Develop Reference

Air Resistance In this simulation causes the velocity to rise drastically

The issue I have is that I'm attempting to add drag to an object in this basic physics simulation (Java [Processing]), but once I add the appropriate formula, it causes the objects velocity to increase drastically in the opposite direction. Of course the problem is that drag for some reason is being calculated too high but I'm not sure why thats happening as I'm using the real world equation.
void setup(){size(1280,720);}
class Circle{
float x,y,r,m,dx,dy,ax,ay,fx,fy;
Circle(float xPos, float yPos, float Radius, float Mass){
x = xPos;
y = yPos;
r = Radius;
m = Mass;
}
void ADD_DRAG(){
fx -= 0.5 * 1.225 * dx * dx * 0.5 * r * PI;
fy -= 0.5 * 1.225 * dy * dy * 0.5 * r * PI;
}
void update(){
ADD_DRAG();
ax = fx / m;
ay = fy / m;
dx += ax / frameRate;
dy += ay / frameRate;
x += dx / frameRate;
y += dy / frameRate;
}
}
Circle[] SceneObjects = {new Circle(50,50,20,20000),new Circle(50,50,2,20)};
void draw(){
background(51);
for (Circle c : SceneObjects){
c.update();
circle(c.x * 3,c.y * 3,c.r * 3);
}
}
void mouseClicked(){
if(SceneObjects[1].fx != 2000)
SceneObjects[1].fx = 2000;
else
SceneObjects[1].fx = 0;
}
This is the code, essentially there is a Circle class which stores the objects properties and then the forces applies are updated each draw loop. The mouseClicked void is just for testing by adding a force to the objects. All and any help is appreciated, thanks!
Maths I am Using:
Rearranged F=ma for ax = fx / m;
Acceleration * time = Speed for dx += ax / frameRate; (frameRate is 1/time)
Distance = Speed * time = for x += dx / frameRate; (same as above)
For drag im using this equation https://www.grc.nasa.gov/WWW/K-12/rocket/drageq.html with the constants eg air density etc added as seen.

There are a couple of things wrong here.
You haven't given us numbers (or a minimal complete example), but the vector algebra is off.
Yes, the acceleration is f = -kv2, and |v|2 = vx2 + vy2, but that doesn't mean that you can decompose f into fx=kvx2 and fy=kvy2. Not only is your magnitude off, but your acceleration is now not (in general) aligned with the motion; the path of your projectile will tend to curve toward a diagonal between the axes (e.g. x=y).
Also, your code always gives acceleration in the negative x and negative y directions. If your projectile happens to start out going that way, your version of air resistance will speed it up.
Finally, your time interval may simply be too large.
There is a better way. The differential equation is v' = -k v|v|, and the exact solution is v = (1/kt) z, (with appropriate choice of the starting time) where z is the unit direction vector. (I don't know how to put a caret over a letter.) This leads to v(t) = (1/t)v(t=1.0)
So you can either work out a fictional time t0 and calculate each new velocity using 1/(kt), or you can calculate the new velocity from the previous velocity: vn+1 =vn/(kd vn + 1), where d is the time interval. (And then of course you have to decompose v into vx and vy properly.)
If you're not familiar with vector algebra, this may seem confusing, but you can't get an air-resistance sim to work without learning the basics.

LWJGL - Making the 3D FPS camera jump

So I am working on my first 3D project and everything went well till I decided to make the FPS character (camera) jump. I tried some methods and all of them didn't look well till I succeeded to do something that works most of the time. Now the problem is the "most of the time" - Which should be all the time.
The problem is that when I click the jump button continuously it starts to freak out. I tried to set the position always back to zero when I exceed it but it still freaks out sometimes although less often. Any suggestions how to do it in order for it to work all the time? (I am working with OpenGL and java without an engine)
The jumping part code:
if (Keyboard.isKeyDown(Keyboard.KEY_SPACE) && !jumping
&& position.y >= temp) { //temp - floor height
jumping = true;
}
gravity = (float) ((walkingSpeed * 0.00003) * delta);//delta - time
//System.out.println(delta);
if (position.y < temp) { //In the air
speed = speed + gravity;
position.y = position.y + speed;
}
if (jumping) {
speed = speed - (float) ((walkingSpeed * 0.0006) * delta);
position.y = position.y + speed;
jumping = false;
}
if (position.y > temp) //**Supposed** to solve the problem
position.y = temp;

