I'm currently making a 2D pool game where i have to use real physics simulation. I have done the circle collision and elastic collision so far, But I want a formula which can find the collision response velocity, which differs when a ball collides with other at different points thanks in advance.
There are many approaches, but if you can afford to make the balls overlap a bit (that is, to make part of the ball "enter" the other) you can turn it into a spring-damper system and solve with Hooke's law.
Since Hooke's law give you the force, you need to integrate it to find the momentum. Momentum divided by mass is the velocity you're looking for.
Take a look at this excellent intro of spring physics for game development (that also has a link for his intro on numerical integration).
edit: if you're looking for a practical solution I suggest the Box2D physics engine.
Pool collision can be considered as elastic collision throughout the board, with friction slowing down its movement.
Don;t think the collision response in terms of angles to the circle. Using vectors will ease the problem.
The circle-circle collision velocity response is easy:
1. When collision is detected
2. FInd the normal velocity of the balls acting toward the other ball.
3. Interchange the Normal velocity between the two balls
4. Resolve the velocity in x and y direction
A very helpful webiste to find the velocity response in terms of vectors: http://archive.ncsa.illinois.edu/Classes/MATH198/townsend/math.html
Related
I want to have a 3d dice that can be dropped onto a surface and land face down. I also want to give the cube a random rotation velocity so the cube rotates in mid air before landing so I get a random result.
I've looked around but I cant find anything on the subject.
I know how to render and spawn the dice as well as have it affected by gravity and how to give it a random rotation velocity as well as how to stop it once it hits a surface but how can I make sure it lands face down and then how can I tell which face is facing upward so I can get the value that the dice landed on?
What you want is rigid body physics simulation. I would recommend using a physics simulation library, such as bullet.
Physics libraries usually provide functions to know if an object is "sleeping" (not moving). This can be used to trigger the dice value readout.
To know which face is facing upward, you can get the transformation matrix M of your cube, apply it to a unit vector and look where this result vector is pointing to.
If you prefer implementing the physics by yourself, those papers are really good to know the basics of rigid body simulation :
https://www.cs.cmu.edu/~baraff/sigcourse/notesd1.pdf
https://www.cs.cmu.edu/~baraff/sigcourse/notesd2.pdf
I have some questions for correctly implementing a system that add gravity to my player while still detecting and correcting collision with the floor. I understand the basic math for the AABB and adding gravity vector to the players velocity vector then adding it to the position. For some reason when I try the player stops for the first few frames then eventually the velocity builds up to be more than the tile width and it goes through. I guess my real question is how to properly implement the gravity with the collision. Do I make gravity vector 0, 0 when it hits the floor or when I am just standing on the floor my collision detection will constantly move me out of the floor? I really don't know the flow of the logic with this situation.
Edit 1:
I am trying to make the simple engine myself to gain experience with programming. I kind of solved the one problem, I now can stop on the floor. My current logic is:
add gravity to velocity, check for collision, adjust the velocity by the offset of the collision, if any, add velocity to the position then set velocity to 0.
m_velocity += m_gravity;
glm::vec2 mtd = collideWithObject(objectVector);
m_velocity -= mtd;
m_position += m_velocity;
m_velocity.x = 0.0f;
m_velocity.y = 0.0f;
It works but I am not sure if that is the flow, I guess I just want to know what is the most common way to implement this.
For some reason when I try the player stops for the first few frames then eventually the velocity builds up to be more than the tile width and it goes through.
If you are applying physics in increments - such as once every frame - you must account for the infinite increments that exist between each of those points.
For a simple "plane collision", like your floor, don't test if your current AABB collides with the floor. Create the smallest AABB that includes your current AABB and the last AABB. If that box collides, you've collided with the plane.
as #MorphingDragon mentioned, you should consider Box2D, many games use Box2D.
For your question "Do I make gravity vector 0, 0 when it hits the floor or when I am just standing on the floor my collision detection will constantly move me out of the floor? I really don't know the flow of the logic with this situation.". I just assume you know Verlet integration, for calculate your new position, you don't need to change your gravity, [as you know, gravity is everywhere on earth, or you want to do a game in space, ;)] you just need to handle the collision detection logic as "when collision happens, just make the collision point satisfy my constraints", and your constraint should be "all point should not be placed under the floor, otherwise just move it and make it sit on the floor".
The collection detection and constraint solver theory should be very common in modern physical engine and easy to understand and implement.
Hope this help.
Thanks
An
I am building an IOS game in Cocos2d - Chipmunk - Spritebuilder. I need to make a characters orbit around around a point, and I was having quite some difficulty in implementing orbits with real physics.
