Developing ball movement

The movement of the ball is based on the mathematical principles of trigonometry and Pythagoras theorem, so these principles were researched.
h = overall velocity of the ball (the hypotenuse)
x = x component of the ball velocity
y = y component of the ball velocity
0 = theta, angle of the path of the ball, set to a randomly generated number between 35o and 55o

x = sin 0 * h
y = cos 0 * h

Trigonometry:
Trigonometry can be used to calculate angles. In right-angled triangles, where there is a hypotenuse, the term SOHCAHTOA can be used:

• SOH = sine = opposite/hypotenuse
• CAH = cosine = adjacent/hypotenuse
• TOA = tan = opposite/adjacent

Pythagoras theorem:
In a right-angled triangle, the hypotenuse is equal to the sum of the other two sides. Often written as: a2+b2=c2

Random number generation:
For the ball to leave the paddle at the start of each game using a different angle, a random number between two set boundary numbers should be generated and control the ball’s initial movement. The boundary numbers are 35o and 55o as these were considered suitable angles between which to project the ball from the paddle.
To create a random number between these boundaries the srand code is implemented to initialise the random number generator, using processor clicks, as these values are different every time the program runs. The boundary angles are then set and the angle must be between these values, it is then multiplied by 2pi/360, and converted to radians. The ball velocity in x and y are then calculated and the remainder of the random number is divided by 2, giving an answer of 0 or 1, allowing the x component to be reversed, changing to direction the ball takes as it leaves the paddle.

Creating the ball

The design ideas for the ball and testing suggested that the ball should be yellow, to ensure that it stands out against the background of the game board, the video image of the players.

The ball has the same diameter (in pixels) as the height of the paddle, to keep continuity and for aesthetic purposes. A small white rectangle has been added to the yellow ball to create a pseudo 3D effect and add detail to the ball.

The ball has been coded to move only within the borders of the game board. This required some mathematical work, to calculate the velocity of the ball, it's projected position from an initial state to the next during one time step, the distance the ball travels in the x and y axis in a single time step and when it should rebound from the border, accounting for the radius of the ball.

Planning

I've been busy planning my ideas for the project. I've been creating initial design ideas for the game board/screen and have been trying to work out where the objects will be placed on the screen, how they will interact with one another and specifiying some names for key variables.

The project is heavily based on mathematics, to understand the collision detection and spatial position of objects on the screen. I have been researching and working in my logbook at this planning stage so that I have firm ideas in place before trying to code the game.