//三维几何函数库
#include <math.h>
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
struct point3{double x,y,z;};
struct line3{point3 a,b;};
struct plane3{point3 a,b,c;};
//计算cross product U x V
point3 xmult(point3 u,point3 v){
point3 ret;
ret.x=u.y*v.z-v.y*u.z;
ret.y=u.z*v.x-u.x*v.z;
ret.z=u.x*v.y-u.y*v.x;
return ret;
}
//计算dot product U . V
double dmult(point3 u,point3 v){
return u.x*v.x+u.y*v.y+u.z*v.z;
}
//矢量差 U - V
point3 subt(point3 u,point3 v){
point3 ret;
ret.x=u.x-v.x;
ret.y=u.y-v.y;
ret.z=u.z-v.z;
return ret;
}
//取平面法向量
point3 pvec(plane3 s){
return xmult(subt(s.a,s.b),subt(s.b,s.c));
}
point3 pvec(point3 s1,point3 s2,point3 s3){
return xmult(subt(s1,s2),subt(s2,s3));
}
//两点距离,单参数取向量大小
double distance(point3 p1,point3 p2){
return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y)+(p1.z-p2.z)*(p1.z-p2.z));
}
//向量大小
double vlen(point3 p){
return sqrt(p.x*p.x+p.y*p.y+p.z*p.z);
}
//判三点共线
int dots_inline(point3 p1,point3 p2,point3 p3){
return vlen(xmult(subt(p1,p2),subt(p2,p3)))<eps;
}
//判四点共面
int dots_onplane(point3 a,point3 b,point3 c,point3 d){
return zero(dmult(pvec(a,b,c),subt(d,a)));
}
//判点是否在线段上,包括端点和共线
int dot_online_in(point3 p,line3 l){
return zero(vlen(xmult(subt(p,l.a),subt(p,l.b))))&&(l.a.x-p.x)*(l.b.x-p.x)<eps&&
(l.a.y-p.y)*(l.b.y-p.y)<eps&&(l.a.z-p.z)*(l.b.z-p.z)<eps;
}
int dot_online_in(point3 p,point3 l1,point3 l2){
return zero(vlen(xmult(subt(p,l1),subt(p,l2))))&&(l1.x-p.x)*(l2.x-p.x)<eps&&
(l1.y-p.y)*(l2.y-p.y)<eps&&(l1.z-p.z)*(l2.z-p.z)<eps;
}
//判点是否在线段上,不包括端点
int dot_online_ex(point3 p,line3 l){
return dot_online_in(p,l)&&(!zero(p.x-l.a.x)||!zero(p.y-l.a.y)||!zero(p.z-l.a.z))&&
(!zero(p.x-l.b.x)||!zero(p.y-l.b.y)||!zero(p.z-l.b.z));
}
int dot_online_ex(point3 p,point3 l1,point3 l2){
return dot_online_in(p,l1,l2)&&(!zero(p.x-l1.x)||!zero(p.y-l1.y)||!zero(p.z-l1.z))&&
(!zero(p.x-l2.x)||!zero(p.y-l2.y)||!zero(p.z-l2.z));
}
//判点是否在空间三角形上,包括边界,三点共线无意义
int dot_inplane_in(point3 p,plane3 s){
return zero(vlen(xmult(subt(s.a,s.b),subt(s.a,s.c)))-vlen(xmult(subt(p,s.a),subt(p,s.b)))-
vlen(xmult(subt(p,s.b),subt(p,s.c)))-vlen(xmult(subt(p,s.c),subt(p,s.a))));
}
int dot_inplane_in(point3 p,point3 s1,point3 s2,point3 s3){
return zero(vlen(xmult(subt(s1,s2),subt(s1,s3)))-vlen(xmult(subt(p,s1),subt(p,s2)))-
vlen(xmult(subt(p,s2),subt(p,s3)))-vlen(xmult(subt(p,s3),subt(p,s1))));
}
//判点是否在空间三角形上,不包括边界,三点共线无意义
int dot_inplane_ex(point3 p,plane3 s){
return dot_inplane_in(p,s)&&vlen(xmult(subt(p,s.a),subt(p,s.b)))>eps&&
vlen(xmult(subt(p,s.b),subt(p,s.c)))>eps&&vlen(xmult(subt(p,s.c),subt(p,s.a)))>eps;
