Procedural Street Modelling In Houdini 1 | Houdini中程序式街道生成 I
路网的程序式生成前人曾经提出过多种方式，比如用模板，用L-System，用代理(Agent-Based)，用张量场(Tensor Field)。其中比较实用的是L系统和张量场，前者也就是CityEngine中使用的方式。[Parish and Muller, 2001]这里的L系统不是传统的字符串替换的L系统，虽然思想一致，用递归替换的方式衍生，但在Extended L系统中，可替换的可以是复杂的带变量的函数，而不仅仅是简单的Turtle移动了。这我们后面再说，这里主要讲张量场的实现[Chen, 2008]
基本思路是：
- 根据地形生成张量场，可以多个张量场叠加
- 根据张量场生成道路
张量定义是
它可以有两个互相垂直的本征向量，这个特性很好，很多路网交叉口是垂直的。
1 张量场生成
可以有多种，比如格网的，轴向的。延海岸线和河流线可以有顺应边缘的张量场，沿高度图也可以有顺应梯度的张量场。
以下为houdini的实现
多种张量场可以叠加混合起来
以下为houdini的实现
之后呢这些张量场还可以加噪声。。。
2 主干路生成
从一些随机点开始沿主本征向量方向走，隔一段距离布一个种子点，直到走不下去；按一定规则选一个种子点开始按次本征向量方向移动，布种子点直到走不动；继续选种子点，换方向，布种子点。
当还有种子点，循环：
选取优先级最高的种子点
直到走不动，循环：
沿某个本征向量方向移动
隔一定距离布种子点
切换到另一个本征向量方向
单个流线移动策略：
就跟着本征向量走就好了，退出条件：1. 出边界了 2. 到了退化点 3. 回到起点了 4. 超出最大长度 5. 离另一个流线太近了，如果这样就往前找一找看能不能接上
种子优先度策略：
到水的距离，到退化点的距离，到城市中心的距离，几个距离按负幂指数加起来作为评价函数。种子是放优先队列里的。
基本思路还是比较简单的，但在houdini里实现起来并不那么容易，下面是一个演示动画
2008-SG-Chen-InteractiveProceduralStreetModeling.pdf
http://martindevans.me/game-development/2015/12/11/Procedural-Generation-For-Dummies-Roads/
用线来生成路面和路中的面：
44da13e618ca8b399f004e713603e54e17cb.pdf
curve to street
function int getNearPointId(vector sideDir; vector lineDir; int ptnum; int otherpt){
int neibs[] = neighbours(0, ptnum);
if(len(neibs) == 1){
return neibs[0];
}
else{
vector thispos = point(0, "P", ptnum);
float minAngle = 6.28;
int minId = neibs[0];
foreach(int id; neibs){
if(id == otherpt){
continue;
}
vector otherPos = point(0, "P", id);
vector toDir = normalize(otherPos - thispos);
float dotLine = dot(toDir, -lineDir);
float dotDir = dot(toDir, sideDir);
float acos = acos(dotLine);
if(dotDir < 0){
acos = 6.28 - acos;
}
if(acos < minAngle){
minAngle = acos;
minId = id;
}
}
return minId;
}
}
//left: isleft = 1; right : isleft = 0;
function vector getGuideDir(int ptstart; int ptend; int isLeft){
vector pos1 = point(0, "P", ptstart);
vector pos2 = point(0, "P", ptend);
vector toVec = normalize(pos2 - pos1);
vector up = {0,1,0};
if(isLeft > 0.5){
return cross(up, toVec);
}else{
return cross(toVec, up);
}
}
function vector2 solveIntersection(vector start1; vector start2; vector dir1; vector dir2){
vector2 dir1xz, dir2xz;
dir1xz.x = dir1.x;
dir1xz.y = dir1.z;
dir2xz.x = dir2.x;
dir2xz.y = dir2.z;
if(abs(dot(normalize(dir1xz), normalize(dir2xz))) > 0.9999){
vector2 rtresult;
rtresult.x = (start1.x + start2.x) / 2;
rtresult.y = (start1.z + start2.z) / 2;
return rtresult;
}
vector2 start1xz, start2xz;
start1xz.x = start1.x;
start1xz.y = start1.z;
start2xz.x = start2.x;
start2xz.y = start2.z;
float t2 = ( start1xz.x * dir1xz.y - start1xz.y * dir1xz.x + start2xz.y * dir1xz.x - start2xz.x * dir1xz.y) / ( dir2xz.x * dir1xz.y - dir2xz.y * dir1xz.x);
