how to create a branching vein/river like structure on a square grid
I am trying to procedurally generate some rivers.
I have a flat (no concept of elevation) square grid as base and want to draw a branching structure on it like shown
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I think generating rivers is a backward approach as you would need to tweak a lot of things according to their shape later on which will be hard. I would instead create random terrain height map and extract features from it (as in the real world) which is much easier and closer to reality. In the final map you ignore the height and use flat one (if you really want a flat map). Here are few things you can extract from height map:
Rivers and lakes
by seeding random high altitude point and following it downhill to sea level or edge of map.
vegetation or ground
from slope and altitude you can determine if ground is sand,dirt,rock. If there are trees, bushes, grass or whatever.
Here look at this QA: random island generator
and some river overview:
The way you tweak the terrain generation will affect also the river shapes (no need to generate just islands).
The Seeds are working also for this approach.
[Edit1] promised C++ code
This basically generate random height map and then seed and downhill follow the rivers (lakes are generated automatically if the terrain block downhill watter flow). The terrain type is also determined from slope and altitude.
//--------------------------------------------------------------------------- picture pic; //--------------------------------------------------------------------------- void map_random(int _xs,int _ys) { // config int h0=-1000,h1=3000; // [m] terrain elevation range int h_water= 0; // [m] sea level int h_sand=15; // [m] sand level int h_evergreen=1500; // [m] evergreen level int h_snow=2000; // [m] snow level int h_rock=1800; // [m] mountine rock level float a_rock=60.0; // [deg] mountine rock slope float d_pixel=35.0; // [m] pixel size int d_river_w=5; // [pixel] river max width int d_river_l=150; // [pixel] river base length per width increase bool _island=true; // types enum _cover_enum { _cover_none=0, _cover_water, // sea _cover_snow, _covers, _cover_shift=0, _cover_mask=15, }; DWORD _cover[_covers]= { // RRGGBB 0x00000000, // none 0x00003080, // watter (sea) 0x00EEEEEE, // snow }; enum _terrain_enum { _terrain_dirt=0, _terrain_sand, _terrain_rock, _terrain_water, // streams,rivers,lakes _terrain_temp, // temp _terrains, _terrain_shift=4, _terrain_mask=15, }; DWORD _terrain[_terrains]= { // RRGGBB 0x00301510, // dirt 0x00EEC49A, // sand 0x006F6F6F, // rock 0x00006080, // water (streams,rivers,lakes) 0x00006080, // temp }; enum _flora_enum { _flora_none=0, _flora_grass, _flora_hardwood, _flora_evergreen, _flora_deadwood, _floras, _flora_shift=8, _flora_mask=15, }; DWORD _flora[_floras]= { // RRGGBB 0x00000000, // none 0x007F7F3F, // grass 0x001FFF1F, // hardwood 0x00007F00, // evergreen 0x007F3F1F, // deadwood }; // variables float a,b,da; int c,t,f; int