}
int dot_inplane_ex(point3 p,point3 s1,point3 s2,point3 s3){
return dot_inplane_in(p,s1,s2,s3)&&vlen(xmult(subt(p,s1),subt(p,s2)))>eps&&
vlen(xmult(subt(p,s2),subt(p,s3)))>eps&&vlen(xmult(subt(p,s3),subt(p,s1)))>eps;
}
//判两点在线段同侧,点在线段上返回0,不共面无意义
int same_side(point3 p1,point3 p2,line3 l){
return dmult(xmult(subt(l.a,l.b),subt(p1,l.b)),xmult(subt(l.a,l.b),subt(p2,l.b)))>eps;
}
int same_side(point3 p1,point3 p2,point3 l1,point3 l2){
return dmult(xmult(subt(l1,l2),subt(p1,l2)),xmult(subt(l1,l2),subt(p2,l2)))>eps;
}
//判两点在线段异侧,点在线段上返回0,不共面无意义
int opposite_side(point3 p1,point3 p2,line3 l){
return dmult(xmult(subt(l.a,l.b),subt(p1,l.b)),xmult(subt(l.a,l.b),subt(p2,l.b)))<-eps;
}
int opposite_side(point3 p1,point3 p2,point3 l1,point3 l2){
return dmult(xmult(subt(l1,l2),subt(p1,l2)),xmult(subt(l1,l2),subt(p2,l2)))<-eps;
}
//判两点在平面同侧,点在平面上返回0
int same_side(point3 p1,point3 p2,plane3 s){
return dmult(pvec(s),subt(p1,s.a))*dmult(pvec(s),subt(p2,s.a))>eps;
}
int same_side(point3 p1,point3 p2,point3 s1,point3 s2,point3 s3){
return dmult(pvec(s1,s2,s3),subt(p1,s1))*dmult(pvec(s1,s2,s3),subt(p2,s1))>eps;
}
//判两点在平面异侧,点在平面上返回0
int opposite_side(point3 p1,point3 p2,plane3 s){
return dmult(pvec(s),subt(p1,s.a))*dmult(pvec(s),subt(p2,s.a))<-eps;
}
int opposite_side(point3 p1,point3 p2,point3 s1,point3 s2,point3 s3){
return dmult(pvec(s1,s2,s3),subt(p1,s1))*dmult(pvec(s1,s2,s3),subt(p2,s1))<-eps;
}
//判两直线平行
int parallel(line3 u,line3 v){
return vlen(xmult(subt(u.a,u.b),subt(v.a,v.b)))<eps;
}
int parallel(point3 u1,point3 u2,point3 v1,point3 v2){
return vlen(xmult(subt(u1,u2),subt(v1,v2)))<eps;
}
//判两平面平行
int parallel(plane3 u,plane3 v){
return vlen(xmult(pvec(u),pvec(v)))<eps;
}
int parallel(point3 u1,point3 u2,point3 u3,point3 v1,point3 v2,point3 v3){
return vlen(xmult(pvec(u1,u2,u3),pvec(v1,v2,v3)))<eps;
}
//判直线与平面平行
int parallel(line3 l,plane3 s){
return zero(dmult(subt(l.a,l.b),pvec(s)));
}
int parallel(point3 l1,point3 l2,point3 s1,point3 s2,point3 s3){
return zero(dmult(subt(l1,l2),pvec(s1,s2,s3)));
}
//判两直线垂直
int perpendicular(line3 u,line3 v){
return zero(dmult(subt(u.a,u.b),subt(v.a,v.b)));
}
int perpendicular(point3 u1,point3 u2,point3 v1,point3 v2){
return zero(dmult(subt(u1,u2),subt(v1,v2)));
}
//判两平面垂直
int perpendicular(plane3 u,plane3 v){
return zero(dmult(pvec(u),pvec(v)));
}
int perpendicular(point3 u1,point3 u2,point3 u3,point3 v1,point3 v2,point3 v3){
return zero(dmult(pvec(u1,u2,u3),pvec(v1,v2,v3)));
}
//判直线与平面平行
