I was trying to use opengl using c. The code which I wrote leaves gaps within the lines i.e. draws dotted lined whereas the one which I found on the net draws perfectly. I don't get that, if there is no difference in the code which I wrote and the one I found on the net, Why does this happen?
I tried surfing through the sites. I also read DDA Line Drawing Algoruthm have errors
however, couldn't find the solution
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
//comment the following line when not on windows
//#include <windows.h>
#include <GL/gl.h>
#include <GL/glut.h>
void Init(void); //used to initialize the stuff such as ortho2D and matrix mode;
void renderFunction(void); //this function is called in the glutDisplayFunc
void drawAxes(void); //used to draw the axes
void dda(const float, const float, const float, const float); //the actual implementation of the algorithm
main(argc, argv)
char** argv;
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(300,300);
glutInitWindowPosition(100,100);
glutCreateWindow(argv[1]);
Init();
glutDisplayFunc(renderFunction);
glutMainLoop();
return EXIT_FAILURE;
}
void Init(void) {
glClear(GL_COLOR_BUFFER_BIT);
glColor3f(1.0, 1.0, 1.0);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluOrtho2D(-500, 500, -500, 500);
}
void renderFunction(void) {
drawAxes();
int x0, y0, x1, y1;
while(1) {
printf("ENTER THE CO-ORDINATES OF THE FIRST POINT: ");
scanf("%d %d",&x0 ,&y0);
printf("ENTER THE CO-ORDINATES OF THE SECOND POINT: ");
scanf("%d %d",&x1 ,&y1);
dda(x0, y0, x1, y1);
}
}
void drawAxes(void) {
dda(-500, 0, 500, 0);
dda(0, -500, 0, 500);
}
void dda(x0, y0, x1, y1)
const float x0, y0, x1, y1;
{
float dx = x1 - x0;
float dy = y1 - y0;
int steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy);
float xInc = dx/(float)steps;
float yInc = dy/(float)steps;
float x = x0;
float y = y0;
glBegin(GL_LINES);
int i = 0;
for(i = 0; i < steps; i++) {
glVertex2i((int)x, (int)y);
x += xInc;
y += yInc;
}
glEnd();
glFlush();
}
The code which I found on the net:
#include<stdio.h>
#include<math.h>
#include<GL/freeglut.h>
#include<GL/gl.h>
void dda(int x0, int y0, int x1, int y1){
int steps;
float Xinc; float Yinc; float X,Y;
//DDA Calculation start
int dx = x1-x0;
int dy = y1-y0;
steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy);
Xinc = dx/(float)steps;
Yinc = dy/(float)steps;
X=x0;
Y=y0;
//DDA Calculation end
int i;
glColor3f(0.0, 0.0, 0.0);
// glOrtho(-1.0,1.0,-1.0, 1.0,1.0,-1.0);
glBegin(GL_POINTS);
for(i=0 ; i<steps ; i++){
glVertex2i((int)X,(int)Y);
X+=Xinc;
Y+=Yinc;
}
glEnd();
}
void axis(){
dda(-750,0,750,0);
dda(0,-750,0,750);
}
void renderF(void){
gluOrtho2D(750,-750,750,-750);
axis();
//Diagonal Vertex 1
int x1 = 500;
int y1 = 500;
//Diagonal Vertex 2
int x2 = -500;
int y2 = -500;
int v = x1;
int u = v/2;
dda(-v,v,-v,-v);
glFlush();
}
int main(int argc, char** argv){
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(500,500);
glutInitWindowPosition(100,100);
glutCreateWindow("Hello");
glClearColor(1.0, 1.0, 1.0, 0.0);
glClear(GL_COLOR_BUFFER_BIT);
glutDisplayFunc(renderF);
glutMainLoop();
return 0;
}
The difference is that your code uses GL_LINES whereas the other code uses GL_POINTS.
When you draw GL_POINTS then each drawn vertex fills one pixel (when point size is 1).
When you draw GL_LINES then every pair of vertices draws a line between them. In your code it essentially means that vertices 0 and 1 fill the 0th pixel, vertices 2 and 3 fill the 2nd pixel, etc... no pairs fill the odd pixels.
Possible solutions:
Use GL_POINTS as in the original code.
Use GL_LINE_STRIP.
