使用贝塞尔绘制曲线代码分享贝塞尔曲线

导读structxy{intx;inty;xy(){}xy(intm){x=m;y=m;}xy(intx,inty){this->x=x;this->y=y;}....

struct xy{int x;int y;xy(){}xy(int m){x=m;y=m;}xy(int x,int y){this->x=x;this->y=y;}xy operator *(xy&m){return xy(x *m.x,y *m.y);}xy operator /(xy&m){return xy(x /m.x,y /m.y);}xy operator %(xy&m){return xy(x %m.x,y %m.y);}xy operator (xy&m){return xy(x m.x,y m.y);}xy operator -(xy&m){return xy(x -m.x,y -m.y);}xy operator <<(xy&m){return xy(x<<m.x,y<<m.y);}xy operator >>(xy&m){return xy(x>>m.x,y>>m.y);}xy operator &(xy&m){return xy(x &m.x,y &m.y);}xy operator |(xy&m){return xy(x |m.x,y |m.y);}xy operator ^(xy&m){return xy(x ^m.x,y ^m.y);}xy operator *=(xy&m){x *=m.x;y *=m.y;return *this;}xy operator /=(xy&m){x /=m.x;y /=m.y;return *this;}xy operator %=(xy&m){x %=m.x;y %=m.y;return *this;}xy operator =(xy&m){x =m.x;y =m.y;return *this;}xy operator -=(xy&m){x -=m.x;y -=m.y;return *this;}xy operator <<=(xy&m){x<<=m.x;y<<=m.y;return *this;}xy operator >>=(xy&m){x>>=m.x;y>>=m.y;return *this;}xy operator &=(xy&m){x &=m.x;y &=m.y;return *this;}xy operator |=(xy&m){x |=m.x;y |=m.y;return *this;}xy operator ^=(xy&m){x ^=m.x;y ^=m.y;return *this;}xy operator *(int m){return xy(x *m,y *m);}xy operator /(int m){return xy(x /m,y /m);}xy operator %(int m){return xy(x %m,y %m);}xy operator (int m){return xy(x m,y m);}xy operator -(int m){return xy(x -m,y -m);}xy operator <<(int m){return xy(x<<m,y<<m);}xy operator >>(int m){return xy(x>>m,y>>m);}xy operator &(int m){return xy(x &m,y &m);}xy operator |(int m){return xy(x |m,y |m);}xy operator ^(int m){return xy(x ^m,y ^m);}xy operator *=(int m){x *=m;y *=m;return *this;}xy operator /=(int m){x /=m;y /=m;return *this;}xy operator %=(int m){x %=m;y %=m;return *this;}xy operator =(int m){x =m;y =m;return *this;}xy operator -=(int m){x -=m;y -=m;return *this;}xy operator <<=(int m){x<<=m;y<<=m;return *this;}xy operator >>=(int m){x>>=m;y>>=m;return *this;}xy operator &=(int m){x &=m;y &=m;return *this;}xy operator |=(int m){x |=m;y |=m;return *this;}xy operator ^=(int m){x ^=m;y ^=m;return *this;}bool operator <(xy&m){return((unsigned(x) <unsigned(m.x))&&(unsigned(y) <unsigned(m.y)));}bool operator >(xy&m){return((unsigned(x) >unsigned(m.x))&&(unsigned(y) >unsigned(m.y)));}bool operator <=(xy&m){return((unsigned(x)<=unsigned(m.x))&&(unsigned(y)<=unsigned(m.y)));}bool operator >=(xy&m){return((unsigned(x)>=unsigned(m.x))&&(unsigned(y)>=unsigned(m.y)));}bool operator ==(xy&m){return((unsigned(x)==unsigned(m.x))&&(unsigned(y)==unsigned(m.y)));}bool operator <(int m){return((unsigned(x) <unsigned(m))&&(unsigned(y) <unsigned(m)));}bool operator >(int m){return((unsigned(x) >unsigned(m))&&(unsigned(y) >unsigned(m)));}bool operator <=(int m){return((unsigned(x)<=unsigned(m))&&(unsigned(y)<=unsigned(m)));}bool operator >=(int m){return((unsigned(x)>=unsigned(m))&&(unsigned(y)>=unsigned(m)));}bool operator ==(int m){return((unsigned(x)==unsigned(m))&&(unsigned(y)==unsigned(m)));}xy operator !