int perpendicular(line3 l,plane3 s){
return vlen(xmult(subt(l.a,l.b),pvec(s)))<eps;
}
int perpendicular(point3 l1,point3 l2,point3 s1,point3 s2,point3 s3){
return vlen(xmult(subt(l1,l2),pvec(s1,s2,s3)))<eps;
}
//判两线段相交,包括端点和部分重合
int intersect_in(line3 u,line3 v){
if (!dots_onplane(u.a,u.b,v.a,v.b))
return 0;
if (!dots_inline(u.a,u.b,v.a)||!dots_inline(u.a,u.b,v.b))
return !same_side(u.a,u.b,v)&&!same_side(v.a,v.b,u);
return dot_online_in(u.a,v)||dot_online_in(u.b,v)||dot_online_in(v.a,u)||dot_online_in(v.b,u);
}
int intersect_in(point3 u1,point3 u2,point3 v1,point3 v2){
if (!dots_onplane(u1,u2,v1,v2))
return 0;
if (!dots_inline(u1,u2,v1)||!dots_inline(u1,u2,v2))
return !same_side(u1,u2,v1,v2)&&!same_side(v1,v2,u1,u2);
return dot_online_in(u1,v1,v2)||dot_online_in(u2,v1,v2)||dot_online_in(v1,u1,u2)||dot_online_in(v2,u1,u2);
}
//判两线段相交,不包括端点和部分重合
int intersect_ex(line3 u,line3 v){
return dots_onplane(u.a,u.b,v.a,v.b)&&opposite_side(u.a,u.b,v)&&opposite_side(v.a,v.b,u);
}
int intersect_ex(point3 u1,point3 u2,point3 v1,point3 v2){
return dots_onplane(u1,u2,v1,v2)&&opposite_side(u1,u2,v1,v2)&&opposite_side(v1,v2,u1,u2);
}
//判线段与空间三角形相交,包括交于边界和(部分)包含
int intersect_in(line3 l,plane3 s){
return !same_side(l.a,l.b,s)&&!same_side(s.a,s.b,l.a,l.b,s.c)&&
!same_side(s.b,s.c,l.a,l.b,s.a)&&!same_side(s.c,s.a,l.a,l.b,s.b);
}
int intersect_in(point3 l1,point3 l2,point3 s1,point3 s2,point3 s3){
return !same_side(l1,l2,s1,s2,s3)&&!same_side(s1,s2,l1,l2,s3)&&
!same_side(s2,s3,l1,l2,s1)&&!same_side(s3,s1,l1,l2,s2);
}
//判线段与空间三角形相交,不包括交于边界和(部分)包含
int intersect_ex(line3 l,plane3 s){
return opposite_side(l.a,l.b,s)&&opposite_side(s.a,s.b,l.a,l.b,s.c)&&
opposite_side(s.b,s.c,l.a,l.b,s.a)&&opposite_side(s.c,s.a,l.a,l.b,s.b);
}
int intersect_ex(point3 l1,point3 l2,point3 s1,point3 s2,point3 s3){
return opposite_side(l1,l2,s1,s2,s3)&&opposite_side(s1,s2,l1,l2,s3)&&
opposite_side(s2,s3,l1,l2,s1)&&opposite_side(s3,s1,l1,l2,s2);
}
//计算两直线交点,注意事先判断直线是否共面和平行!
//线段交点请另外判线段相交(同时还是要判断是否平行!)
point3 intersection(line3 u,line3 v){
point3 ret=u.a;
double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))
/((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));
ret.x+=(u.b.x-u.a.x)*t;
ret.y+=(u.b.y-u.a.y)*t;
ret.z+=(u.b.z-u.a.z)*t;
return ret;
}
point3 intersection
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资源评论
- zsk137269383272012-04-24个人认为相当好,里面有很多算法!很实用
- zdzhuhuishan2012-10-21代码很好,不错。
- NickLee752018-11-02好资料,参考书
- 夜伏击2012-11-03都是txt的啊,要是能直接编译的程序就更好了。
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