There are a number of issues in your code that don't synch up with what you are describing:
You have the sign reversed for virtually everything
You are testing for a condition that always evaluates to true (!jumping)
// Only start a jump while on the ground (position.y <= temp)
if (Keyboard.isKeyDown(Keyboard.KEY_SPACE) && position.y <= temp) {
speed = speed + (float) ((walkingSpeed * 0.0006));
// Don't care about the delta time when you jump, just add a fixed amount of
// positive vertical velocity (which gravity will work out over time).
}
// You had gravity going the wrong direction initially
gravity = (float) -((walkingSpeed * 0.00003) * delta);
//System.out.println(delta);
speed = speed + gravity;
position.y = position.y + speed;
if (position.y < temp) { // Don't sink into the ground
position.y = temp;
speed = 0.0; // Scrub off acceleration due to gravity
}

Object not moving in correct direction

Alright, I'm trying to do some simple object moving in the direction of where you touched the screen.
If I touch directly northwest of the object, it'll kind of move into the direction of the touch position. If I touch directly southeast of the object, it will kind of move into the direction of the touch position as well. However, if I touch directly northeast of the object, it'll move into the opposite direction towards the southwest. If I touch directly southwest of the object, it'll also move to the opposite direction towards northeast.
Also, if I touch north of the object, but just a little to the west, it will go straight west with a little to the north. Same with touching west of the object with a little bit to the north, it'll go straight north with a little bit to the west. Same thing for other directions.
Really, all the directions are from somewhat to obviously incorrect. I've been doing some paper calculations as well and I've seemed to be getting some correct angles, but at this point I'm completely stumped.
Does anyone know what the problem may be?
package com.badlogic.androidgames.texasholdem;
import java.util.List;
import android.util.FloatMath;
import com.badlogic.androidgames.framework.Game;
import com.badlogic.androidgames.framework.Graphics;
import com.badlogic.androidgames.framework.Input.TouchEvent;
import com.badlogic.androidgames.framework.Screen;
public class MainMenuScreen extends Screen {
public static float TO_RADIANS = (1 / 180.0f) * (float) Math.PI;
public static float TO_DEGREES = (1 / (float) Math.PI) * 180;
float num_x = 0; // Position of object on X axis
float num_y = 0; // Position of object on Y axis
float angle = 0;
public MainMenuScreen(Game game) {
super(game);
}
public void update(float deltaTime) {
Graphics g = game.getGraphics();
List<TouchEvent> touchEvents = game.getInput().getTouchEvents();
game.getInput().getKeyEvents();
int len = touchEvents.size();
for(int i = 0; i < len; i++) {
TouchEvent event = touchEvents.get(i);
if(event.type == TouchEvent.TOUCH_UP) {
if(inBounds(event, 0, 0, g.getWidth(), g.getHeight()) ) {
// Calculate the angle of the direction between two points
angle = (float) Math.atan2(event.x - num_x, event.y - num_y) * TO_DEGREES;
if (angle < 0)
angle += 360;
// This is just to give me numbers on the Math.atan2 result, angle, to/from X position, and to/from Y position
System.out.println("Pressed! - ATAN: " + Math.atan2(event.x - num_x, event.y - num_y)
+ " - ANGLE:" + angle + " - POS: " + event.x + "tx/"
+ (int)num_x + "fx " + event.y + "ty/" + (int)num_y + "fy");
}
}
}
// Moving object in direction at 1f speed
num_x += (1f * (float) Math.cos(angle * TO_RADIANS));
num_y += (1f * (float) Math.sin(angle * TO_RADIANS));
}
private boolean inBounds(TouchEvent event, int x, int y, int width, int height) {
if(event.x > x && event.x < x + width - 1 &&
event.y > y && event.y < y + height - 1)
return true;
else
return false;
}
public void present(float deltaTime) {
Graphics g = game.getGraphics();
g.drawPixmap(Assets.background, 0, 0);
g.drawPixmap(Assets.backcard, (int)num_x, (int)num_y);
}
public void pause() {
Settings.save(game.getFileIO());
}
public void resume() {
}
public void dispose() {
}
}

