circleMidpoint(scrPt c, GLint r) 未定义的标识符,openGL第四章例子 ，画饼状图。

 以下是完整的例子。在第四版 《计算机图形学 with openGL》第四章的例子中，竟然只调用了circleMidpoint(scrPt  &c, GLint r) ，没有实现，我认为是系统方法，怎么找都找不到。openGL 官方文档也没找到，这不会是自定义的吧。我在同类文章中发现 有人写了  circleMidpoint(scrPt  &c, GLint r)   和里面嵌套的void putpixel(GLint x0, GLint y0, GLint x, GLint y)，竟然跑起来了。

为啥没有人提到这个事情，是本道长太菜了？还是这事太简单了，不值一提？

#include "stdafx.h"
#include <GL/glut.h>
#include <stdlib.h>
#include <math.h> using namespace std;const GLdouble twoPi = 6.283185;class scrPt {
public:GLint x, y;
};GLsizei winWidth = 400, winHeight = 300; // Initial display window size.void init(void)
{glClearColor(1.0, 1.0, 1.0, 1.0);glMatrixMode(GL_PROJECTION);gluOrtho2D(0.0, 200.0, 0.0, 150.0);
}
//书上的代码里没有，自己后补的。2-1 
void putpixel(GLint x0, GLint y0, GLint x, GLint y)
{glBegin(GL_POINTS);glVertex2f(x0 + x, y0 + y);glVertex2f(x0 + x, y0 - y);glVertex2f(x0 - x, y0 + y);glVertex2f(x0 - x, y0 - y);glVertex2f(x0 + y, y0 + x);glVertex2f(x0 + y, y0 - x);glVertex2f(x0 - y, y0 + x);glVertex2f(x0 - y, y0 - x);glEnd();}// Midpoint routines for displaying a circle.//书上的代码里没有，自己后补的。2-2
void circleMidpoint(scrPt  &c, GLint r) //中点画圆函数
{int x, y, p;x = 0; y = r; p = 1 - r;while (x <= y) {putpixel(c.x, c.y, x, y);if (p < 0) {p += 2 * x + 1;}else {p += 2 * (x - y) + 1;y--;}x++;}
}
void pieChart(void)
{scrPt circCtr, piePt;GLint radius = winWidth / 4;         // Circle radius.GLdouble sliceAngle, previousSliceAngle = 0.0;GLint k, nSlices = 12;               // Number of slices.GLfloat dataValues[12] = { 10.0, 7.0, 13.0, 5.0, 13.0, 14.0, 3.0, 16.0, 5.0, 3.0, 17.0, 8.0 };GLfloat dataSum = 0.0;circCtr.x = winWidth / 2;            // Circle center position.circCtr.y = winHeight / 2;circleMidpoint(circCtr, radius);    // Call a midpoint circle-plot routine.for (k = 0; k < nSlices; k++)dataSum += dataValues[k];for (k = 0; k < nSlices; k++) {sliceAngle = twoPi * dataValues[k] / dataSum + previousSliceAngle;piePt.x = circCtr.x + radius * cos(sliceAngle);piePt.y = circCtr.y + radius * sin(sliceAngle);glBegin(GL_LINES);glVertex2i(circCtr.x, circCtr.y);glVertex2i(piePt.x, piePt.y);glEnd();previousSliceAngle = sliceAngle;}
}void displayFcn(void)
{glClear(GL_COLOR_BUFFER_BIT);         // Clear display window.glColor3f(0.0, 0.0, 1.0);             // Set circle color to blue.pieChart();glFlush();
}void winReshpeFcn(GLint newWidth, GLint newHeight)
{glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D(0.0, GLdouble(newWidth), 0.0, GLdouble(newHeight));glClear(GL_COLOR_BUFFER_BIT);/* Reset display-window size parameters. */winWidth = newWidth;winHeight = newHeight;
}void main(int argc, char** argv)
{glutInit(&argc, argv);glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);glutInitWindowPosition(100, 100);glutInitWindowSize(winWidth,winHeight);glutCreateWindow("Pie Chart");init();glutDisplayFunc(displayFcn);glutReshapeFunc(winReshpeFcn);glutMainLoop();
}