Reference no: EM133134154

Mathematics

In this assessment we are going to use a visual programming language to solve complex real world problems. Visual programming languages are becoming more common in software development, such as in Unreal Engine 4 which uses Blueprints, and in Unity which uses Bolt.

All problems will be in 2-dimensions, although the questions may seem like they are in 3-dimensional.

Let's start by defining our visual programming language. Our visual programming language will use a graph style system where each vertex, node, is a function that computes some values, similar to a mathematical function.
To define a new function in our language we will use the following format.
Feel free to draw functions on paper or using graphing software like diagrams.net.

To solve complex problems we need to string numerous functions together. For example let's take a situation where a player in a game is driving a car and has hit a speed boost which will make the car rotate 90 degrees and then increase its velocity by a factor of 3.

Let the player's current velocity be labelled as PX1 and PY1, where PX1 is the X component of the velocity vector, and PY1 is the Y component of the velocity vector. Let the player's velocity after the speed boost be labelled as PX2 and PY2.

This would be a suitable solution. Rotate Vector and Scale Vector would be defined above this graph.

Problem 1: You are working with a team to build a user interface for the bridge, the cockpit, of a brand new spacecraft. Your team is currently focused on showing the distance to the spacecraft's destination onto a screen in the cockpit of the spacecraft.

A software developer on your team has created a function which displays the distance on the screen:

Your job is to compute the distance to the destination and then provide that value to the above function that your teammate has created.

To do this you should define the following
functions:

a) Vector from Point 1 to Point 2
b) Magnitude of Vector

You also have access to two pieces of data:
a) The spacecraft's location as a point in 2D space (X, Y).
b) The destination's location as a point in 2D space (X, Y). ?

Where SCX is the spacecraft's location X component, and SCY is the spacecraft's location Y component. You can name these whatever you want.
Your final solution should use both these functions. You could start solving this by:
a) Defining both functions (like how Scale Vector is defined above).
b) Compute the magnitude (length) to the destination.
c) Providing the magnitude to your teammates function.

Problem 2

Within the new spacecraft your team is helping to build are numerous robots which perform automated duties, such as cleaning ? and simple repairs. Some repairs to the craft are more complicated and riskier, such as repairing the hull where any small mistake could lead to a breach and expose the craft to the vacuum of space, likely turning all the human crew into frozen popsicles.

To assist the human crew with such complicated repairs, the robots should also be manually controllable. Robots are magnetized to a surface and can only move around the surface in 2-dimensions, i.e. they can never go upwards or downwards, similar to a roomba.

Your team has moved on from the spacecraft bridge user interface to programming the manual controls of the robots. There are 4 keys able to control a robot on a 2D surface ↑,→,↓,←. One of your team members has programmed a function to retrieve the input of a key as a 2D vector.

Another one of your teammates will handle moving the robot in a certain direction and has provided you the following function (no need to define this function!):

Your code will be run every time a key is pressed and it should determine the direction that the robot should move in. The final function in your code should be the one above. Your teammate notes that the direction should never exceed a length of 1.

Problem 3

Your new spacecraft should continuously be checking for any nearby objects that could potentially cause damage to the spacecraft, such as space debris, comets, and giant space monsters.

However your spacecraft only has one LIDAR sensor, a sensor which sends out a pulse of light that bounces off objects and back to the sensor. If you shot a pulse out at small increments until the full 360 degrees was covered it would take far too long and some objects may hit the spacecraft!

Your team comes up with a solution, you will use the LIDAR sensor to send a pulse of light in a random direction, and with enough pulses you should be able to cover a lot of directions and have confidence that no objects will cause the spacecraft damage.

Your role is to generate the 2-dimensional vector that will determine where to shoot the LIDAR light pulse.

Problem 4

Now that your spacecraft has information about its surroundings we want to determine if the spacecraft will collide with any of the objects the LIDAR sensor detected.

There may be thousands of objects detected but most will not have a chance to collide with the spacecraft, perhaps a distant asteroid was detected but is not heading in a direction that will result in a collision with the spacecraft.

One of your teammates will handle the logic for an intersection, you however are tasked with determining if an intersection occurs between two circles and how deep an intersection between those two circles is.

Your code will run for all objects, represented as circles ? , around the spacecraft and you have been provided with the following data:

• The CenterPoint of the circle representing the spacecraft (X, Y).
• The CenterPoint of the circle representing the object (X, Y).
• The diameter of each circle.

Problem 5

Powering the LIDAR sensor, robots, lasers and various other systems takes a LOT of power! To generate this power the spacecraft is covered in solar panels.

The bridge crew, such as the pilot, would find it beneficial to have an estimation of how much power the spacecraft will gain at a certain position and rotation.

Each solar panel has an associated normal, which is a vector which points in the direction away from the solar panel's upward face.

Your team is putting together some software which will estimate the power that the spacecraft should receive so that the bridge crew can try a bunch of different rotations and positions facing stars to optimize the amount of power they will generate.

Solar panels facing a star will be 100% efficient, solar panels 90 degrees or more from the direction the star emits light will capture no light and thus be 0% efficient.

Your role is to calculate how efficient the solar panel power generation output will be between a certain solar panel and a star. This output should be up to 100%, representing the maximum efficiency where the solar panel is perfectly facing the star and thus will generate the maximum amount of energy.

You are provided the following data:

• A 2D vector from a star to the position of the solar panel.
• A normalized 2D vector representing the direction the solar panel is facing. (the solar panel's normal)

You can name these variables however you see fit, you may choose the following naming.

Where SUNTOSCX is the vector's X coordinate from the Sun to Spacecraft, SPNX is the vector's X coordinate representing the upwards direction of the Solar Panel referred to as the Solar Panel's Normal.