if event x> x then x must be positive to move toward event.x
the problem here is that when event.x< x then your moving x must be negative
int dx,dy;
dx = (1f * (float) Math.cos(angle * TO_RADIANS));
dy = (1f * (float) Math.sin(angle * TO_RADIANS));
if(event.x<x){
dx=-dx;}
if(event.y<y){
dy=-dy;}
num_x+=dx;
num_y+=dy;
this way is simpler but less precise....
public void update(){
//(find dif between item x, and touch x)
float xdif=destx-x;
float ydif=desty-y;
if(x<destx){
dx=xdif/8;
}
else if(x>destx){
//we devide both x and y differences by the same number
dx=xdif/8;
}
else if(x==destx){
dx=0;
}
if(y<desty){
dy=ydif/5;
}
else if(y>desty){
dy=ydif/5;
}
else if(y==desty){
dy=0;
}
x+=dx;
y+=dy;
there u go, pathing in a straight line between two points, item.x and touch x.

Firstly, the math - I think the problem is that, for example, tan(135deg) = tan (-45deg) = -1. Therefore, atan has return values ranging between -90deg and 90deg as a resolution to ambiguity (look at its graph here). I think La5t5tarfighter's solution - negating the x movement in some cases - is on the right track, but you need to negate the y component in those cases as well. You could try that, but it would be much simpler if you used libGDX's Vector2 class. This is how I'd do it:
move.set(touchX, touchY); // y should be through flipping or unproject() before this
move.sub(objectPos); // move now points from object to where you touched
move.nor(); // now 1 unit long
move.scl(SPEED*deltaTime); // multiplied by a constant and delta - framerate-independent
objectPos.add(move);
You could even chain it into just one line if you want:
objectPos.add(move.set(x,y).sub(objectPos).nor().scl(SPEED*deltaTime));
Secondly, you're not using a Camera. I'm not completely sure what the default coordinate system is, but I believe the y axis points up which is not the same as the one used for inputs - Input.getY() is given with an y axis pointing down from the top left corner. If you had a Camera, you'd do this:
cam.unproject(someVector.set(Gdx.input.getX(), Gdx.input.getY(), 0));
Lacking that, you might need to flip the y axis:
event.y = Gdx.graphics.getHeight() - event.y;
Still, this could be wrong. Try drawing the object right at the touch position - if I'm right in this, it'll seem mirrored vertically. If it draws correctly where you touch, ignore this part.