Or the best of all, just use the OpenGL functionality of rasterizing the line for you:
void dda(float x0, float y0, float x1, float y1)
{
glBegin(GL_LINES);
glVertex2f(x0, y0);
glVertex2f(x1, y1);
glEnd();
}
Related
The following code shows a straight cylinder/pipe in OpenGL C language.
#include <stdio.h>
#include <stdlib.h>
#include <GL/glut.h>
#include <math.h>
#define PI 3.1415927
void draw_cylinder(GLfloat radius, GLfloat height, GLubyte R, GLubyte G, GLubyte B)
{
GLfloat x = 0.0;
GLfloat y = 0.0;
GLfloat angle = 0.0;
GLfloat angle_stepsize = 0.1;
// Draw the tube
glColor3ub(R-40,G-40,B-40);
glBegin(GL_QUAD_STRIP);
angle = 0.0;
while( angle < 2*PI ) {
x = radius * cos(angle);
y = radius * sin(angle);
glVertex3f(x, y , height);
glVertex3f(x, y , 0.0);
angle = angle + angle_stepsize;
}
glVertex3f(radius, 0.0, height);
glVertex3f(radius, 0.0, 0.0);
glEnd();
// Draw the circle on top of cylinder
glColor3ub(R,G,B);
glBegin(GL_POLYGON);
angle = 0.0;
while( angle < 2*PI ) {
x = radius * cos(angle);
y = radius * sin(angle);
glVertex3f(x, y , height);
angle = angle + angle_stepsize;
}
glVertex3f(radius, 0.0, height);
glEnd();
}
void display(void)
{
glClear(GL_COLOR_BUFFER_BIT);
glLoadIdentity();
glTranslatef(-0.5,0.0,-2.5);
glRotatef(100.0, 0.725, 1.0, 1.0);
draw_cylinder(0.15, 1.0, 255, 160, 100);
glFlush();
}
void reshape(int width, int height)
{
if (width == 0 || height == 0) return;
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(35.0, (GLdouble)width/(GLdouble)height,0.5, 20.0);
glMatrixMode(GL_MODELVIEW);
glViewport(0, 0, width, height);
}
int main(int argc, char **argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(640,580);
glutCreateWindow("Create Cylinder");
glClearColor(0.0,0.0,0.0,0.0);
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutMainLoop();
return 0;
}
At the moment it draws a straight cylinder/pipe. And I wanted to curve it to look like this.
First I recommend to split the cylinder into slices. The following cone will draw exactly the same cylinder, but it splits the cylinder int slices. The slices have different colors to visualize the effect.
GLfloat h0, h1, angle, x, y;
int i, j;
int slices = 8;
for ( i = 0; i < slices; i++ )
{
h0 = (float)i / (float)slices;
h1 = (float)(i+1) / (float)slices;
glColor3f( 1.0f-h0, 0.0, h1 );
glBegin(GL_QUAD_STRIP);
for ( j = 0; j <= 360; ++ j )
{
angle = PI * (float)j * PI / 180.0f;
x = radius * cos(angle);
y = radius * sin(angle);
glVertex3f( x, y, h0 );
glVertex3f( x, y, h1 );
}
glEnd();
}
Then you have to define a bend radius and a bend start and end angle. The following code draw a bended pipe form bend_ang0 to bend_ang1, with a radius bend_radius. The bend angles can be calculated in relation to the bend radius and the length of the pipe:
GLfloat w0, w1, ang0, ang1, angle, x, y, xb, yb, zb;
int i, j;
int slices = 8;
GLfloat bend_radius = 1.0f;
GLfloat bend_angle, bend_ang0, bend_ang1;
bend_angle = bend_radius * height;
bend_ang0 = -bend_angle/2.0f;
bend_ang1 = bend_angle/2.0f;
for ( i = 0; i < slices; i++ )
{
w0 = (float)i / (float)slices;
w1 = (float)(i+1) / (float)slices;
ang0 = bend_ang0 + (bend_ang1-bend_ang0) * w0;
ang1 = bend_ang0 + (bend_ang1-bend_ang0) * w1;
glColor3f( 1.0f-w0, 0.0, w1 );
glBegin(GL_QUAD_STRIP);
for ( j = 0; j <= 360; ++ j )
{
angle = PI * (float)j * PI / 180.0f;
x = radius * cos(angle) + bend_radius;
y = radius * sin(angle);
xb = sin( ang0 ) * x;
yb = y;
zb = cos( ang0 ) * x;
glVertex3f( xb, yb, zb );
xb = sin( ang1 ) * x;
yb = y;
zb = cos( ang1 ) * x;
glVertex3f( xb, yb, zb );
}
glEnd();
}
For the following image I activated the depth test and changed the model view matrix:
void display(void)
{
glEnable( GL_DEPTH_TEST );
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
glTranslatef(0.0f, -0.5f, -4.0f);
glRotatef(-90.0f, 1.0f, 0.0, 0.0f);
draw_cylinder(0.15, 2.0, 255, 160, 100);
glFlush();
}
Currently you are drawing the entire height of the cylinder in one go ... to create a curved surface you must instead take your existing code and have it create a succession of tiny cylinders each with a tiny height then stack them up to consume the original height.
