Swing along the tangent.

Game Mechanics
#1

Hello,
I am am stuck with my java code. Need help. I have been trying to create a swing movement for an animated java ball. I have managed to get the ball moving in a circular manner. With this:

 theta = theta + Math.toRadians(10); 
x = a + r*Math.cos(theta);
y = b + r*Math.sin(theta) ;

This just sets the ball in circular motion. I am wanting to swing the ball from particular point in a motion of a tangent to the circle as given in the image figure below. Could anyone please help me with this?

#2

You can find the slope of that tangent line by using the derivative of a circle: dy/dx = -x/y. You plug in (ballX - circleCenterX) for x, and (ballY - circleCenterY) for y to find the slope(m). You then set the deltaX and deltaY values for the ball using some trig: deltaX = speed/sqrt(m^2 + 1), and deltaY = deltaX * m (You will sometimes have to negate the direction based on whether you are above or below the center of the circle, and for clockwise/counter-clockwise rotation).

#3

Ugh ok so look at a sine curve
BOINK:

http://upload.wikimedia.org/wikipedia/commons/0/02/Simple_sine_wave.svg

have a single value that is equal to the current tick and then use this to calculate how far to rotate the ball each time ie movement = Math.sin(Math.toRadians(tick_count)); this will generate a nice curve value that will swing , simply apply the rotation to the end point about the central point , this will make the swing go up , if you want to start your swing from the central position where velocity is at its maximum then perform Math.cos(Math.toRadians(tick_count));. If you are wondering why its because sin(0) is 0 hence starting on the lowest velocity and cos(0) is 1.

Hope this helped

#4

That was quite close to satisfaction although quite complicated for me. Anyway, I think that solved my problem. Thank you for that wonderful explaination @Icass @Longarmx :slight_smile: