Introduction
Lets break down the problem into manageable parts.
- Finding the coordinates of the mirror gives us something for the laser to aim at.
- Determining the coordinates of each end of the mirror allows us to calculate the angle of incidence/reflection at each end of the mirror.
- The angle of reflection can be used to determine where the laser beam(s) hits the side of the box.
- Where the laser beam(s) hits the side of the box shows us how close we are to the target.
- Adjusting the mirror angle will change where the laser beam(s) hits the sides of the box.
- Writing a menu driven program will allow the user to change the mirror angle and thus where the laser beam(s) hit the sides of the box.
Coordinates
The problem diagram suggests the coordinate's origin (0,0) is in the lower left corner of the box. What coordinate system system should you use?
The Mirror's Coordinates
The problem diagram shows the mirror's center is at (x=90,y=64) with the coordinate's origin (0,0) in the lower left corner of the box.
Finding the coordinates of the mirror giving us something for the laser to aim at. Given a tilt angle of 20°, calculate the top and bottom coordinates of the mirror. Remember, Python's sine and cosine functions use radians. You must convert the angle in degrees to radians. Calculate the coordinates of the top and bottom of the mirror.
Note: We expect to be tilting the mirror at various angles. Isolate the mirror coordinate code in a function so it can be reused.
The Target's Coordinates
The problem diagram shows the target's center is at (x=0,y=48) with the coordinate's origin (0,0) in the lower left corner of the box. The total length of the target is 10.
The Laser's Coordinates
The problem diagram shows the laser located at at (x=0,y=24) with the coordinate's origin (0,0) in the lower left corner of the box.
Reflected Laser Beam
Given the mirror's end points, calculate where the reflected laser bean hits the box wall. Calculate both the bottom and top reflection. Is the target between top and bottom reflected points? If not, try tilting the mirror.
Reflected Laser Beam
Calculate a laser beam's reflection point coordinates and reflection angle. Remember, the angle of incidence equals the angle of reflection.
Links
my Python Code Example: line_intersection.py
my Python Code Example: test_line_intersection.py
my Python Code Example: parallel_lines.py
my Python Code Example: angle_between_two_vectors.py
my Python Code Example: two_vector_angle.py
Sympy Line.intersection() method
how to find the intersection of two lines python
Program for Point of Intersection of Two Lines
How to check if two given line segments intersect?
Compute The Intersection Point of Two Lines