Bézier Spline Curves

思路：

每次套公式得到x,y,的值并且逐步改变点的坐标

// ====== Computer Graphics Experiment #7 ======// |              Bezier curve                 |// =============================================//// Requirement:// (1) Implement algorithm to draw Bezier curve.// (2)Implement interactive method to specify //     Bezier curve control points by mouse clicking.// (3) Implement display callback function#include <windows.h>#include <GL/glut.h>#include <math.h>#include <stdio.h>// 2D point classclass CPoint2D{public:float x, y;};int n_cp; // Number of control pointsint ic_cp; // Control point counterint i_cp; // Index of control point being movedCPoint2D *control_points; // Coordinates of control points// Program window sizeint pw_width, pw_height;int running_state;// 0 --- Setting up control points.// 1 --- Normal state. // 2 --- Moving control point.void plotPoint(CPoint2D bezCurvePt){glPointSize(1.0f);glBegin(GL_POINTS);glVertex2f(bezCurvePt.x, bezCurvePt.y);glEnd();}void binomialCoeffs(GLint n, GLint *C){GLint k, j;for (k = 0; k <= n; k++){C[k] = 1;for (j = n; j >= k + 1; j--)C[k] *= j;for (j = n - k; j >= 2; j--)C[k] /= j;}}void computeBezPt(GLfloat u, CPoint2D *bezPt, GLint nCtrlPts, CPoint2D *ctrlPts, GLint *C){GLint k, n = nCtrlPts-1;GLfloat bezBlendFcn;bezPt->x = bezPt->y  = 0;for (k = 0; k < nCtrlPts; k++){bezBlendFcn = C[k] * pow(u, k)*pow(1 - u, n - k);bezPt->x += ctrlPts[k].x*bezBlendFcn;bezPt->y += ctrlPts[k].y*bezBlendFcn;}}// Draw Bezier curvevoid Draw_Bezier(CPoint2D *ctrlPts, int nCtrlPts, int nBezCurvePts)// nctrl  --- Number of control points// cp --- Array of control points// m  --- Number of subdivision{// Write your code here CPoint2D bezCurvePt;GLfloat u;GLint *C, k;C = new GLint[nCtrlPts];binomialCoeffs(nCtrlPts - 1, C);for (k = 0; k <= nBezCurvePts; k++){u = GLfloat(k) / GLfloat(nBezCurvePts);computeBezPt(u, &bezCurvePt, nCtrlPts,ctrlPts,C);plotPoint(bezCurvePt);}delete[]C;}// Display callback functionvoid display(void){glClear (GL_COLOR_BUFFER_BIT);// Draw control points// Write your code here glColor4ub(255, 0, 0,255);glPointSize(10.0f);glBegin(GL_POINTS);printf("\n%d %f %f \n", ic_cp,control_points[ic_cp-1].x, control_points[ic_cp-1].y);for(int i=0;i<ic_cp;i++)glVertex2f(control_points[i].x,control_points[i].y);glEnd();// Draw control graph// Write your code hereglColor3f(255, 0.0, 0.0);glEnable(GL_LINE_STIPPLE);glLineStipple(2, 0x0f0f);glLineWidth(2);glBegin(GL_LINES);for (int i = 1; i < ic_cp; i++){glVertex2f(control_points[i - 1].x, control_points[i - 1].y);glVertex2f(control_points[i].x, control_points[i].y);}glDisable(GL_LINE_STIPPLE);glEnd();// Draw Bezier curve// Write your code here Draw_Bezier(control_points,ic_cp,1000);glutSwapBuffers();}// Mouse callback functionvoid mouse_func(int button, int state, int x, int y){    float dis; if (button==GLUT_LEFT_BUTTON){if ((state==GLUT_DOWN)&(running_state==0)&(ic_cp<n_cp)){ control_points[ic_cp].x=x;control_points[ic_cp].y=pw_height-y;ic_cp++;if (ic_cp==n_cp)running_state=1;glutPostRedisplay();}else if ((state==GLUT_DOWN)&(running_state==1)){             for (int i=0 ;i<n_cp;i++){dis=(x-control_points[i].x)*(x-control_points[i].x)+(pw_height-y-control_points[i].y)*(pw_height-y-control_points[i].y);if (dis < 0)dis = -dis;if (dis<10){i_cp=i;running_state=2;break;}}}else if ((state==GLUT_DOWN)&(running_state==2)){ control_points[i_cp].x=x;control_points[i_cp].y=pw_height-y;glutPostRedisplay();}else if ((state==GLUT_UP)&(running_state==2)){ running_state=1;}}}// Mouse motion callback functionvoid motion_func(int x, int y){   if (running_state==2){control_points[i_cp].x=x;        control_points[i_cp].y=pw_height-y;        glutPostRedisplay();}}// Initialization functionvoid init(void){glClearColor (0.0, 0.0, 0.0, 0.0);glEnable(GL_LINE_STIPPLE);    }// Reshape callback functionvoid reshape(int w, int h){pw_width=w;pw_height=h;glViewport(0, 0,  w,  h);glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D (0.0, w, 0.0, h);}// Keyboard callback functionvoid keyboard(unsigned char key, int x, int y){switch (key) {case 27:exit(0);}} // Main program entranceint main(int argc, char* argv[]){// Input number of control pointsprintf("Number of control points = ");scanf("%d", &n_cp);if (n_cp<2) return 1;control_points=new CPoint2D[n_cp];running_state=0;ic_cp=0;glutInit(&argc, argv);glutInitDisplayMode (GLUT_RGB | GLUT_DOUBLE);glutInitWindowSize(500, 500);glutCreateWindow("Test Bézier Curve");init();glutReshapeFunc(reshape);glutKeyboardFunc(keyboard);glutMouseFunc(mouse_func);    glutMotionFunc(motion_func);glutDisplayFunc(display);glutMainLoop();delete [] control_points;return 0;}