacles. The gripper's dimensions are assumed to be 1x1 (width x height).

The function should return a number representing the adjusted distance. If a path is impossible (the gripper cannot reach the end point without colliding with an obstacle), return Infinity.

Key Requirements:

• Collision Detection: The function must accurately determine if the gripper, positioned at a given point, would collide with any of the obstacles. A collision occurs if any part of the gripper overlaps with any part of an obstacle.
• Euclidean Distance: The base distance is the straight-line Euclidean distance between the start and end points.
• Adjustment for Obstacles: The function needs to increase the distance to account for the need to maneuver around obstacles. This adjustment is a simplification; we're not calculating a precise path, just an adjusted distance. A simple adjustment is to add a small penalty for each obstacle that lies on the direct line between start and end.
• Impossibility: If the gripper cannot reach the end point without colliding with an obstacle, the function should return Infinity.

Expected Behavior:

The function should take three arguments:

• start: An object with x and y properties representing the starting coordinates of the gripper's top-left corner.
• end: An object with x and y properties representing the ending coordinates of the gripper’s top-left corner.
• obstacles: An array of objects, where each object has x and y properties representing the top-left corner of a rectangular obstacle (also 1x1).

Edge Cases to Consider:

• Empty obstacles array: The distance should be the standard Euclidean distance.
• Start and end points are the same: The distance should be 0.
• Obstacles directly blocking the path: The distance should be increased significantly.
• Obstacles very close to the start or end points: Requires careful collision detection.
• Start or end point coinciding with an obstacle: Should return Infinity.

Examples

Example 1:

Input: start = {x: 0, y: 0}, end = {x: 5, y: 0}, obstacles = [{x: 2, y: 0}]
Output: 5.142135623730951
Explanation: The Euclidean distance is 5.  There's an obstacle directly in the path. We add a penalty (approximately 0.14) to account for the need to maneuver around it.  (This penalty is a simplification for demonstration purposes).

Example 2:

Input: start = {x: 0, y: 0}, end = {x: 5, y: 5}, obstacles = [{x: 2, y: 2}]
Output: 7.0710678118654755
Explanation: The Euclidean distance is approximately 7.07. The obstacle is not directly in the path, so the adjustment is minimal.

Example 3:

Input: start = {x: 0, y: 0}, end = {x: 1, y: 1}, obstacles = [{x: 0.5, y: 0.5}]
Output: Infinity
Explanation: The obstacle is directly in the path, and the gripper cannot pass through it.

Constraints

• All coordinates (x, y) will be non-negative numbers.
• The gripper dimensions are fixed at 1x1.
• Obstacle dimensions are fixed at 1x1.
• The number of obstacles will be between 0 and 100.
• The Euclidean distance calculation should be reasonably accurate (avoid floating-point errors that significantly impact the result).
• Performance: The function should execute in a reasonable time (less than 100ms) for the given constraints.

Notes

• The "adjustment" for obstacles is a simplification. A more sophisticated approach would involve pathfinding algorithms (e.g., A*), but this challenge focuses on a basic collision detection and distance adjustment.
• Consider using the Math.sqrt() function for calculating the Euclidean distance.
• Think carefully about how to implement the collision detection logic. It's crucial for the accuracy of the results.
• The penalty for obstacles on the direct path is a design choice. You can experiment with different penalty values to see how they affect the results. A simple approach is to add a constant value.
• The problem is designed to be solvable with relatively simple logic. Don't overcomplicate the solution.