This tutorial emphasizes the following: This is a progression starting from very basic Pygame ideas, through 1D and 2D (pure Python) physics engines, ending with an application of the Box2D physics engine. There is a physics instructor behind this. This Flash movie is for people interested in programming various types of game physics such as throwing/catching, bouncing, among others.
- Video Game Physics Tutorial - Part I: An Introduction to Rigid Body Dynamics
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- The Physics Classroom Topics
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- Appendix: Vectors
- Rigid Body Dynamics
- Introduction to 2D Game Physics with Pygame
The following sequence of topics reflects the J-term course given at Gustavus Adolphus College in This content was originally presented with a mixture of lecture and lab; most of this had verbal explanation. It's posted here to support future offerings of the course and for the curious out there who may want to try this on their own. It's a great way to gain useful coding experience and learn the Python language. Many of the features of the last topic on this page are demonstrated here using a live HTML-5 Canvas.
The revision history includes a discussion of the scope of the J-term course. The Windows-install. More recent versions can be found, but this set is certain to work. This page describes a couple of my adventures with the RPi: python-physics engines of course and a few words on setting up a music server. You'll find details on the Linux installation of the working environment and discussion on the changes made to these scripts to get them running well on the RPi. There's a video that shows the surprisingly good performance of these scripts on the RPi If you watch it to the end, you'll see my wife getting the best of me in Puck Popper.
This page also has a good summary of the keyboard and mouse controls that are used in most of the scripts. This first assignment illustrates the display window and event-handling features that are used from Pygame. Drawing, erasing, and screen updating are viewed in the Pygame window. Keyboard and mouse events are interpreted and used to control the drawing algorithms.
A game loop keeps repeating the process: erase, draw, update the screen. Holding down the "e" key enables screen erasing every time through the game loop. Holding down the "f" inhibits the flip operation that is use to update the screen at the end of the game loop.
Video Game Physics Tutorial - Part I: An Introduction to Rigid Body Dynamics
The two mouse buttons are used to change the color of the circle. The video starts with the erase feature. With erasing enabled, the ball seems animated the drawing tail does not persist. Later the flip screen update operation is inhibited these are drawn in memory but not to the screen. Finally a combination of erasing and flip inhibiting cause the ball to lag behind and then catch up to the cursor.
This first look at a 1D-physics engine does so without any rendering in the Pygame display window. Instead, this outputs to a simple text string that is printed to the command line.
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The 1 version is fully functional with only one page of Python code. The 2 version can be executed with command-line parameters and facilitates running the various examples in the video.
The Physics Classroom Topics
The video is best viewed in full-screen mode so that the preliminary text, before each example run, can be read. Near the beginning of the video, an annotation block is used to help the viewer direct and keep his gaze on the first row of output.
This first row yields the intended animation effect: move, draw, erase, repeat. There is an animated-gif capture of the "first row" displayed at the top of the code discussion page. This rendering approach has the added advantage of preserving the frame history. As the viewer looks up to higher rows on the screen he is looking back in time, frame by frame row by row. This can help in visualizing and understanding wall collisions and the associated position corrections that are made.
The 1D framework introduces the relationship between the screen and the physics world. It also brings in the first taste of Euler's method in animating the motion. There are no car-wall or car-car collisions here; no gravity.
Cars just pass through each other and walls and no acceleration from gravity. OOP classes are used here to organize the code and prepare for the object nature of the games to follow. The video shows five short demos press keyboard numbers 1 through 5. The first two are two-car animations.
The last three show stacks of cars spreading out due to the differences in their velocities. The car in the middle of the stack has zero velocity. At any point in time, the relative velocity of any pair of cars is proportional to the separation distance between them kind of like Hubble's law. Euler's method comes to life here.
Velocities are changing under the accelerating influence of gravity. For now, we'll just do the stickiness correction; later there will be several video demos of this issue.
A coefficient of restitution is used to model the energy loss in the wall collisions. Notice the apparent settling of the cars at the end of the video.
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Note: You can watch in full-screen mode using the YouTube controls in the lower right corner of each video. Esc to get back to this page. Car-car collision physics and car-car stickiness correction are added here.
This script uses the "c" and the "s" keys to toggle two algorithmic features that help to illustrate the collisions and stickiness. The "c" key toggles the "color-transfer" feature which, when enabled, causes the colors of two colliding cars to swap.
So when two cars start to settle near a wall under the influence of gravity, they collide frequently and the colors will swap quickly to show the cars are still colliding. If this feature is off the cars will appear to settle, but the cars really don't settle in our basic physic engine! Later with Box2D we will show true settling. The "s" toggles the stickiness correction on and off.
So if you turn off the correction, the cars will be pulled into each other as they settle. Hit the "s" key again and they will unstick with a little pop. A combination of the "c" and "s" key is used at the tail end of the video. Sorry, this one runs a little long kind of like watching paint dry. The user gets to interact with the objects on the screen. Cursor spring and drag forces are calculated based on the separation distance between the cursor and the selected car and the velocity of the car.
Cars are selected by clicking on the car or holding down the mouse button and letting the car run over the cursor. Cursors attach at the center of the car. Each mouse button invokes a different cursor tether with a different spring constant and car drag coefficient.
Rigid Body Dynamics
The left mouse button is medium, the right mouse button is stiff, and the center roller button has the softest spring. The video closes with me trying to pull the car into the wall. The color transfer "c" is turned on so the frequent collisions are illustrated. Note you can again turn off the stickiness correction here "s" and pull the cars into the wall; then toggle it off and watch them pop out not so much "paint drying" here since you can pull them in pretty quickly, especially with the stiffer of the three cursor tethers.
Gui here, not just sticky ha ha. Controls have been added for stickiness and color-transfer toggles as well as a gravity slider for simulating that bad cruise-liner experience and a button to freeze the cars. If gravity is set to zero, a freeze operation will stop the cars and they will stay that way until Car mass is visualized here by hollowing out the lighter cars. The video shows 10 of the 13 demos. The demo number is indicated in the window title upper part of the Pygame window frame.
Demo 4 shows the inelastic collisions between a set of cars where the total momentum of the set is zero before and after the collision a reverse explosion. Most of the other demos make use of the color-transfer feature to highlight the transfer of momentum through cars like Newton's cradle.
A description of each demo is in the PDF. The video shows the server window and one client's game-pad window also running on the server's computer. Another client running on a networked laptop is connected but not visible in the video. The state U:up or D:down of the a-s-d-w keys of each client are also rendered on the server screen. Please note that this client works only for this assignment.
The last mouse locations when mouse button is down are drawn each game loop. This causes the dynamic tails effect. One Friday we ran this server on the computer that hosts the projector in the lecture room.
Many students connected using the client. For a while we tried this with no verbal communication. It was interesting to see how cooperative this became in spite of the silence.
Introduction to 2D Game Physics with Pygame
The multiplayer techniques introduced here are applied in the 2D-Physics Engine Framework topic below. This vector class is used in all the 2D assignments that follow. The test code illustrates most of the features that will be used.
The video shows a vector sandbox that is based on the vector class. There are seven demos that are run start these using the number keys above the letters on the keyboard. Each demo uses a set of vectors ranging in set size from 2 to Vectors can be selected with the mouse click and drag over the arrow head.
Components include x, y, unit normal red , unit perpendicular red , and the projection of the selected vector onto a second vector.