绘制3D球体在C / C ++ [英] Drawing 3D sphere in C/C++

问题描述

我在寻找一种算法，可以借鉴小分辨率一个很好看的3D球体。我发现布氏圈算法但它的2D绘图。我只需要球的边界（我并不需要它填补）。我也用Google搜索这个问题的解决办法，但我没有发现任何东西。 这文章没有帮助（什么是蛮力算法？ ）。我不能使用任何OpenGL库，我需要香草C / C ++的解决方案。谢谢你在前进。

I am looking for an algorithm which can draw a nice looking 3D sphere on small resolution. I found Bresenham's circle algorithm but it's for 2D drawing. I just need spheres borders (I don't need it filled). I also googled for a solution of the problem but I didn't find anything. This article doesn't help (what is the brute force algorithm?). I can't use any OpenGL libraries, I need vanilla C/C++ solution. Thank you in advance.

推荐答案

如果我得到它的权利要渲染球体表面的所有体素

if I get it right you want to render all surface Voxels of sphere

• 蛮力是O（R ^ 3）


• 如果你只是从投影平面的光线并计算出3个坐标然后你O（R ^ 2）


• 而是要确保没有体素都在思念你必须从所有3架飞机中投影



• 这仍然是O（R ^ 2）

• the brute force is O(R^3)
• if you just project rays from plane and compute the 3-th coordinate then you get O(R^2)
• but to make sure that no Voxels are missing you have to do this projection from all 3 planes

• which is still O(R^2)

它看起来像这样：

• LED立方体16x16x16

现在的算法：

1. 计算可见边框

1. compute visible bounding box

• 无需渲染整个渲染空间


• 只是球...

需要一个平面（XY为例）

take one plane (XY for example)

• 从所有的X射线投，边框内ÿ点


• 仅有2 for循环


• 和计算的Z坐标所在的射线命中


• 通过球体方程（X-X0）^ 2 +（Y-Y0）^ 2 +（Z-Z0）^ 2 = R ^ 2


• 所以 Z = Z0 +/-开方（R ^ 2 - （X-X0）^ 2 - （Y-Y0）^ 2）


• 和渲染两个像素。

做第2步的所有平面（XY，YZ，XZ）

do the step 2 for all planes (xy,yz,xz)

在C ++中的code是这样的：

The code in C++ looks like this:

//---------------------------------------------------------------------------
//--- LED cube class ver: 1.00 ----------------------------------------------
//---------------------------------------------------------------------------
#ifndef _LED_cube_h
#define _LED_cube_h
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
const int _LED_cube_size=16;
//---------------------------------------------------------------------------
class LED_cube
    {
public:
    int n,map[_LED_cube_size][_LED_cube_size][_LED_cube_size];

    LED_cube()              { n=_LED_cube_size; }
    LED_cube(LED_cube& a)   { *this=a; }
    ~LED_cube()             { }
    LED_cube* operator = (const LED_cube *a) { *this=*a; return this; }
    //LED_cube* operator = (const LED_cube &a) { /*...copy...*/ return this; }
    void cls(int col);                                  // clear cube with col 0x00BBGGRR
    void sphere(int x0,int y0,int z0,int r,int col);    // draws sphere surface with col 0x00BBGGRR
    void glDraw();                                      // render cube by OpenGL as 1x1x1 cube at 0,0,0
    };
//---------------------------------------------------------------------------
void LED_cube::cls(int col)
    {
    int x,y,z;
    for (x=0;x<n;x++)
     for (y=0;y<n;y++)
      for (z=0;z<n;z++)
       map[x][y][z]=col;
    }
//---------------------------------------------------------------------------
void LED_cube::sphere(int x0,int y0,int z0,int r,int col)
    {
    int x,y,z,xa,ya,za,xb,yb,zb,xr,yr,zr,xx,yy,zz,rr=r*r;
    // bounding box
    xa=x0-r; if (xa<0) xa=0; xb=x0+r; if (xb>n) xb=n;
    ya=y0-r; if (ya<0) ya=0; yb=y0+r; if (yb>n) yb=n;
    za=z0-r; if (za<0) za=0; zb=z0+r; if (zb>n) zb=n;
    // project xy plane
    for (x=xa,xr=x-x0,xx=xr*xr;x<xb;x++,xr++,xx=xr*xr)
     for (y=ya,yr=y-y0,yy=yr*yr;y<yb;y++,yr++,yy=yr*yr)
        {
        zz=rr-xx-yy; if (zz<0) continue; zr=sqrt(zz);
        z=z0-zr; if ((z>0)&&(z<n)) map[x][y][z]=col;
        z=z0+zr; if ((z>0)&&(z<n)) map[x][y][z]=col;
        }
    // project xz plane
    for (x=xa,xr=x-x0,xx=xr*xr;x<xb;x++,xr++,xx=xr*xr)
     for (z=za,zr=z-z0,zz=zr*zr;z<zb;z++,zr++,zz=zr*zr)
        {
        yy=rr-xx-zz; if (yy<0) continue; yr=sqrt(yy);
        y=y0-yr; if ((y>0)&&(y<n)) map[x][y][z]=col;
        y=y0+yr; if ((y>0)&&(y<n)) map[x][y][z]=col;
        }
    // project yz plane
    for (y=ya,yr=y-y0,yy=yr*yr;y<yb;y++,yr++,yy=yr*yr)
     for (z=za,zr=z-z0,zz=zr*zr;z<zb;z++,zr++,zz=zr*zr)
        {
        xx=rr-zz-yy; if (xx<0) continue; xr=sqrt(xx);
        x=x0-xr; if ((x>0)&&(x<n)) map[x][y][z]=col;
        x=x0+xr; if ((x>0)&&(x<n)) map[x][y][z]=col;
        }
    }
//---------------------------------------------------------------------------
void LED_cube::glDraw()
    {
    #ifdef __gl_h_
    int x,y,z;
    float p[3],dp=1.0/float(n-1);
    glEnable(GL_BLEND);
    glBlendFunc(GL_ONE,GL_ONE);

    glPointSize(2.0);

    glBegin(GL_POINTS);

    for (p[0]=-0.5,x=0;x<n;x++,p[0]+=dp)
     for (p[1]=-0.5,y=0;y<n;y++,p[1]+=dp)
      for (p[2]=-0.5,z=0;z<n;z++,p[2]+=dp)
        {
        glColor4ubv((BYTE*)(&map[x][y][z]));
        glVertex3fv(p);
        }
    glEnd();
    glDisable(GL_BLEND);
    glPointSize(1.0);
    #endif
    }
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
#endif
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------

类的使用：

LED_cube cube;
cube.cls(0x00202020); // clear space to dark gray color
int a=cube.n>>1;      // just place sphere to middle and size almost the whole space
int r=a-3;
cube.sphere(a,a,a,r,0x00FFFFFF);
cube.glDraw();        // just for mine visualization you have to rewrite it to your rendering system

如果你想用C仅

• 然后分解类公正的全球函数和变量...


• 和翻译C ++ operatos X ++， - ，+ =， - =，* =，......为C风格的X = X + 1，...

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