“画"一个 3d 线到一个数组中 [英] "Draw" a 3d line into an array
问题描述
我正在寻找一种解决方案，就像
您需要:
作为球体的端点
请参阅上面链接中的
add_sphere.在端点处切割的光盘
为此，我们需要
U,V基向量(相互垂直的向量并与自身成直线).有了这些，我们可以简单地使用任何2D圆形像素采集并将它们轻松转换为3D体素位置.因此，如果u,v是以(0,0)为中心的某个 2D 圆中的坐标，则:x = x0 + u*U.x + v*V.xy = y0 + u*U.y + v*V.yz = z0 + u*U.z + v*V.z(x,y,z)对应于 3D 圆体素坐标，中心为(x0,y0,z0).有关详细信息，请参阅对于
128x128x128卷这样初始化://init volume raytracervol.gl_init();vol.beg();国际r,a,b,c;r=10.0；a=r+1;b=vol.size-r-2;c=体积大小＞＞1；//BBGGRRvol.add_line(a,a,a,b,a,a,r,0x00FF2020);vol.add_line(a,b,a,b,b,a,r,0x00FF2020);vol.add_line(a,a,a,a,b,a,r,0x00FF2020);vol.add_line(b,a,a,b,b,a,r,0x00FF2020);vol.add_line(a,a,b,b,a,b,r,0x00FF2020);vol.add_line(a,b,b,b,b,b,r,0x00FF2020);vol.add_line(a,a,b,a,b,b,r,0x00FF2020);vol.add_line(b,a,b,b,b,b,r,0x00FF2020);vol.add_line(a,a,a,a,a,b,r,0x00FF2020);vol.add_line(a,b,a,a,b,b,r,0x00FF2020);vol.add_line(b,a,a,b,a,b,r,0x00FF2020);vol.add_line(b,b,a,b,b,b,r,0x00FF2020);vol.add_sphere(c,c,c,c>>1,0x00FF8040);vol.add_sphere(a,c,c,r,0x004080FF);vol.add_sphere(b,c,c,r,0x0080FF40);vol.add_sphere(c,a,c,r,0x00FF4080);vol.add_sphere(c,b,c,r,0x00AAAAAA);vol.add_box(c,c,a,r,r,r,0x0060FF60);vol.add_box(c,c,b,r,r,r,0x00FF2020);卷结束()；I am looking for a solution do "draw" a 3d line (filled cylinder) into a 3d array using python just like the skimage.draw.line function does for 2 arrays.
The line should have a starting point
(x1, y1, z1), an end point(x2, y2, z2), and a radiusR.I had a look at an example for a 2d line but I was not able to modify it to work in the 3d case.
I was thinking about drawing successive ellipses into the array, but I was not able to figure out how to calculate the two axes and the rotation angle.
Maybe there is a much simpler approach to this problem?
解决方案Let assume this GLSL volumetric back raytracer as a start point. To make a filled 3D line like this:
You need:
endpoints as spheres
see the
add_spherein the link above.discs cut at the endpoints
for that we need
U,Vbasis vectors (perpendicular vectors to each other and to line itself). With those we can simply use any 2D circle pixels acquisition and convert them to 3D voxel positions with ease. So ifu,vare coordinates in some 2D circle centered at(0,0)then:x = x0 + u*U.x + v*V.x y = y0 + u*U.y + v*V.y z = z0 + u*U.z + v*V.z(x,y,z)are corresponding to 3D circle voxel coordinate with center(x0,y0,z0). For more info see my C++ glCircle3D implementation.line body
As wee got all the voxel positions in the disc around
x0,y0,z0endpoint of the line just cast a line from each of it with the same slope as line(x0,y0,z0),(x1,y1,z1)which are the endpoints of your line.
