Billiards

Applications of geometry in billiards game programming

Billiards game is a game that uses geometric math a lot, and I made this game for the purpose of learning, studying, and improving my geometric math.

To make this game we'll need to apply a lot of geometry math, here we use vectors and trigonometry.

What are vectors used for?

They are used to determine an object's position, or velocity.

What are trigonometric used for?

They are used for the purpose of calculating the angle of an object.

How did I apply them in programming

For example, we have ball position (x₁: 400; y₁: 290) and mouse position (x₂: 1107; y₂: 12).

How do we calculate the angle of the stick?

First we need to calculate the opposite side:
Next, we have to calculate the hypotenuse side:
After calculate the opposite, hypotenuse sides then we calculate the angle of the stick (use inverse sine):
We need to check if x₁ > x₂ then the angle = 180° - angle: angle = 180 - angle.
If the angle < 0 then the angle will add 360°: angle += 360.

Finally the angle of the stick is 158.524°.

Full of the code:

double opposite = vector2.getY() - vector.getY();
double hypotenuse = std::hypot(vector2.getX() - vector.getX(), vector2.getY() - vector.getY());

double degrees = (std::asin(opposite / hypotenuse) * 180) / PI + 180;

if (vector.getX() > vector2.getX()) degrees = 180 - degrees;
if (degrees < 0) degrees += 360;

stick->setAngle(degrees);