vector2 result = start2xz + t2 * dir2xz;
return result;
}
function vector getOffsetPosition(int pt1; int ptmid; int pt2; float offsetDist1; float offsetDist2; vector dirGuide){
vector pos1 = point(0, "P", pt1);
vector posmid = point(0, "P", ptmid);
vector pos2 = point(0, "P", pt2);
vector to1 = normalize(pos1 - posmid);
vector to2 = normalize(pos2 - posmid);
vector cross1 = cross(to1, dirGuide);
vector cross2 = cross(to2, dirGuide);
cross1.x = 0;
cross1.z = 0;
cross2.x = 0;
cross2.z = 0;
vector offsetVec1 = cross(cross1, to1);
vector offsetVec2 = cross(cross2, to2);
vector start1 = posmid + offsetDist1 * normalize(offsetVec1);
vector start2 = posmid + offsetDist2 * normalize(offsetVec2);
vector2 resultVecXZ = solveIntersection(start1, start2, to1, to2);
vector resultVec;
resultVec.x = resultVecXZ.x;
resultVec.z = resultVecXZ.y;
resultVec.y = (start1.y + start2.y) / 2;
return resultVec;
}
int pts[] = primpoints(0, @primnum);
//printf("lens %sn", len(pts));
float width = 0.02;
if(len(pts) == 2){
vector pos1 = point(0, "P", pts[0]);
vector pos2 = point(0, "P", pts[1]);
vector linedir = normalize(pos2 - pos1);
vector up = {0,1,0};
vector leftDir = getGuideDir(pts[0], pts[1], 1);
vector rightDir = getGuideDir(pts[0], pts[1], 0);
int ptidleftnear2 = getNearPointId(leftDir, linedir, pts[1], pts[0]);
int ptidleftnear1 = getNearPointId(leftDir, -linedir, pts[0], pts[1]);
vector ln2Dir = getGuideDir(pts[1], ptidleftnear2, 1);
vector ln1Dir = getGuideDir(ptidleftnear1, pts[0], 1);
int ptidrightnear2 = getNearPointId(rightDir, linedir, pts[1], pts[0]);
int ptidrightnear1 = getNearPointId(rightDir, -linedir, pts[0], pts[1]);
vector rn2Dir = getGuideDir(pts[1], ptidrightnear2, 0);
vector rn1Dir = getGuideDir(ptidrightnear1, pts[0], 0);
vector left1 = getOffsetPosition(ptidleftnear1, pts[0], pts[1], width, width, ln1Dir + leftDir);
vector left2 = getOffsetPosition(pts[0], pts[1], ptidleftnear2, width, width, ln2Dir + leftDir);
vector right1 = getOffsetPosition(ptidrightnear1, pts[0], pts[1], width, width, rn1Dir + rightDir);
vector right2 = getOffsetPosition(pts[0], pts[1], ptidrightnear2, width, width, rn2Dir + rightDir);
int addleft1 = addpoint(0, left1);
int addleft2 = addpoint(0, left2);
@ptidleftnear1 = ptidleftnear1;
@ptidleftnear2 = ptidleftnear2;
@pos1 = pts[0];
@pos2 = pts[1];
int addright1 = addpoint(0, right1);
int addright2 = addpoint(0, right2);
addprim(0, "poly", addleft1, addleft2, addright2, addright1);
}
CityEngine L-system
https://josauder.github.io/procedural_city_generation/
http://martindevans.me/game-development/2015/12/27/Procedural-Generation-For-Dummies-Lots/