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();
}