When put together in C++ (sorry I do not code in python) I got this:
void volume::add_line(int x0,int y0,int z0,int x1,int y1,int z1,int r,GLuint col) { if (!_init) return; int i,n,x,y,z,cx,cy,cz,dx,dy,dz,kx,ky,kz; // endpoints are (half)spheres add_sphere(x0,y0,z0,r,col); add_sphere(x1,y1,z1,r,col); // DDA constants kx=0; dx=x1-x0; if (dx>0) kx=+1; if (dx<0) { kx=-1; dx=-dx; } dx++; n=dx; ky=0; dy=y1-y0; if (dy>0) ky=+1; if (dy<0) { ky=-1; dy=-dy; } dy++; if (n<dy) n=dy; kz=0; dz=z1-z0; if (dz>0) kz=+1; if (dz<0) { kz=-1; dz=-dz; } dz++; if (n<dz) n=dz; // basis vectors double U[3],V[3],N[3]={x1-x0,y1-y0,z1-z0},u,v,rr=r*r; vector_one(N,N); // unit vector vector_ld(U,1.0,0.0,0.0); if (fabs(vector_mul(U,N))>=0.75) vector_ld(U,0.0,1.0,0.0); // |dot(U,N)|<0.75 means (1.0,0.0,0.0) is nearly parallel to N so chose (0.0,1.0,0.0) instead vector_mul(U,U,N); // U = U x N vector_mul(V,U,N); // V = U x N vector_one(U,U); // U /= |U| vector_one(V,V); // V /= |V| // disc for (u=-r;u<=+r;u++) for (v=-r;v<=+r;v++) if (u*u+v*v<=rr) { x=x0+double((u*U[0])+(v*V[0])); y=y0+double((u*U[1])+(v*V[1])); z=z0+double((u*U[2])+(v*V[2])); // DDA line for (cx=cy=cz=n,i=0;i<n;i++) { if ((x>=0)&&(x<size)&&(y>=0)&&(y<size)&&(z>=0)&&(z<size)) data[z][y][x]=col; cx-=dx; if (cx<=0) { cx+=n; x+=kx; } cy-=dy; if (cy<=0) { cy+=n; y+=ky; } cz-=dz; if (cz<=0) { cz+=n; z+=kz; } } } }The
vector_xxxfunctions are just my 3D vector math and just dot,cross product and normalize to unit size are used which is easy to implement. You can see them here:There are still things that can be improved like the spheres could be just half spheres and their generation can be joined with the disc stuff ... as the dot between normal and not offseted 3D sphere coordinate is either positive/zero/negative which distinct endpoint half-sphere and disc ... that would also fully eliminate the need for
U,V.Also depending on used HW and circumstances there might be also faster approaches like analytical (filling BBOX based on distance from line) if fast vector math is combined with massive parallelism like on GPU.
After some tweaking in my engine (added zoom and handle some accuracy problem) I got this result:
for
128x128x128volume inited like this:// init volume raytracer vol.gl_init(); vol.beg(); int r,a,b,c; r=10.0; a=r+1; b=vol.size-r-2; c=vol.size>>1; //BBGGRR vol.add_line(a,a,a,b,a,a,r,0x00FF2020); vol.add_line(a,b,a,b,b,a,r,0x00FF2020); vol.add_line(a,a,a,a,b,a,r,0x00FF2020); vol.add_line(b,a,a,b,b,a,r,0x00FF2020); vol.add_line(a,a,b,b,a,b,r,0x00FF2020); vol.add_line(a,b,b,b,b,b,r,0x00FF2020); vol.add_line(a,a,b,a,b,b,r,0x00FF2020); vol.add_line(b,a,b,b,b,b,r,0x00FF2020); vol.add_line(a,a,a,a,a,b,r,0x00FF2020); vol.add_line(a,b,a,a,b,b,r,0x00FF2020); vol.add_line(b,a,a,b,a,b,r,0x00FF2020); vol.add_line(b,b,a,b,b,b,r,0x00FF2020); vol.add_sphere(c,c,c,c>>1,0x00FF8040); vol.add_sphere(a,c,c,r,0x004080FF); vol.add_sphere(b,c,c,r,0x0080FF40); vol.add_sphere(c,a,c,r,0x00FF4080); vol.add_sphere(c,b,c,r,0x00AAAAAA); vol.add_box(c,c,a,r,r,r,0x0060FF60); vol.add_box(c,c,b,r,r,r,0x00FF2020); vol.end();这篇关于“画"一个 3d 线到一个数组中的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