One approach would be to introduce a new function which becomes the parent of your
void draw_cylinder(GLfloat radius, GLfloat height, GLubyte R, GLubyte G, GLubyte B)
perhaps call it
draw_curved_cylinder
inside this new function you have a loop where you make calls to draw_cylinder giving it the parameters of each of these tiny cylinders ... currently your draw function blindly stretches the height from 0 to your given height ... replace that with settings for the given tiny cylinder ... also to make the final cylinder curved each tiny cylinder must have its X and Y coordinates follow the curved trajectory so in that new function draw_curved_cylinder increment those so they vary as your synthesize each new tiny cylinder
PS - be aware that you are not using modern OpenGL - glBegin is obsolete and should be avoided
I am trying to draw some shapes in the openGL window. I draw these shapes based on the values in a particular matrix. I am using glut which has a function glutDisplayFunc that takes 1 parameter, a function callback taking no arguments and returns void. But I need to draw an image on the window based on a matrix which I cannot pass to the function callback.
This is an example code
#include<stdio.h>
#include<GL/glut.h>
#include<math.h>
#define pi 3.142857
void mat()
{
int a[2][2];
//
for(int i=0;i<2;i++)
for (int j = 0; j < 2; ++j)
{
scanf("%d",&a[i][j]);
}
}
// function to initialize
void myInit (void)
{
glClearColor(0.0, 0.0, 0.0, 1.0);
glColor3f(0.0, 1.0, 0.0);
glPointSize(1.0);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluOrtho2D(-780, 780, -420, 420);
}
void display (void)
{
glClear(GL_COLOR_BUFFER_BIT);
glBegin(GL_POINTS);
float x, y, i;
for ( i = 0; i < (2 * pi); i += 0.001)
{
x = 200 * cos(i);
y = 200 * sin(i);
glVertex2i(x, y);
}
glEnd();
glFlush();
}
int main (int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
// giving window size in X- and Y- direction
glutInitWindowSize(1366, 768);
glutInitWindowPosition(0, 0);
glutCreateWindow("Circle Drawing");
myInit();
glutDisplayFunc(display);
glutMainLoop();
}
I need to be able to use the matrix a in function mat to define the center of 2 circles. How do I draw the window from within the mat function?
Edit:included code and fixed some typos
void display(void)
{
glClear(GL_COLOR_BUFFER_BIT);
//-----------
float a[4][4] = {
1,0,0,0,
0,1,0,0,
0,0,1,0,
0,0,0,1 };
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glLoadMatrixf((float*)a);
//----------
glBegin(GL_POINTS);
float x, y, i;
for (i = 0; i < (2 * pi); i += 0.001)
{
x = 200 * cos(i);
y = 200 * sin(i);
glVertex2i(x, y);
}
glEnd();
glFlush();
}
In general you can load the current model view matrix, by setting the GL_MODELVIEW matrix mode (glMatrixMode), and loading the matrix by glLoadMatrixf.
Optionally the matrix can be multiplied to the current matrix by glMultMatrix.
But in both cases, the matrix has to be 4x4 Transformation matrix. The parameter to both functions is a pointer to an array of 16 floats respectively an 2 dimensional 4x4 float-array.
Init a 4x4 Identity matrix and read the upper left 2x2, to set up a rotation matrix around the z-axis:
Further, I recommend to read an rotation angle in degree and to calculate the rotation axis by the trigonometric functions sin respectively cos.
