在OpenGL中绘制N-Pointed Star - C ++

Question

我编写了一个输入n并绘制N-point星的代码，

就像这个：

当n = 5并提交

n = 7或8或16或25时的问题......

我在星图中遇到问题它变成这样：

当n = 7并填充时

这是我的代码：

#include <iostream>
#include <ctime>
#include <vector>
#include <glut.h>

using namespace std;

float starCenterX, starCenterY, starRadius;
int numPoints;
bool bDrawFill = false;

void DrawStar (float cx, float cy, float radius, int numPoints);
void DrawStarFilled (float cx, float cy, float radius, int numPoints);


float width, height;    // global variables to store window width and height

// render text
void renderBitmapString (float x, float y, float z, void* font, const char* string) 
{
    const char *c;
    glRasterPos3f (x, y,z);
    for (c = string; *c != '\0'; c++)
        glutBitmapCharacter (font, *c);
}

void init ()
{
    glClearColor (1.0, 1.0, 1.0, 0.0);  // set display-window color to white
}

void reshape (int width, int height)
{
    ::width = width;
    ::height = height;

    glViewport (0, 0, width, height);

    glMatrixMode (GL_PROJECTION);       // set projection parameters
    glLoadIdentity ();
    gluOrtho2D (0.0, width, 0.0, height);

    glMatrixMode (GL_MODELVIEW);        // set projection parameters
    glLoadIdentity ();
}

void display ()
{
    glClear (GL_COLOR_BUFFER_BIT);      // clear display window

    glColor3f (0, 0, 1);
    renderBitmapString (10, height - 20, 0, GLUT_BITMAP_TIMES_ROMAN_24, "Name   : Saif Badran");
    renderBitmapString (10, height - 50, 0, GLUT_BITMAP_TIMES_ROMAN_24, "ID         : 0142852");
    renderBitmapString (10, height - 80, 0, GLUT_BITMAP_TIMES_ROMAN_24, "Section : 2");

    DrawStar(starCenterX,starCenterY,starRadius,numPoints);

    if(bDrawFill)
        DrawStarFilled(starCenterX,starCenterY,starRadius,numPoints);

    glFlush ();         // process all openGl routines as quickly as possible
}

void processNormalKeys (unsigned char key, int x, int y) 
{
    if(key=='w' || key=='W')
        starCenterY+=4;
    else if(key=='z' || key=='Z')
        starCenterY-=4;
    else if(key=='a' || key=='A')
        starCenterX-=4;
    else if(key=='d' || key=='D')
        starCenterX+=4;
    else if(key=='f' || key=='F')
        bDrawFill = (bDrawFill==1?0:1);
}

void mouseClick (int button, int state, int x, int y)
{
    if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN)
    {
        starCenterX = x;
        starCenterY = height - y;
    }
}

void activeMouseMotion (int x, int y)
{
    starRadius = abs(starCenterX-x);
}


void main (int argc, char** argv)
{
    cout<<"Enter number of points : ";
    cin>>numPoints;
    numPoints = (numPoints < 2) ? 2 : numPoints;

    glutInit (&argc, argv);                         // initialize GLUT
    glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB);   // set display mode
    glutInitWindowPosition (20, 20);        // set top left display window position
    glutInitWindowSize (600, 600);          // set display window width and height
    glutCreateWindow ("Homework#2 : Star Drawing"); // create display window

    init ();                                // execute initialization function

    glutKeyboardFunc (processNormalKeys);
    glutMouseFunc (mouseClick);
    glutMotionFunc (activeMouseMotion);
    glutReshapeFunc (reshape);
    glutDisplayFunc (display);              // send graphics to display window
    glutIdleFunc (display);
    glutMainLoop ();                        // dispaly everthing and wait
}

void DrawStar (float cx, float cy, float radius, int numPoints)
{

    const float DegToRad = 3.14159 / 180;
    glColor3f(1.0,0.0,0.0);
    glBegin (GL_POINTS);
    int count = 1;
        for (int i = 0; i <= 360; i+=360/(numPoints*2)) {
            float DegInRad = i * DegToRad;
            if(count%2!=0)
                glVertex2d (cx + cos (DegInRad) * radius, cy + sin (DegInRad) * radius);
            else
                glVertex2d ((cx + cos (DegInRad) * radius/2), (cy + sin (DegInRad) * radius/2));
        count++;
        }
    glEnd();

    glBegin (GL_LINE_LOOP);
    count = 1;
        for (int i = 0; i <= 360; i+=360/(numPoints*2)) {
            float DegInRad = i * DegToRad;
            if(count%2!=0)
                glVertex2d (cx + cos (DegInRad) * radius, cy + sin (DegInRad) * radius);
            else
                glVertex2d ((cx + cos (DegInRad) * radius/2), (cy + sin (DegInRad) * radius/2));
        count++;
        }
    glEnd();
}

void DrawStarFilled (float cx, float cy, float radius, int numPoints)
{
    const float DegToRad = 3.14159 / 180;

    glBegin (GL_TRIANGLE_FAN);
    int count = 1;
                glVertex2f(starCenterX, starCenterY);
        for (int i = 0; i <= 360; i+=360/(numPoints*2)) {
            float DegInRad = i * DegToRad;
            if(count%2!=0)
                glVertex2d (cx + cos (DegInRad) * radius, cy + sin (DegInRad) * radius);
            else
                glVertex2d ((cx + cos (DegInRad) * radius/2), (cy + sin (DegInRad) * radius/2));
        count++;
        }

    glEnd();
}

Answer 1

问题出在这一行：

for (int i = 0; i <= 360; i+=360/(numPoints*2)) {

对于numPoints = 5 ，对于每个步骤， i将以360/(2*5) = 36递增。

对于numPoints = 7 ，对于每个步骤， i将以360/(2*7) = 25 （整数除法，截断25.714...至25 ） 25.714... 。 因此，每一步都有0.714..度的损失。 Cummulated，这是： 360 - 14 * 25 = 10度。 这可以在输出图片上看到。

为了解决这个问题，我们可以使用浮点变量作为步进计数器，并使用从浮点除法获得的浮点值来递增它，例如使用360.0作为分子。 （实际上360.0存储为double ，将其存储为单个精度float ，应该是360.0f ）。

for (float i = 0; i <= 360; i+=360.0/(numPoints*2)) {

但是这样做，我们可能在i <= 360比较时遇到麻烦，浮点运算导致量化误差（ i可能比“数学”值略小或大）。 因此，最好保留循环的整数计数器，然后执行浮点运算。 这段代码部分：

    for (int i = 0; i <= 360; i+=360/(numPoints*2)) {
        float DegInRad = i * DegToRad;

然后会改为：

    for (int i = 0; i <= numPoints*2; i++) {
        float DegInRad = i * 360.0/(numPoints*2) * DegToRad;