Step by Step solution about How to resolve the algorithm Animate a pendulum step by step in the C programming language

This C code is a simple simulation of a pendulum. It uses the GLUT library to create a window and handle the graphics, and the GL library to draw the pendulum.

The main function initializes the simulation parameters and then calls the init_gfx function to create the window and set up the GLUT callbacks. The init_gfx function sets up the display mode, window size, and idle function, and then creates the window.

The render function is called whenever the window needs to be redrawn. It updates the position of the pendulum and then draws it using OpenGL. The update_position function uses the current angle and angular velocity to calculate the new position of the pendulum. The draw_pendulum function draws the pendulum using a line from the pivot point to the bob.

The elappsed function is used to measure the time between frames. It uses the gettimeofday function to get the current time and then calculates the elapsed time since the last frame.

The main function calls the glutMainLoop function to start the GLUT event loop. The event loop will call the render function whenever the window needs to be redrawn and will also handle any other events, such as keyboard and mouse input.

Here is a breakdown of the main function:

• The alpha variable is initialized to 4 * atan2(1, 1) / 2.1. This is the initial angle of the pendulum.
• The E variable is initialized to length * g * (1 - cos(alpha)). This is the initial energy of the pendulum.
• The accl variable is initialized to -g / length * sin(alpha). This is the initial acceleration of the pendulum.
• The omega variable is initialized to 0. This is the initial angular velocity of the pendulum.
• The gettimeofday function is called to get the current time. This time will be used to measure the time between frames.
• The init_gfx function is called to create the window and set up the GLUT callbacks.
• The glutMainLoop function is called to start the GLUT event loop. The event loop will call the render function whenever the window needs to be redrawn and will also handle any other events, such as keyboard and mouse input.

This code is a simple simulation of a pendulum using OpenGL. It includes the header files necessary for the program to run and defines some global variables. It also includes a function to calculate the elapsed time between two points in time and a function to resize the window.

The render function is the main loop of the program. It calculates the position of the pendulum based on the current angle, angular velocity, and acceleration. It then draws the pendulum and updates the angle, angular velocity, and acceleration for the next frame.

The init_gfx function initializes the graphics system and creates the window.

The main function initializes the global variables, calls the init_gfx function, and then enters the main loop of the program.

Here is a more detailed explanation of the code:

• The resize function is called when the window is resized. It sets the viewport and projection matrix to match the new window size.

• The render function is called every time the window needs to be redrawn. It calculates the position of the pendulum based on the current angle, angular velocity, and acceleration. It then draws the pendulum and updates the angle, angular velocity, and acceleration for the next frame.

• The init_gfx function initializes the graphics system and creates the window.

• The main function initializes the global variables, calls the init_gfx function, and then enters the main loop of the program.

#include <stdlib.h>
#include <math.h>
#include <GL/glut.h>
#include <GL/gl.h>
#include <sys/time.h>

#define length 5
#define g 9.8
double alpha, accl, omega = 0, E;
struct timeval tv;

double elappsed() {
	struct timeval now;
	gettimeofday(&now, 0);
	int ret = (now.tv_sec - tv.tv_sec) * 1000000
		+ now.tv_usec - tv.tv_usec;
	tv = now;
	return ret / 1.e6;
}

void resize(int w, int h)
{
	glViewport(0, 0, w, h);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();

	glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();
	glOrtho(0, w, h, 0, -1, 1);
}

void render()
{
	double x = 320 + 300 * sin(alpha), y = 300 * cos(alpha);
	resize(640, 320);
 	glClear(GL_COLOR_BUFFER_BIT);

	glBegin(GL_LINES);
	glVertex2d(320, 0);
	glVertex2d(x, y);
	glEnd();
	glFlush();

	double us = elappsed();
	alpha += (omega + us * accl / 2) * us;
	omega += accl * us;

	/* don't let precision error go out of hand */
	if (length * g * (1 - cos(alpha)) >= E) {
		alpha = (alpha < 0 ? -1 : 1) * acos(1 - E / length / g);
		omega = 0;
	}
	accl = -g / length * sin(alpha);
}

void init_gfx(int *c, char **v)
{
	glutInit(c, v);
	glutInitDisplayMode(GLUT_RGB);
	glutInitWindowSize(640, 320);
	glutIdleFunc(render);
	glutCreateWindow("Pendulum");
}

int main(int c, char **v)
{
	alpha = 4 * atan2(1, 1) / 2.1;
	E = length * g * (1 - cos(alpha));

	accl = -g / length * sin(alpha);
	omega = 0;

	gettimeofday(&tv, 0);
	init_gfx(&c, v);
	glutMainLoop();
	return 0;
}