Finally read the xy translation components:
#define _USE_MATH_DEFINES
#include <math.h>
float a[4][4];
void mat()
{
// init identity matrix
for(int i = 0; i < 4; i++)
for (int j = 0; j < 4; ++j)
a[i][j] = (i==j) ? 1.0f : 0.0f;
// read the angle in degrees
float angle_degree;
scanf("%f", &angle_degree);
// convert the angle to radian
float angle_radiant = angle_degree * (float)M_PI / 180.0f;
// set rotation around z-axis
float cos_ang = cos(angle_radiant);
float sin_ang = sin(angle_radiant);
a[0][0] = cos_ang;
a[0][1] = -sin_ang;
a[1][0] = sin_ang;
a[1][1] = cos_ang;
// read translation
scanf("%f", &a[3][0]);
scanf("%f", &a[3][1]);
}
void display (void)
{
glMatrixMode(GL_MODELVIEW);
glLoadMatrixf(&a[0][0]);
// [...]
}
The following code shows a straight cylinder/pipe in OpenGL C language.
#include <stdio.h>
#include <stdlib.h>
#include <GL/glut.h>
#include <math.h>
#define PI 3.1415927
void draw_cylinder(GLfloat radius, GLfloat height, GLubyte R, GLubyte G, GLubyte B)
{
GLfloat x = 0.0;
GLfloat y = 0.0;
GLfloat angle = 0.0;
GLfloat angle_stepsize = 0.1;
// Draw the tube
glColor3ub(R-40,G-40,B-40);
glBegin(GL_QUAD_STRIP);
angle = 0.0;
while( angle < 2*PI ) {
x = radius * cos(angle);
y = radius * sin(angle);
glVertex3f(x, y , height);
glVertex3f(x, y , 0.0);
angle = angle + angle_stepsize;
}
glVertex3f(radius, 0.0, height);
glVertex3f(radius, 0.0, 0.0);
glEnd();
// Draw the circle on top of cylinder
glColor3ub(R,G,B);
glBegin(GL_POLYGON);
angle = 0.0;
while( angle < 2*PI ) {
x = radius * cos(angle);
y = radius * sin(angle);
glVertex3f(x, y , height);
angle = angle + angle_stepsize;
}
glVertex3f(radius, 0.0, height);
glEnd();
}
void display(void)
{
glClear(GL_COLOR_BUFFER_BIT);
glLoadIdentity();
glTranslatef(-0.5,0.0,-2.5);
glRotatef(100.0, 0.725, 1.0, 1.0);
draw_cylinder(0.15, 1.0, 255, 160, 100);
glFlush();
}
void reshape(int width, int height)
{
if (width == 0 || height == 0) return;
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(35.0, (GLdouble)width/(GLdouble)height,0.5, 20.0);
glMatrixMode(GL_MODELVIEW);
glViewport(0, 0, width, height);
}
int main(int argc, char **argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(640,580);
glutCreateWindow("Create Cylinder");
glClearColor(0.0,0.0,0.0,0.0);
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutMainLoop();
return 0;
}
At the moment it draws a straight cylinder/pipe. And I wanted to curve it to look like this.
First I recommend to split the cylinder into slices. The following cone will draw exactly the same cylinder, but it splits the cylinder int slices. The slices have different colors to visualize the effect.
