main.cpp

B-spline曲線是包含Bezier曲線的通用數學表示法。

//------------------------------------------------------------
/// \file	Main.cpp
/// \author	Rob Bateman
/// \date	9-feb-2005
/// \brief	This is a very simple example of a bezier curve
//------------------------------------------------------------

#include <stdlib.h>
#include <GL/glut.h>

// 4 control points for our cubic bezier curve
float Points[4][3] = {
	{ 10,10,0 },
	{  5,10,2 },
	{ -5,0,0 },
	{-10,5,-2}
};

// the level of detail of the curve
unsigned int LOD=20;

//------------------------------------------------------------	OnKeyPress()
//
void OnKeyPress(unsigned char key,int,int) {
	switch(key) {

	// increase the LOD
	case '+':
		++LOD;
		break;

	// decrease the LOD
	case '-':
		--LOD;

		// have a minimum LOD value
		if (LOD<3)
			LOD=3;
		break;
	default:
		break;
	}

	// ask glut to redraw the screen for us...
	glutPostRedisplay();
}

//------------------------------------------------------------	OnDraw()
//
void OnDraw() {

	// clear the screen & depth buffer
	glClear(GL_DEPTH_BUFFER_BIT|GL_COLOR_BUFFER_BIT);

	// clear the previous transform
	glLoadIdentity();

	// set the camera position
	gluLookAt(	1,10,30,	//	eye pos
				0,0,0,	//	aim point
				0,1,0);	//	up direction

	glColor3f(1,0,1);

	// we will draw lots of little lines to make our curve
	glBegin(GL_LINE_STRIP);

	for(int i=0;i!=LOD;++i) {

		// use the parametric time value 0 to 1
		float t = (float)i/(LOD-1);

		// nice to pre-calculate 1.0f-t because we will need it frequently
		float it = 1.0f-t;

		// calculate blending functions
		float b0 = t*t*t;
		float b1 = 3*t*t*it;
		float b2 = 3*t*it*it;
		float b3 =  it*it*it;

		// calculate the x,y and z of the curve point by summing
		// the Control vertices weighted by their respective blending
		// functions
		//
		float x = b0*Points[0][0] +
				  b1*Points[1][0] +
				  b2*Points[2][0] +
				  b3*Points[3][0] ;

		float y = b0*Points[0][1] +
				  b1*Points[1][1] +
				  b2*Points[2][1] +
				  b3*Points[3][1] ;

		float z = b0*Points[0][2] +
				  b1*Points[1][2] +
				  b2*Points[2][2] +
				  b3*Points[3][2] ;

		// specify the point
		glVertex3f( x,y,z );
	}
	glEnd();

	// draw the Control Vertices
	glColor3f(0,1,0);
	glPointSize(3);
	glBegin(GL_POINTS);
		for(int i=0;i!=4;++i) {
			glVertex3fv( Points[i] );
		}
	glEnd();

	// draw the hull of the curve
	glColor3f(0,1,1);
	glBegin(GL_LINE_STRIP);
		for(int i=0;i!=4;++i) {
			glVertex3fv( Points[i] );
		}
	glEnd();

	// currently we've been drawing to the back buffer, we need
	// to swap the back buffer with the front one to make the image visible
	glutSwapBuffers();
}


//------------------------------------------------------------	OnInit()
//
void OnInit() {
	// enable depth testing
	glEnable(GL_DEPTH_TEST);
}

//------------------------------------------------------------	OnExit()
//
void OnExit() {
}

//------------------------------------------------------------	OnReshape()
//
void OnReshape(int w, int h)
{
	if (h==0)
		h=1;

	// set the drawable region of the window
	glViewport(0,0,w,h);

	// set up the projection matrix
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();

	// just use a perspective projection
	gluPerspective(45,(float)w/h,0.1,100);

	// go back to modelview matrix so we can move the objects about
	glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();
}


//------------------------------------------------------------	main()
//
int main(int argc,char** argv) {

	// initialise glut
	glutInit(&argc,argv);

	// request a depth buffer, RGBA display mode, and we want double buffering
	glutInitDisplayMode(GLUT_DEPTH|GLUT_RGBA|GLUT_DOUBLE);

	// set the initial window size
	glutInitWindowSize(640,480);

	// create the window
	glutCreateWindow("Bezier Curve: +/- to Change Level of Detail");

	// set the function to use to draw our scene
	glutDisplayFunc(OnDraw);

	// set the function to handle changes in screen size
	glutReshapeFunc(OnReshape);

	// set the function for the key presses
	glutKeyboardFunc(OnKeyPress);
	
	// run our custom initialisation
	OnInit();

	// set the function to be called when we exit
	atexit(OnExit);

	// this function runs a while loop to keep the program running.
	glutMainLoop();
	return 0;
}