So far, I have tried two methods, one is creating a distance joint from the player to the planet, and then applying a 90 degree force on the player where an angle is created between the end of the distance joint and an imaginary line drawn at a 90 angle to it. He moves around crazily and this method is not working for me.
I then tried calculating 180 points on the circumference at a radius from the planet (which is the bounds of detecting and implementing its effects on the player) - and then in a scheduled update method [character.physicsbody applyForce:nextCircumferencePoint]; This does not work, as he does not follow the path exactly and is quite far from it. I am thinking that I need to also apply a gravitational force towards the planet which would cause him to circle it. Though I don't know how to calculate that force, apply it, or if it would even help.
A third method which would never work, but was used for testing was to set his position to the next circumference point. He does orbit, but any collision won't work (such as if a piece of space junk goes in his way.) He will simply be positioned right over any other object. This world great if you don't need collisions, are writing your own physics engine. This is not a polished way of doing things, so will avoid it.
Please correct anything I have already done and tell me how it would work, or shed light on other options and how to implement them.
Check out my answer here. It's for box2d, but you can do it with Chipmunk. If bodyA position will change, orbit will be same. You just need to change speed of body movement for your needs, just increase smoothness and slow down your update method.
I am making a simple 3D OpenGL game. At the moment I have four bounding walls, a random distribution of internal walls and a simple quad cube for my player.
I want to set up collision detection between the player and all of the walls. This is easy with the bounding walls as i can just check if the x or z coordinate is less than or greater than a value. The problem is with the interior walls. I have a glGenList which holds small rectangular wall segments, at the initial setup i randomly generate an array of x,z co ordinates and translate these wall segments to this position in the draw scene. I have also added a degree of rotation, either 45 or 90 which complicates the collision detection.
Could anyone assist me with how I might go about detecting collisions here. I have the co ordinates for each wall section, the size of each wall section and also the co ordinates of the player.
Would i be looking at a bounded box around the player and walls or is there a better alternative?
I think your question is largely about detecting collision with a wall at an angle, which is essentially the same as "detecting if a point matches a line", which there is an answer for how you do here:
How can I tell if a point belongs to a certain line?
(The code may be C#, but the math behind it applies in any language). You just have to replace the Y in those formulas for Z, since Y appears to not be a factor in your current design.
There has been MANY articles and even books written on how to do "good" collision detection. Part of this, of course, comes down to a "do you want very accurate or very fast code" - for "perfect" simulations, you may sacrifice speed for accuarcy. In most games, of the players body "dents" the wall just a little bit because the player has gone past the wall intersection, that's perhaps acceptable.
It is also useful to "partition the space". The common way for this is "Binary space partitioning", which is nicely described and illustrated here:
http://en.wikipedia.org/wiki/Binary_space_partition
Books on game programming should cover basic principles of collision detection. There is also PLENTY of articles on the web about it, including an entry in wikipedia: http://en.wikipedia.org/wiki/Collision_detection
Short of making a rigid body physics engine, one could use point to plane distance to see if any of the cubes corner points are less than 0.0f away from the plane (I would use FLT_MIN so the points have a little radius to them). You will need to store a normalized 3d vector (vector of length 1.0f) to represent the normal of the plane. If the dot product between the vector from the center of the plane to the point and the plain normal is less than the radius you have a collision. After that, you can take the velocity (the length of the vector) of the cube, multiply it by 0.7f for some energy absorption and store this as the cubes new velocity. Then reflect the normalized velocity vector of the cube over the normal of the plane, then multiply that by the previously calculated new velocity of the cube.
If you really want to get into game physics, grab a pull from this guys github. I've used his book for a Physics for games class. There are some mistakes in the book so be sure to get all code samples from github. He goes through making a mass aggregate physics engine and a rigid body one. I would also brush up on matrices and tensors.
I'm new to using Box2d and really can't find a consistent answer to my question so please excuse me.
I'm writing a game for the iPhone -- who isn't these days -- and I'm using Cocos2d and Box2D. I have objects that move around in the game and I would like to give them a more of a curved path. From my studies I know that I should use body of type b2_kinematicBody which allows me to change the linear velocity every tick and keeps them from colliding with my other flying bodies. I do understand that if I know my current position (x,y) and my next position in the step (x1,y1) I would be able to compute the vector for velocity. Does anybody have a good way to give an object a defined curved path? I'm thinking it has to be some kind of parametric equation.
Take a look at bezier curves. After curve defenition you can compute the derivative (it's easy for bezier) and use it as a velocity for your body
OH whats the game called? sounds like a good one. have you looked into maybe just doing that in version 2.0