(){return xy( !x, !y);}xy operator ~(){return xy( ~x, ~y);}xy operator (){return xy( x, y);}xy operator -(){return xy( -x, -y);}xy get_number(){xy m=0;if(x>0)m.x= x;if(x<0)m.x=-x;if(y>0)m.y= y;if(y<0)m.y=-y;return m;}xy get_flag(){xy m=0;if(x>0)m.x= 1;if(x<0)m.x=-1;if(y>0)m.y= 1;if(y<0)m.y=-1;return m;}int sqrt_xx_yy(){return sqrt(xx_yy());}void x_y(){int v=x;x=y;y=v;}int xx(){return x*x;}int yy(){return y*y;}int xx_yy(){return (x*x y*y);}xy operator =(xy&m){x=m.x;y=m.y;return *this;}xy operator =(int m){x=m;y=m;return *this;}xy operator (int){xy temp=*this; x; y;return temp;}xy operator (){x ;y ;return *this;}xy operator --(int){xy temp=*this;--x;--y;return temp;}xy operator --(){x--;y--;return *this;}};struct xyf{float x;float y;xyf(){}xyf(float m){x=m;y=m;}xyf(float x,float y){this->x=x;this->y=y;} xyf(xy m){this->x=m.x;this->y=m.y;}xyf operator *(xyf&m){return xyf(x *m.x,y *m.y);}xyf operator /(xyf&m){return xyf(x /m.x,y /m.y);}xyf operator (xyf&m){return xyf(x m.x,y m.y);}xyf operator -(xyf&m){return xyf(x -m.x,y -m.y);}xyf operator *=(xyf&m){x *=m.x;y *=m.y;return *this;}xyf operator /=(xyf&m){x /=m.x;y /=m.y;return *this;}xyf operator =(xyf&m){x =m.x;y =m.y;return *this;}xyf operator -=(xyf&m){x -=m.x;y -=m.y;return *this;}xyf operator *(float m){return xyf(x *m,y *m);}xyf operator /(float m){return xyf(x /m,y /m);}xyf operator (float m){return xyf(x m,y m);}xyf operator -(float m){return xyf(x -m,y -m);}xyf operator *=(float m){x *=m;y *=m;return *this;}xyf operator /=(float m){x /=m;y /=m;return *this;}xyf operator =(float m){x =m;y =m;return *this;}xyf operator -=(float m){x -=m;y -=m;return *this;}xyf get_number(){xyf m=0;if(x>0)m.x= x;if(x<0)m.x=-x;if(y>0)m.y= y;if(y<0)m.y=-y;return m;}xyf get_flag(){xyf m=0;if(x>0)m.x= 1;if(x<0)m.x=-1;if(y>0)m.y= 1;if(y<0)m.y=-1;return m;}float sqrt_xx_yy(){return sqrt(xx_yy());}void x_y(){float v=x;x=y;y=v;}float xx(){return x*x;}float yy(){return y*y;}float xx_yy(){return (x*x y*y);}xyf operator =(xy&m){x=m.x;y=m.y;return *this;}xyf operator =(xyf&m){x=m.x;y=m.y;return *this;}xyf operator =(float m){x=m;y=m;return *this;}xyf operator (int){xyf temp=*this; x; y;return temp;}xyf operator (){x ;y ;return *this;}xyf operator --(int){xyf temp=*this;--x;--y;return temp;}xyf operator --(){x--;y--;return *this;}};int paint_line(xy r,xy *da){// float->int (f 0.5)// [-0.5, 0.5)=0// [ 0.5, 1.5)=1// [ 1.5, 2.5)=2 // x*a b*y=0; // (x v)*a=x*a v*a; // (y v)*a=y*a v*a; xy n=r.get_number(); xy f=r.get_flag(); xy nn=n*2; xy d=0; xy*db=da; *db =d; if(n.y<n.x){ int v=n.x; while(d.x!