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empyrean123
10-24-2011, 08:39 PM
I am trying to find the way to generate bezier curve using de casteljau algorithm for one of my assignment here. I am able to generate bezier curve using normal method but unable to start on generating using the above algorithm. It will be of great help if someone can suggest me to right direction or share any piece of code you have. I am not just asking as is. I worked a lot on it and wrote the following code myself to generate the curve.
I found a web applet which does exactly i needed. ( Demo for De Castaljeau Algorithm (http://www2.mat.dtu.dk/people/J.Gravesen/cagd/decast.html)). suggest me how to achieve that


#include <iostream>
using std::cerr;
using std::endl;
#include <stdlib.h>
//using std::exit;
#include <GL/glut.h> // GLUT stuff, includes OpenGL headers as well
#include <windows.h>
#include <math.h>
#include <gl/Gl.h>
#include <gl/Glu.h>


int SCREEN_HEIGHT = 480;
// Keep track of times clicked, on 3 clicks draw.
int NUMPOINTS = 0;

// Point class to keep it a little cleaner.
class Point {
public:
float x, y, z;
void setxy(float x2, float y2) { x = x2; y = y2; }
const Point & operator=(const Point &amp;rPoint) {
x = rPoint.x;
y = rPoint.y;
z = rPoint.z;

return *this;
}

};

Point abc[4];

void myInit() {
glClearColor(0.0,0.0,0.0,0.0);
glColor3f(1.0,0.0,0.0);
glPointSize(4.0);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluOrtho2D(0.0,640.0,0.0,480.0);

}

void drawDot(int x, int y) {
glBegin(GL_POINTS);
glVertex2i(x,y);
glEnd();
glFlush();
}

void drawLine(Point p1, Point p2) {
glBegin(GL_LINES);
glVertex3f(p1.x, p1.y, p1.z);
glVertex3f(p2.x, p2.y, p2.z);

glEnd();
glFlush();
}

// Calculate the next bezier point.
Point drawBezier(Point A, Point B, Point C, Point D, double t) {
Point P;




P.x = pow((1 - t), 3) * A.x + 3 * t * pow((1 -t), 2) * B.x + 3 * (1-t) * pow(t, 2)* C.x + pow (t, 3)* D.x;
P.y = pow((1 - t), 3) * A.y + 3 * t * pow((1 -t), 2) * B.y + 3 * (1-t) * pow(t, 2)* C.y + pow (t, 3)* D.y;
P.z = pow((1 - t), 3) * A.z + 3 * t * pow((1 -t), 2) * B.z + 3 * (1-t) * pow(t, 2)* C.z + pow (t, 3)* D.z;

return P;
}

void myMouse(int button, int state, int x, int y) {
// If left button was clicked
if(button == GLUT_LEFT_BUTTON &amp;&amp; state == GLUT_DOWN) {
// Store where the user clicked, note Y is backwards.
abc[NUMPOINTS].setxy((float)x,(float)(SCREEN_HEIGHT - y));
NUMPOINTS++;

// Draw the red dot.
drawDot(x, SCREEN_HEIGHT - y);

// If 3 points are drawn do the curve.
if(NUMPOINTS == 4) {
glColor3f(1.0,1.0,1.0);
// Draw two legs of the triangle
drawLine(abc[0], abc[1]);
drawLine(abc[1], abc[2]);
drawLine(abc[2], abc[3]);
//drawLine(abc[3], abc[4]);
Point POld = abc[0];
/* Draw each segment of the curve. Make t increment in
smaller amounts for a more detailed curve. */
for(double t = 0.0;t <= 1.0; t += 0.1) {
Point P = drawBezier(abc[0], abc[1], abc[2], abc[3], t);
drawLine(POld, P);
POld = P;
}
glColor3f(1.0,0.0,0.0);
NUMPOINTS = 0;
}
}
}

void myDisplay() {
glClear(GL_COLOR_BUFFER_BIT);
glFlush();
}

int main(int argc, char *argv[]) {
glutInit(&amp;argc, argv);
glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
glutInitWindowSize(640,480);
glutInitWindowPosition(100,150);
glutCreateWindow("Bezier Curve");

glutMouseFunc(myMouse);
glutDisplayFunc(myDisplay);

myInit();
glutMainLoop();

return 0;
}

mobeen
10-24-2011, 10:24 PM
DeCasteljau algorithm is a simple recursive application of linear interpolation on hte given control points. Check this: http://www.cubic.org/docs/bezier.htm

aqnuep
10-25-2011, 02:20 AM
Again, some homework, huh? :)