GLfloat h0, h1, angle, x, y;
int i, j;
int slices = 8;
for ( i = 0; i < slices; i++ )
{
h0 = (float)i / (float)slices;
h1 = (float)(i+1) / (float)slices;
glColor3f( 1.0f-h0, 0.0, h1 );
glBegin(GL_QUAD_STRIP);
for ( j = 0; j <= 360; ++ j )
{
angle = PI * (float)j * PI / 180.0f;
x = radius * cos(angle);
y = radius * sin(angle);
glVertex3f( x, y, h0 );
glVertex3f( x, y, h1 );
}
glEnd();
}
Then you have to define a bend radius and a bend start and end angle. The following code draw a bended pipe form bend_ang0 to bend_ang1, with a radius bend_radius. The bend angles can be calculated in relation to the bend radius and the length of the pipe:
GLfloat w0, w1, ang0, ang1, angle, x, y, xb, yb, zb;
int i, j;
int slices = 8;
GLfloat bend_radius = 1.0f;
GLfloat bend_angle, bend_ang0, bend_ang1;
bend_angle = bend_radius * height;
bend_ang0 = -bend_angle/2.0f;
bend_ang1 = bend_angle/2.0f;
for ( i = 0; i < slices; i++ )
{
w0 = (float)i / (float)slices;
w1 = (float)(i+1) / (float)slices;
ang0 = bend_ang0 + (bend_ang1-bend_ang0) * w0;
ang1 = bend_ang0 + (bend_ang1-bend_ang0) * w1;
glColor3f( 1.0f-w0, 0.0, w1 );
glBegin(GL_QUAD_STRIP);
for ( j = 0; j <= 360; ++ j )
{
angle = PI * (float)j * PI / 180.0f;
x = radius * cos(angle) + bend_radius;
y = radius * sin(angle);
xb = sin( ang0 ) * x;
yb = y;
zb = cos( ang0 ) * x;
glVertex3f( xb, yb, zb );
xb = sin( ang1 ) * x;
yb = y;
zb = cos( ang1 ) * x;
glVertex3f( xb, yb, zb );
}
glEnd();
}
For the following image I activated the depth test and changed the model view matrix:
void display(void)
{
glEnable( GL_DEPTH_TEST );
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
glTranslatef(0.0f, -0.5f, -4.0f);
glRotatef(-90.0f, 1.0f, 0.0, 0.0f);
draw_cylinder(0.15, 2.0, 255, 160, 100);
glFlush();
}
Currently you are drawing the entire height of the cylinder in one go ... to create a curved surface you must instead take your existing code and have it create a succession of tiny cylinders each with a tiny height then stack them up to consume the original height.
One approach would be to introduce a new function which becomes the parent of your
void draw_cylinder(GLfloat radius, GLfloat height, GLubyte R, GLubyte G, GLubyte B)
perhaps call it
draw_curved_cylinder
inside this new function you have a loop where you make calls to draw_cylinder giving it the parameters of each of these tiny cylinders ... currently your draw function blindly stretches the height from 0 to your given height ... replace that with settings for the given tiny cylinder ... also to make the final cylinder curved each tiny cylinder must have its X and Y coordinates follow the curved trajectory so in that new function draw_curved_cylinder increment those so they vary as your synthesize each new tiny cylinder
PS - be aware that you are not using modern OpenGL - glBegin is obsolete and should be avoided
I am writing code to draw the figure
but my code gives
as you can see the middle circle is missing.
My code:
#include <stdio.h>
#include <stdlib.h>
#include <GL/glut.h>
#include <math.h>
float width, height, r = 0.3, change = 0;
void draw(float tx, float ty)
{
glBegin(GL_LINE_LOOP);
for(int i = 1; i <= 1200; i++)
{
float x1, y1, theta;
theta = (2 * 3.14159 * i) / 1200;
x1 = r * cosf(theta) * height / width;
y1 = r * sinf(theta);
glVertex3f(x1 , y1 ,0);
}
glEnd();
glTranslatef(tx, ty, 0);
}
void display()
{
float p[6][2];
int j = 0;
if (change == 0)
change = 1;
else if (change == 1)
change = 0;
width = glutGet(GLUT_WINDOW_WIDTH);
height = glutGet(GLUT_WINDOW_HEIGHT) ;
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glColor3f(1.0f, 0.0f, 0.0f);
glMatrixMode(GL_MODELVIEW);
glBegin(GL_LINE_LOOP);
for(int i = 1; i <= 1200; i++)
{
float theta, x1, y1;
theta = (2 * 3.14159 * i) / 1200;
x1 = r * cosf(theta) * height / width;
y1 = r * sinf(theta);
glVertex3f(x1, y1, 0);
if (i == 100 | i == 300 | i == 500 | i == 700 | i == 900 | i == 1100)
{
if(change == 0){
p[j][0] = x1;
p[j][1] = y1;
j++;
}
}
}
glEnd();
for(int i=0;i<6 && change == 0;i++){
draw(p[i][0],p[i][1]);
}
glutSwapBuffers();
}
void main(int argc,char *argv[])
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
glutInitWindowSize(700,500);
glutCreateWindow("circles");
glutDisplayFunc(display);
glutMainLoop();
}
Issue is when i translate first circle in draw function the center circle drawn is also translated to that point which is merged with other circle.My doubt is how to translate only one circle not the center one i tried translating by using push and pop matrix but it doesn't work.
Thank you.
glTranslatef() changes the current matrix by appending a translation. So your translations will just accumulate. And since you do not have a transform between the first two circles, they will appear at the same positions. Your program basically does the following:
Draw Circle
draw()
Draw Circle
Move up, right (p[0])
draw()
Draw Circle
Move up (p[1])
draw()
Draw Circle
Move up left (p[2])
...