=r.x){ d.x =f.x; v-=nn.y; if(v<0){ v =nn.x; d.y =f.y; } *db =d; } }else{ int v=n.y; while(d.y!=r.y){ d.y =f.y; v-=nn.x; if(v<0){ v =nn.y; d.x =f.x; } *db =d; } } return (db-da);}int paint_line(xy a,xy b,xy *da){ int dn=paint_line(b-a,da); for(int i=0;i<dn;i )da[i] =a; return dn;}/*struct xy64{__int64 x;__int64 y;xy64(){}xy64(__int64 m){x=m;y=m;}xy64(__int64 x,__int64 y){this->x=x;this->y=y;}xy64 operator *(xy64&m){return xy64(x *m.x,y *m.y);}xy64 operator /(xy64&m){return xy64(x /m.x,y /m.y);}xy64 operator %(xy64&m){return xy64(x %m.x,y %m.y);}xy64 operator (xy64&m){return xy64(x m.x,y m.y);}xy64 operator -(xy64&m){return xy64(x -m.x,y -m.y);}xy64 operator <<(xy64&m){return xy64(x<<m.x,y<<m.y);}xy64 operator >>(xy64&m){return xy64(x>>m.x,y>>m.y);}xy64 operator &(xy64&m){return xy64(x &m.x,y &m.y);}xy64 operator |(xy64&m){return xy64(x |m.x,y |m.y);}xy64 operator ^(xy64&m){return xy64(x ^m.x,y ^m.y);}xy64 operator *=(xy64&m){x *=m.x;y *=m.y;return *this;}xy64 operator /=(xy64&m){x /=m.x;y /=m.y;return *this;}xy64 operator %=(xy64&m){x %=m.x;y %=m.y;return *this;}xy64 operator =(xy64&m){x =m.x;y =m.y;return *this;}xy64 operator -=(xy64&m){x -=m.x;y -=m.y;return *this;}xy64 operator <<=(xy64&m){x<<=m.x;y<<=m.y;return *this;}xy64 operator >>=(xy64&m){x>>=m.x;y>>=m.y;return *this;}xy64 operator &=(xy64&m){x &=m.x;y &=m.y;return *this;}xy64 operator |=(xy64&m){x |=m.x;y |=m.y;return *this;}xy64 operator ^=(xy64&m){x ^=m.x;y ^=m.y;return *this;}xy64 operator *(__int64 m){return xy64(x *m,y *m);}xy64 operator /(__int64 m){return xy64(x /m,y /m);}xy64 operator %(__int64 m){return xy64(x %m,y %m);}xy64 operator (__int64 m){return xy64(x m,y m);}xy64 operator -(__int64 m){return xy64(x -m,y -m);}xy64 operator <<(__int64 m){return xy64(x<<m,y<<m);}xy64 operator >>(__int64 m){return xy64(x>>m,y>>m);}xy64 operator &(__int64 m){return xy64(x &m,y &m);}xy64 operator |(__int64 m){return xy64(x |m,y |m);}xy64 operator ^(__int64 m){return xy64(x ^m,y ^m);}xy64 operator *=(__int64 m){x *=m;y *=m;return *this;}xy64 operator /=(__int64 m){x /=m;y /=m;return *this;}xy64 operator %=(__int64 m){x %=m;y %=m;return *this;}xy64 operator =(__int64 m){x =m;y =m;return *this;}xy64 operator -=(__int64 m){x -=m;y -=m;return *this;}xy64 operator <<=(__int64 