Download as ODP, PPTX
![Approximately
net_force = sum(forces)
acceleration = force / mass
velocity += acceleration * dt
position += velocity * dt
forces = [GRAVITY * mass]
+ rotational equivalents
Time step](https://image.slidesharecdn.com/programmingphysicsgameswithopengl-130705023940-phpapp02/85/Programming-physics-games-with-Python-and-OpenGL-26-320.jpg)
Programming physics games with Python and OpenGL
- 1. Programming Physics Games with OpenGL Daniel Pope ~@lordmauve Code samples are available at https://bitbucket.org/lordmauve/physicsgames
- 2. Outline • Introduction toOpenGL • Introduction to physics engines • Connecting the two • A bit more about physics engines • Tips on writing games
- 9. What is OpenGL? • Low-level 2Dand 3D graphics library • Usually hardware accelerated • Can only draw points, lines, triangles • But triangles can be textured • GPUs can evaluate a short program for each vertex or fragment in a high-level language
- 10. What is a physics engine? Given a modelof the world at time t Apply physical laws to compute a model of the world at time t + ∆t (for small ∆t)
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- 16. OpenGL wrapper/scenegraph • Higher levelAPI • Window Creation • Texture Loading • Sprites/Texture Atlases • Model Loading/Rendering/Animation • PVS – Potentially Visible Set calculation • Graphics Algorithms
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- 19. apt-get install python-box2d apt-getinstall python-pyglet (pyBox2D == 2.0.2ish)
- 20. What a game does while True: dt =wait_one_frame() process_input() update_world(dt) draw_world()
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- 23. A physics simulation • Newton's Laws •Collisions • Constraints (eg. Joints)
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- 25. Rotational Equivalents Linear Angular Mass/Inertia Momentof Inertia Force Moment/Torque Position Angle Velocity Angular Velocity Acceleration Angular Acceleration Momentum Angular Momentum Impulse Angular Impulse
- 26. Approximately net_force = sum(forces) acceleration= force / mass velocity += acceleration * dt position += velocity * dt forces = [GRAVITY * mass] + rotational equivalents Time step
- 27. Collisions • Detect whentwo shapes intersect • Broad phase (O(n log n)?, approximate) • Narrow phase (O(n²)) • Exchange momentum • Move them apart, keep them apart
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- 29. Separating Axis Theorem Given two convexshapes, it is possible to draw a straight line between them if and only if the two do not intersect.
- 30. Bodies Collections of shapes Computecentre of mass Compute moment of inertia
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- 32. Linking physical objects with OpenGL • Draw sprites •Create physical models corresponding to sprites • Instantiate objects into physics simulation Each frame: • Step time • Read position + angle of body • Draw OpenGL quads/sprites at position + angle
- 33. (0, 1) (0, 0)(1, 0) (1, 1) (0, 1) (0, 0) (1, 0) (1, 1) Texture Coordinates
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- 36. Collision Callbacks What happens ingame when shapes collide? Register a callback to take action • Destroy/change the object • Create a joint • Play a sound
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- 38. Joints • pin joint– bodies attached at a point, can rotate • prismatic joint – keep bodies aligned, like a piston or a train on a rail • distance joint – keep points on the two bodies at the same distance from one another, like a tow-bar or crank shaft • pulley joint – the position of a body along one axis is linked to the position of another body along another axis
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- 40. Joint motors/limits • Motors applytorques or forces between the bodies • Joints can have limits – your knees do not bend backwards
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- 42. Features I've not yet mentioned • Collision groups/masks •Sensors • Non-rotating bodies/Infinite moment of inertia • Introspecting the world • Sleeping
- 43. Complications I've skipped over • Constraint solving •Overconstraint • Stability
- 45. Graphics and Sound • Cute andcolourful is attractive • Simple shapes and outlines are much easier than other styles • Free/CC game art resources available
- 47. The art of tuning a physics engine • Tuning magicnumbers: • Forces • Torques • Density/Friction/Restitution • Re-shaping bodies/redrawing sprites • At which point does a force act? • Joints/joint limits/joint motors • Collision groups/filters
- 48. “To every actionthere is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.” - Archimedes
- 49. Compound effects • Buoyancy • Lift •Explosions • Soft bodies • Drag effects • Joints or objects 'snapping'
- 52. Physics Games • Intuitive forplayers • The game is mastering the physics • Constrain degrees of freedom to balance difficulty/reward/punishment
- 53. Physics Puzzles Overlapping constraints • Physicalconstraints • Thing in the way • Thing not in the right place • How to overcome gravity • Wrong physical behaviour unless... • Non-physical constraints • Player can't breathe underwater • Only x can pass through this barrier
- 54. Reasons to use a physics engine • Tons ofmaths for free • Cool effects/cheap animations • Game world responds to player; player is empowered/immersed • Extra layer of complexity/interest for the player • Intuitive puzzles
- 55. Reasons not to use a physics engine • Extra dependency/painto install • Time consuming to tune • Too many degrees of freedom may make some mechanics difficult or impossible to work in
- 56. Daniel Pope @lordmauve Code samplesare available at https://bitbucket.org/lordmauve/physicsgames
Editor's Notes
- #28 Very fast moving objects (eg. bullets) may have passed completely through each other in a single time step – compute time of first intersection