2d balls not colliding properly

I'm just trying to code a nice looking physics game.
The ball collision looks nice but if the balls are colliding too slow, they "stick" in each other. I have no clue why they do.
Here's my collision function:
private void checkForCollision(ArrayList<Ball> balls) {
for (int i = 0; i < balls.size(); i++) {
Ball ball = balls.get(i);
if (ball != this && ball.intersects(this)) {
this.collide(ball, false);
}
}
}
public boolean intersects(Ball b) {
double dx = Math.abs(b.posX - posX);
double dy = Math.abs(b.posY - posY);
double d = Math.sqrt(dx * dx + dy * dy);
return d <= (radius + b.radius);
}
private void collide(Ball ball, boolean b) {
double m1 = this.radius;
double m2 = ball.radius;
double v1 = this.motionX;
double v2 = ball.motionX;
double vx = (m1 - m2) * v1 / (m1 + m2) + 2 * m2 * v2 / (m1 + m2);
v1 = this.motionY;
v2 = ball.motionY;
double vy = (m1 - m2) * v1 / (m1 + m2) + 2 * m2 * v2 / (m1 + m2);
if (!b)
ball.collide(this, true);
System.out.println(vx + " " + vy);
motionX = vx * BOUNCEOBJECT;
motionY = vy * BOUNCEOBJECT;
}
But this is what happens when they collide with a low speed:
So do you have an idea?
EDIT:
The update of Alnitak works very nice... but one problem is still there... if i add gravity like this:
public void physic() {
motionY += GRAVITY; // <= this part (GRAVITY is set to 0.3D)
checkForCollision(screen.balls);
keyMove();
bounceWalls();
posX += motionX;
posY += motionY;
}
They still move into each other. I think this is the wrong way to add gravity, or isn't it?
And I think I did something wrong with the collision formula, because they don't fall right:
!
and then they slowly sink into the ground.
EDIT:
found an AMAZING tutorial: http://www.ntu.edu.sg/home/ehchua/programming/java/J8a_GameIntro-BouncingBalls.html

This is a common problem that happens because sometimes the delta-v of the bouncing ball is insufficient to take it back out of the collision zone.
So the collision routine reverses the direction again, taking it back inside the other ball, ad-infinitum.
You should add a sufficient offset (in the direction of the collision force) to the position of the ball to ensure that the newly calculated positions are no longer colliding.
Alternatively, check whether the balls would collide once you add the new motion values:
public boolean intersects(Ball b) {
double dx = b.posX - (posX + motionX); // no need for Math.abs()
double dy = b.posY - (posY - motionY);
double d = dx * dx + dy * dy; // no need for Math.sqrt()
return d < (radius + b.radius) * (radius + b.radius);
}
but you should also change ball.intersects(this) to intersects(ball).
They may appear to collide slightly too early, but on a fast moving ball it probably won't be visible.

(m1 - m2) * v1 / (m1 + m2) + 2 * m2 * v2 / (m1 + m2);
This has an integer value 2. Please make it 2.0f or 2.0d then check it out. It must be the problem for small speeds. Becuse integer constant autocasts multiplied doubles.
If this does not work, then Alnitak 's answer would be helpful.
If you need real nice physics, you should use the force then convert it to velocity then convert it to displacement . Look at integrator techniques like Runge Kutta and Euler Integration
Force-->acceleration-->velocity-->displacement
if collision occurs, just update the force then the rest will be flowing.
----> http://codeflow.org/entries/2010/aug/28/integration-by-example-euler-vs-verlet-vs-runge-kutta/ <-----
http://www.forums.evilmana.com/game-programming-theory/euler-vs-verlet-vs-rk4-physics/
http://www.newagepublishers.com/samplechapter/001579.pdf
http://cwx.prenhall.com/bookbind/pubbooks/walker2/
Verlet integration is a point between Runge-Kutta-4 and Euler Integration preferably for molecular dynamics (a good example for bouncing balls if you ommit the electrical fields and bonds)

Just found an AMAZING tutorial:
http://www.ntu.edu.sg/home/ehchua/programming/java/J8a_GameIntro-BouncingBalls.html

OpenGL + Processing: Rotate and move based on direction

I'm trying to rotate and move a triangle into a certain direction, based on the pointing direction of the triangle. In theory, I calculate the sine and cosine of the direction (0-360 degrees) and add these values to the x- and y-position, right? It just doesn't work.
Also, the triangle should point up in the beginning, not down.
public void speedUp() {
float dirX, dirY;
speed *= acceleration;
if(speed > 50) speed = 50;
println("dir: " + direction + " x: " + cos(direction) + " y: " + sin(direction));
dirX = cos(direction);
dirY = sin(direction);
xPos+=dirX;
yPos+=dirY;
}
public void redraw() {
GL gl = pgl.beginGL(); // always use the GL object returned by beginGL
gl.glTranslatef(xPos, yPos, 0);
gl.glRotatef(direction, 0, 0, 1000);
gl.glBegin(GL.GL_TRIANGLES);
gl.glColor4f(0.1, 0.9, 0.7, 0.8);
gl.glVertex3f(-10, -10, 0); // lower left vertex
gl.glVertex3f( 10, -10, 0); // lower right vertex
gl.glVertex3f( 0, 15, 0); // upper vertex
gl.glEnd();
}

