Let's create an openFrameworks project, which draws a moving pendulum in 2D, consisting of a ball dangled on a rubber segment. The example is based on the emptyExample
project in openFrameworks. Perform the following steps to create the project:
emptyExample
project's folder into the folder intended for holding your applications (like apps/myApps
), and rename it to Pendulum
.Pendulum
folder and open this project in your development environment (emptyExample.sln
for Visual Studio, emptyExample.xcodeproj
for Xcode, or emptyExample.workspace
for Code::Blocks).testApp.h
in the development environment, and in the testApp
class declaration add the declarations for the pendulum's center of suspension and the ball's position and velocity:ofPoint pos0; //Center of suspension ofPoint pos; //Ball's position ofPoint velocity; //Ball's velocity
Here ofPoint
is the openFrameworks' class for holding point coordinates, it has x and y members (we will study it in Chapter 2, Drawing in 2D).
testApp.cpp
, and fill the body of the testApp::setup()
function definition:void testApp::setup(){ //Set screen frame rate ofSetFrameRate( 60 ); //Set initial values pos0 = ofPoint( 512, 300 ); pos = ofPoint( 600, 200 ); velocity = ofPoint( 100, 0 ); }
In this function we set the frame rate to 60
frames per second, and we also set initial values for all three points.
testApp::update()
function definition:void testApp::update(){ //Constants float dt = 1.0 / 60.0; //Time step float mass = 0.1; //Mass of a ball float rubberLen = 200.0; //Segment's length float k = 0.5; //Segment's stiffness ofPoint g( 0.0, 9.8 ); //Gravity force //Compute Hooke's force ofPoint delta = pos - pos0; float len = delta.length(); //Vector's length float hookeValue = k * (len - rubberLen); delta.normalize(); //Normalize vector's length ofPoint hookeForce = delta * (-hookeValue); //Update velocity and pos ofPoint force = hookeForce + g; //Resulted force ofPoint a = force / mass; //Second Newton's law velocity += a * dt; //Euler method pos += velocity * dt; //Euler method }
This function updates velocity
and pos
, using Newton's second law and the Euler method. For such a purpose, we compute the force acting on a ball as a sum of Hooke's force between the ball, suspension point, and gravity force.
The details on the Euler method can be seen in the Defining the particle functions section in Chapter 3, Building a Simple Particle System. The information on the Newton's second law, Hooke's force, and gravity force can be seen at the following links:
testApp::draw()
function definition:void testApp::draw(){ //Set white background ofBackground( 255, 255, 255 ); //Draw rubber as a blue line ofSetColor( 0, 0, 255 ); //Set blue color ofLine( pos0.x, pos0.y, pos.x, pos.y ); //Draw line //Draw ball as a red circle ofSetColor( 255, 0, 0 ); //Set red color ofFill(); //Enable filling ofCircle( pos.x, pos.y, 20 ); //Draw circle }
Here we set a white background, draw a rubber as a blue line from pos0
to pos
, and also draw a ball as a red circle. Note that we use the ofFill()
function, which enables openFrameworks' mode to draw filled primitives (circles, rectangles, and triangles). See more details on these drawing functions in Chapter 2, Drawing in 2D.
Play with numerical values in the setup()
and update()
functions and see how it affects the dynamics of the pendulum.