1. CS 282

2.  Questions about Assignment 1?  Questions about last week’s lab?  Otherwise, please sit next to your partner (or someone else if your partner isn’t here)!

3.  We are going to make a ball fall and bounce off a table… with physics!  In a nutshell, ◦ Get a ball to fall in the framework ◦ Collision checking ◦ Changing velocity ◦ Energy Relationships  And for the over achievers… ◦ Realistic animation

4.  First of all, download the framework for today’s lab ( Resources in class website)  Take a look at the framework. Namely ◦ The body class (body.h and body.cpp) ◦ lab3.cpp (the driver)  Notice that the body class has ◦ 3 vectors: position, velocity, acceleration ◦ 2 scalars: mass, energy  So now let’s make the ball fall!

5.  How do you update the position of the ball? ◦ For now, we are going to assume the ball can only move in the y-direction, so ignore x and z. ◦ If you know the velocity and the delta time, you can update the position!  How do we get delta time? ◦ Since we have a clock class, and a clock called “delta_time” in our driver, all we need to do is call the measure_reset() function  We use measure_reset because delta time should be reset after its value is read.

6.  Go into body.cpp ◦ Edit the “update_position” function  Add the C++ equivalent of: y_position = y_position + ( y_velocity * delta_t )  Go into lab3.cpp ◦ Notice the variable “sphere” and its parameters  For this exercise, we let the sphere have an initial velocity of -2.0 ◦ Look at the DrawGLScene() function  Notice the part commented “Sphere Physics”  Under “Sphere Physics” use the global_time object and update_position function to correctly update sphere’s postion.

7.  Our ball fell magnificently! ◦ But it also fell through the table…  Since we never check for a collision between the ball and the table, there is no interaction between them  We need to fix that!

8.  Things to consider when doing collision ◦ The position of your object (in this case, the ball) ◦ It’s size ( radius for us ) ◦ The position of the object we want to check  You want to make the ball stop when it hits the table. ◦ The table is situated at ( 0.0, -0.5, 0.0) ◦ The radius of the ball is 0.5 ◦ Conveniently, this allows us to just check the collision at 0.0  Go into body.cpp ◦ Modify the update_position function  The ball should stop when it touches the table

9.  Our ball now stops at the table… ◦ But something is still wrong  The ball is falling at constant speed – which would be OK if there was no acceleration. ◦ Unfortunately for us, we have gravity  So we need to update our velocity based on acceleration  Acceleration due to gravity is -9.81 m/s 2

10.  Examine the your change to update_position ◦ It should be testing for y_position >=0  Add this same check to update_velocity ◦ Inside the check, add the C++ equivalent of:  y_velocity = y_velocity + (delta_t * gravity)  This should be the only statement inside of this check right now.  At this point, our ball will accelerate until it touches the table.

11.  But something is still missing…

13.  Next we will make the ball bounce.  For now, we will just switch the sign of the y velocity once the ball has hit the ground  Go to body.cpp ◦ In update_velocity, add a check to switch the velocity sign. In other words:  If y_position < 0, switch y_velocity signs  The ball now bounces up and down!

14.  We are still missing one more thing – when the ball hits the ground, it should not bounce up to the same height.  The ball starts off with a certain amount of potential energy. When it hits the ground, this energy is converted to both kinetic and thermal energy.  Thus we our ball will have a lower kinetic energy, and will not bounce as high!

15.  First, you need to figure out the initial potential energy of the ball. ◦ E p = m*g*h  mass * 9.81 * height of the ball ◦ Go to body.cpp, and calculate energy in the constructor (since we know all our parameters at that point already!)  Next, we need to remove some things ◦ Remove the if statement in update_position ◦ Remove the if-else in update_velocity

16.  At this point, your update_velocity and update_position functions should have 1 line of code.  We need to know, however, when the ball has hit the table (or gone underneath it) ◦ Before you change the y-position in update_position, add a check for this and manually set the y-position to 0 (I’ll explain why we do this later).  Inside this check you’ve added, we can know calculate energy and our new velocity!

17.  To account for thermal energy, reduce the ball’s energy by 20% ◦ energy *= 0.8  You have your energy and mass, therefore you can solve this equation for velocity ◦ E k = ½ m*v 2  Math time! Solve the equation for v to get the equation you need. ◦ Now set your y-velocity to this new velocity  Congratulations! You have successfully implemented a (quasi) realistic bouncing ball!

18.  Manually setting the position of the ball to 0 is an incorrect way of animating what’s really occurring. The correct way is to detect the instant the ball hits the table, and subtract that from your recorded delta time. ◦ animation_t = delta_t – collision_t  Then, you can animate the ball bouncing up for this amount of time, and this will be the “realistic” way of animating your ball.