If you want absolute positioning, you have to reset the transform in between. This can either be done with glLoadIdentity() or with the matrix stack. And be sure to draw after setting the transform.
I guess you know, but in any case a little reminder: The entire matrix stack functionality is deprecated in modern OpenGL and you will need to manage the matrices yourself. I assume, when you do this, everything gets a bit clearer. So I'm not sure if there is a good reason to try to understand the interface of the matrix stack functionalities.
If you want to place each circle at a specific location, you can do something like the following:
void drawCircle()
{
glBegin(GL_LINE_LOOP);
for(int i = 1; i <= 1200; i++)
{
float x1, y1, theta;
theta = (2 * 3.14159 * i) / 1200;
x1 = r * cosf(theta) * height / width;
y1 = r * sinf(theta);
glVertex3f(x1 , y1 ,0);
}
glEnd();
}
void display()
{
// ...
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glColor3f(1.0f, 0.0f, 0.0f);
glMatrixMode(GL_MODELVIEW);
drawCircle();
for(int i = 0; i < 6; ++i)
{
float angle = M_PI / 3 * i;
float tx = r * sin(angle);
float ty = r * cos(angle);
glPushMatrix(); //save the current matrix
glTranslatef(tx, ty, 0); //move to the desired location
drawCircle();
glPopMatrix(); //restore the old matrix
}
glutSwapBuffers();
}
I'm trying to do Koch snowflake for a computer graphics course. Searching on the web i've found that a sequence named Thue-morse can approximate the Koch snowflake by using a turtle drawing method.
Here is the code i have so far:
#include <GLUT/glut.h>
#include <math.h>
#include <string.h>
//screen size
#define WIDTH 1024
#define HEIGHT 800
float x, y,mUx,mUy;
//init the turtle environment
void turtleInit(){
x = WIDTH/2; // this is the starting point for the x
y = HEIGHT/2; // this is the starting point for the y
mUx = 1;
mUy = 0;
}
//move the turtle ds units
void turtleMove(float ds){
x += mUx * ds;
y += mUy * ds;
}
//turn left by "ang" radians if positive and right if negative.
void turtleTurn(float ang){
float ux = mUx;
float uy = mUy;
mUx = ux * cos(ang) - uy * sin(ang);
mUy = uy * cos(ang) + ux * sin(ang);
}
//thue morse sequence used to approximate the Koch snowflake
char thue_memoization[10000000];
int thueMorseRecurrenceRelation(int i){
if( thue_memoization[i] != -1 )
return thue_memoization[i];
if ( i % 2 != 0 )
return thue_memoization[i] = 1 - thueMorseRecurrenceRelation(i / 2);
else
return thue_memoization[i] = thueMorseRecurrenceRelation(i / 2);
}
void display( void ){
glClearColor(0, 0, 0, 0);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(-WIDTH, WIDTH, -HEIGHT, HEIGHT, -50, 50);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glBegin(GL_POINTS);
glColor3f(0, 0, 1);
turtleInit();
for (int i = 0; i < 1000000; ++i) {
const static float p = 1;//turtle's step
if ( thueMorseRecurrenceRelation(i) )
turtleTurn(M_PI/3.0);
turtleMove(p);
glVertex2f(x, y);
}
glEnd();
glFlush();
}
int main(int argc,char **argv){
memset(thue_memoization,-1,sizeof(thue_memoization));
thue_memoization[0] = 0; //stop condition for the recurrence relation
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
glutInitWindowPosition(0,0);
glutInitWindowSize(WIDTH, HEIGHT);
glutCreateWindow("Koch snowflake. The winter is comming ...");
glutDisplayFunc(display);
glutMainLoop();
return 0;
}
It worked quite well here.
But i don't understand how the turtleTurn function works. Someone can help me ?
This is the formula for a 2d rotation:
(mUx, mUy) contains the coordinates of the "heading vector" of the turtle, then what turtleTurn(float ang) does is turning this vector by an angle (ang).
If you want a nice explanation of this formula, in particular where the sine and cosine come from, you can take a look at the following page, that
has some drawings that will make it clearer:
https://www.siggraph.org/education/materials/HyperGraph/modeling/mod_tran/2drota.htm