x,y,z,xx,yy,mxs,mys,dx,dy,dx2,dy2,r,r2,ix,l; int xh1,yh1; // topest hill position int **ter=NULL,**typ=NULL; Randomize(); // align resolution to power of 2 for (mxs=1;mxs+1<_xs;mxs<<=1); if (mxs<3) mxs=3; for (mys=1;mys+1<_ys;mys<<=1); if (mys<3) mys=3; ter=new int*[mys+1]; for (y=0;y<=mys;y++) ter[y]=new int[mxs+1]; typ=new int*[mys+1]; for (y=0;y<=mys;y++) typ[y]=new int[mxs+1]; // [Terrain] for (;;) { // diamond & square random height map -> ter[][] dx=mxs; dx2=dx>>1; r=(mxs+mys)<<1; // init step,half step and randomness dy=mys; dy2=dy>>1; r2=r>>1; // set corners values if (_island) { t=-r2; ter[ 0][ 0]=t; ter[ 0][mxs]=t; ter[mys][ 0]=t; ter[mys][mxs]=t; ter[dy2][dx2]=r+r; // top of central hill } else{ ter[ 0][ 0]=Random(r); ter[ 0][mxs]=Random(r); ter[mys][ 0]=Random(r); ter[mys][mxs]=Random(r); } for (;dx2|dy2;dx=dx2,dx2>>=1,dy=dy2,dy2>>=1) // subdivide step until full image is filled { if (!dx) dx=1; if (!dy) dy=1; // diamond (skip first one for islands) if ((!_island)||(dx!=mxs)) for (y=dy2,yy=mys-dy2;y<=yy;y+=dy) for (x=dx2,xx=mxs-dx2;x<=xx;x+=dx) ter[y][x]=((ter[y-dy2][x-dx2]+ter[y-dy2][x+dx2]+ter[y+dy2][x-dx2]+ter[y+dy2][x+dx2])>>2)+Random(r)-r2; // square for (y=dy2,yy=mys-dy2;y<=yy;y+=dy) for (x=dx ,xx=mxs-dx ;x<=xx;x+=dx) ter[y][x]=((ter[y][x-dx2]+ter[y][x+dx2]+ter[y-dy2][x]+ter[y+dy2][x])>>2)+Random(r)-r2; for (y=dy ,yy=mys-dy ;y<=yy;y+=dy) for (x=dx2,xx=mxs-dx2;x<=xx;x+=dx) ter[y][x]=((ter[y][x-dx2]+ter[y][x+dx2]+ter[y-dy2][x]+ter[y+dy2][x])>>2)+Random(r)-r2; for (x=dx2,xx=mxs-dx2;x<=xx;x+=dx) { y= 0; ter[y][x]=((ter[y][x-dx2]+ter[y][x+dx2]+ter[y+dy2][x])/3)+Random(r)-r2; y=mys; ter[y][x]=((ter[y][x-dx2]+ter[y][x+dx2]+ter[y-dy2][x])/3)+Random(r)-r2; } for (y=dy2,yy=mys-dy2;y<=yy;y+=dy) { x= 0; ter[y][x]=((ter[y][x+dx2]+ter[y-dy2][x]+ter[y+dy2][x])/3)+Random(r)-r2; x=mxs; ter[y][x]=((ter[y][x-dx2]+ter[y-dy2][x]+ter[y+dy2][x])/3)+Random(r)-r2; } if (_island) { // recompute middle position after first pass so there can be more central hills if (dx==mxs) ter[dy2][dx2]=Random(r2); // adjust border to underwatter for (y=0;y<=mys;y+=dy2) { ter[y][0]=t; ter[y][mxs]=t; } for (x=0;x<=mxs;x+=dx2) { ter[0][x]=t; ter[mys][x]=t; } } // adjust randomness r>>=1; if (r<2) r=2; r2=r>>1; } // rescale to <h0,h1> xx=ter[0][0]; yy=xx; for (y=0;y<=mys;y++) for (x=0;x<=mxs;x++) { z=ter[y][x]; if (xx>z) xx=z; if (yy<z){ yy=z; xh1=x; yh1=y; } } for (y=0;y<=mys;y++) for (x=0;x<=mxs;x++) ter[y][x]=h0+(((ter[y][x]-xx)*(h1-h0))/(yy-xx)); // test for correctness if (_island) { l=0; for (x=0;x<=mxs;x++) { if (ter[0][x]>h_water) l++; if (ter[mys][x]>h_water) l++; } for (y=0;y<=mys;y++) { if (ter[y][0]>h_water) l++; if (ter[y][mxs]>h_water) l++; } if (l>1+((mxs+mys)>>3)) continue; } break; } // [Surface] for (y=0;y<mys;y++) for (x=0;x<mxs;x++) { z=ter[y][x]; // max slope [deg] a=atan2(ter[y][x+1]-z,d_pixel); b=atan2(ter[y+1][x]-z,d_pixel); if (a<b) a=b; a*=180.0/M_PI; c=_cover_none; if (z<=h_water) c=_cover_water; if (z>=h_snow ) c=_cover_snow; t=_terrain_dirt; if (z<=h_sand) t=_terrain_sand; if (z>=h_rock) t=_terrain_rock; if (a>=a_rock) t=_terrain_rock; f=_flora_none; if (t==_terrain_dirt) { r=Random(100); if (r>10) f=_flora_grass; if (r>50) { if (z>h_evergreen) f=_flora_evergreen; else{ r=Random(h_evergreen); if (r<=z) f=_flora_evergreen; else f=_flora_hardwood; } } if (r<5) f=_flora_deadwood; } typ[y][x]=(c<<_cover_shift)|(t<<_terrain_shift)|(f<<_flora_shift); } // [Rivers] for (ix=10+Random(5),a=0.0,da=2.0*M_PI/float(ix);ix;ix--) { // random start around topest hill a+=da*(0.75+(0.50*Random())); for (l=0;l<10;l++) { b=Random(mxs>>3); x=xh1; x+=float(b*cos(a)); y=yh1; y+=float(b*sin(a)); if ((x<1)||(x>=mxs)) continue; if ((y<1)||(y>=mys)) continue; if (typ[y][x]&0x00F==_cover_water) continue; l=-1; break; } if (l>=0) continue; // safety check for (l=0,r2=0;;) { // stop on map edge if ((x<=0)||(x>=mxs-1)||(y<=0)||(y>=mys-1)) break; // decode generated surface r=typ[y][x]; c=(r>> _cover_shift)& _cover_mask; t=(r>>_terrain_shift)&_terrain_mask; f=(r>> _flora_shift)& _flora_mask; // stop if reached sea if (c==_cover_water) break; // insert river dot radius = r2 dx=x-r2; if (dx<0) dx=0; dx2=x+r2; if (dx2>=mxs) dx2=mxs-1; dy=y-r2; if (dy<0) dy=0; dy2=y+r2; if (dy2>=mys) dy2=mys-1; for (yy=dy;yy<=dy2;yy++) for (xx=dx;xx<=dx2;xx++) if (((xx-x)*(xx-x))+((yy-y)*(yy-y))<=r2*r2) if (((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water) typ[yy][xx]=(typ[yy][xx]&0x00F)|(_terrain_temp<<_terrain_shift); // step to smalest elevation neighbor dx=x; dy=y; z=h1; typ[y][x]=(typ[y][x]&0x00F)|(_terrain_water<<_terrain_shift); xx=x; yy=y; xx--; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } yy--; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } xx++; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } xx++; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } yy++; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } yy++; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } xx--; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } xx--; r=ter[yy][xx]; if ((z>=r)&&(((typ[yy][xx]>>_terrain_shift)&_terrain_mask)!=_terrain_water)) { z=r; dx=xx; dy=yy; } if ((dx==x)&&(dy==y)) { // handle invalid path or need for a lake!!! if (dx>mxs>>1) dx++; else dx--; if (dy>mys>>1) dy++; else dy--; } x=dx; y=dy; // increase river volume with length l++; if (l>d_river_l*(r2+1)) { l=0; if (r2<d_river_w) r2++; } } // make merging of rivers possible for (y=0;y<=mys;y++) for (x=0;x<=mxs;x++) if (((typ[y][x]>>_terrain_shift)&_terrain_mask)==_terrain_water) typ[y][x]=(typ[y][x]&0x00F)|(_terrain_temp<<_terrain_shift); } for (y=0;y<=mys;y++) for (x=0;x<=mxs;x++) if (((typ[y][x]>>_terrain_shift)&_terrain_mask)==_terrain_temp) typ[y][x]=(typ[y][x]&0x00F)|(_terrain_water<<_terrain_shift); // [copy data] rewrite this part to suite your needs for (y=1;y<_ys;y++) for (x=1;x<_xs;x++) { float nx,ny,nz,x0,y0,z0,x1,y1,z1; // (nx,ny,nz) = surface normal nx=0.0; ny=0.0; nz=ter[y][x]; x0=-d_pixel; y0=0.0; z0=ter[y][x-1]; x1=0.0; y1=-d_pixel; z1=ter[y-1][x]; x0-=nx; x1-=nx; y0-=ny; y1-=ny; z0-=nz; z1-=nz; nx=(y0*z1)-(z0*y1); ny=(z0*x1)-(x0*z1); nz=(x0*y1)-(y0*x1); x0=1.0/sqrt((nx*nx)+(ny*ny)+(nz*nz)); nx*=x0; ny*=x0; nz*=x0; // z = ambient light + normal shading nz=(+0.7*nx)+(-0.7*ny)+(+0.7*nz); if (nz<0.0) nz=0.0; nz=255.0*(0.2+(0.8*nz)); z=nz; // r = base color r=typ[y][x]; c=(r>> _cover_shift)& _cover_mask; t=(r>>_terrain_shift)&_terrain_mask; f=(r>> _flora_shift)& _flora_mask; r=_terrain[t]; if (c) r= _cover[c]; if (f){ if (c) r|=_flora[f]; else r=_flora[f]; }; // sea color is depending on depth not surface normal if (c==_cover_water) z=256-((ter[y][x]<<7)/h0); // apply lighting z to color r yy=int(r>>16)&255; yy=(yy*z)>>8; if (yy>255) yy=255; r=(r&0x0000FFFF)|(yy<<16); yy=int(r>> 8)&255; yy=(yy*z)>>8; if (yy>255) yy=255; r=(r&0x00FF00FF)|(yy<< 8); yy=int(r )&255; yy=(yy*z)>>8; if (yy>255) yy=255; r=(r&0x00FFFF00)|(yy ); // set pixel to target image pic.p[y][x].dd=r; } // free ter[][],typ[][] for (y=0;y<=mys;y++) delete[] ter[y]; delete[] ter; ter=NULL; for (y=0;y<=mys;y++) delete[] typ[y]; delete[] typ; typ=NULL; } //---------------------------------------------------------------------------The code is based on the code from the linked Answer of mine but with added features (rivers included). I use my own picture class for images so some members are:
xs,yssize of image in pixelsp[y][x].ddis pixel at(x,y)position as 32 bit integer typeclear(color)- clears entire imageresize(xs,ys)- resizes image to new resolutionbmp- VCL encapsulated GDI Bitmap with Canvas access
You can tweak the
adjust randomnessin Diamond&Square to change the terrain smoothness. Also the height limits and tresholds can be tampered with.To achieve more brunching like rivers seed more start points in clusters so they should merge in time into single or more rivers.
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Your river delta looks much like a tree. Here is some Python code using turtle for Graphics to draw a tree.
# You can edit this code and run it right here in the browser! # Try changing colors or adding your own shapes.
import turtle from random import randint def tree(length,n, ps): """ paints a branch of a tree with 2 smaller branches, like an Y""" if length < (length/n): return # escape the function turtle.pensize(max(ps,1)) turtle.forward(length) # paint the thik branch of the tree lb = 45+randint(-20,20) turtle.left(lb) # rotate left for smaller "fork" branch tree(length * 0.5*(1+randint(-20,20)/100),length/n,ps-1) # create a smaller branch with 1/2 the lenght of the parent branch rb = 45+randint(-20,20) turtle.right(lb+rb) # rotoate right for smaller "fork" branch tree(length * 0.6,length/n,ps-1) # create second smaller branch turtle.left(rb) # rotate back to original heading rt = randint(-20,20) turtle.right(rt) tree(length * 0.45,length/n,ps-1) turtle.left(rt) turtle.backward(length) # move back to original position return # leave the function, continue with calling program turtle.left(90) turtle.penup() turtle.backward(250) turtle.pendown() tree(150,5,5)讨论(0)
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