It looks like you need to convert from polar coordinates(moving about using an angle and a radius) to cartesian coordinates(moving about using the x and y).
The formula looks a bit like this:
x = cos(angle) * radius;
y = sin(angle) * radius;
So, as #Lie Ryan mentions, you also need to multiply with speed (which is your radius in polar coordinates).
Either have your angle in degrees but use radians() when using cos,sin as they work with radians, or use radians, and use degrees() with glRotatef, up to you
Also, you might want to have a look at glPushMatrix() and glPopMatrix(). Bascially, they allow you to nest transformations. Whatever transformations you do withing the blocks, they affect just that block locally.
Here's what I mean, use w,a,s,d keys:
import processing.opengl.*;
import javax.media.opengl.*;
float direction = 0;//angle in degrees
float speed = 0;//radius
float xPos,yPos;
void setup() {
size(600, 500, OPENGL);
}
void keyPressed(){
if(key == 'w') speed += 1;
if(key == 'a') direction -= 10;
if(key == 'd') direction += 10;
if(key == 's') speed -= 1;
if(speed > 10) speed = 10;
if(speed < 0) speed = 0;
println("direction: " + direction + " speed: " + speed);
}
void draw() {
//update
xPos += cos(radians(direction)) * speed;
yPos += sin(radians(direction)) * speed;
//draw
background(255);
PGraphicsOpenGL pgl = (PGraphicsOpenGL) g;
GL gl = pgl.beginGL();
gl.glTranslatef(width * .5,height * .5,0);//start from center, not top left
gl.glPushMatrix();
{//enter local/relative
gl.glTranslatef(xPos,yPos,0);
gl.glRotatef(direction-90,0,0,1);
gl.glColor3f(.75, 0, 0);
gl.glBegin(GL.GL_TRIANGLES);
gl.glVertex2i(0, 10);
gl.glVertex2i(-10, -10);
gl.glVertex2i(10, -10);
gl.glEnd();
}//exit local, back to global/absolute coords
gl.glPopMatrix();
pgl.endGL();
}
You don't actually need the { } for the push and pop matrix calls, I added them like a visual aid. Also, you can do this without push/pop, by concatenating your transforms, but it's handy to know those are there for your when you need them. Might come in handy when you want to shoot some GL_LINES out of that triangle...pew pew pew!
HTH

You have your units messed up. glRotatef excepts degrees and the trigonometrical functions expect radians. This is the most obvious mistake.
Also, speed is never used in your snippet. I suppose that every frame you're using it somehow, but in the code you pasted there's:
xPos+=dirX
Which is basically "add direction to the position" - not making much sense, unless you want to "move it exactly 1 unit in the given direction instantenously at the moment when speedUp() is called. The usual approach for continous movement would be to:
// each frame:
xPos += dirX * speed * deltaTime;
yPos += dirY * speed * deltaTime;

Try this:
dirX = speed * cos(direction);
dirY = speed * sin(direction);

You are obviously new to OpenGl, so I would recommend you, that you look into quaternions to do your roations. Here are two pretty nice article about this matter: Gamedev and Nehe. I would recommend you to use the Quaternion class from the JMonkeyEngine. Just remove the savable and some other interfaces and you can use them with ease. Here they are located: JMonkey Source
I also use the JME math classes for my own projects. I have already striped most of the dependencies and you can download some classes from here: Volume Shadow. However the Quaternion class is missing, but you WILL need Vector3f :D.