m){x<<=m;y<<=m;return *this;}xy64 operator >>=(__int64 m){x>>=m;y>>=m;return *this;}xy64 operator &=(__int64 m){x &=m;y &=m;return *this;}xy64 operator |=(__int64 m){x |=m;y |=m;return *this;}xy64 operator ^=(__int64 m){x ^=m;y ^=m;return *this;}bool operator <(xy64&m){return((unsigned(x) <unsigned(m.x))&&(unsigned(y) <unsigned(m.y)));}bool operator >(xy64&m){return((unsigned(x) >unsigned(m.x))&&(unsigned(y) >unsigned(m.y)));}bool operator <=(xy64&m){return((unsigned(x)<=unsigned(m.x))&&(unsigned(y)<=unsigned(m.y)));}bool operator >=(xy64&m){return((unsigned(x)>=unsigned(m.x))&&(unsigned(y)>=unsigned(m.y)));}bool operator ==(xy64&m){return((unsigned(x)==unsigned(m.x))&&(unsigned(y)==unsigned(m.y)));}bool operator <(__int64 m){return((unsigned(x) <unsigned(m))&&(unsigned(y) <unsigned(m)));}bool operator >(__int64 m){return((unsigned(x) >unsigned(m))&&(unsigned(y) >unsigned(m)));}bool operator <=(__int64 m){return((unsigned(x)<=unsigned(m))&&(unsigned(y)<=unsigned(m)));}bool operator >=(__int64 m){return((unsigned(x)>=unsigned(m))&&(unsigned(y)>=unsigned(m)));}bool operator ==(__int64 m){return((unsigned(x)==unsigned(m))&&(unsigned(y)==unsigned(m)));}xy64 operator !(){return xy64( !x, !y);}xy64 operator ~(){return xy64( ~x, ~y);}xy64 operator (){return xy64( x, y);}xy64 operator -(){return xy64( -x, -y);}xy64 get_number(){xy64 m=0;if(x>0)m.x= x;if(x<0)m.x=-x;if(y>0)m.y= y;if(y<0)m.y=-y;return m;}xy64 get_flag(){xy64 m=0;if(x>0)m.x= 1;if(x<0)m.x=-1;if(y>0)m.y= 1;if(y<0)m.y=-1;return m;}__int64 sqrt_xx_yy(){return sqrt(xx_yy());}void x_y(){__int64 v=x;x=y;y=v;}__int64 xx(){return x*x;}__int64 yy(){return y*y;}__int64 xx_yy(){return (x*x y*y);}xy64 operator =(xy64&m){x=m.x;y=m.y;return *this;}xy64 operator =(__int64 m){x=m;y=m;return *this;}xy64 operator (int){xy64 temp=*this; x; y;return temp;}xy64 operator (){x ;y ;return *this;}xy64 operator --(int){xy64 temp=*this;--x;--y;return temp;}xy64 operator --(){x--;y--;return *this;}};void bezier_call(xy64*sa,int sn,__int64 ti,int bit){ if(sn<=1)return; for(int si=0;(si 1)<sn;si )sa[si]=sa[si] (((sa[si 1]-sa[si])*ti)>>bit); bezier_call(sa,sn-1,ti,bit);}int bezier(xy*sa,int sn,xy*da){ xy64 ta[4]; if(1<=sn&&sn<=nof(ta)){}else return 0; xy tnxy=0; for(int si=0;(si 1)<sn;si ){ tnxy =(sa[si 1]-sa[si]).get_number();// abs() } int tn=tnxy.x tnxy.y; if(tn>0){}else return 0; int bit; for(bit=0;(1<<bit)<tn;bit ); tn=1<<bit;///////////// if(bit<=16){}else return 0; const int bit3=bit*3; xy64 sa64[nof(ta)]; for(int i=0;i<sn;i ){ sa64[i]=xy64(sa[i].x,sa[i].y); sa64[i]<<=bit3; }; int dn=0; for(int ti=0;ti<tn;ti ){ for(int i=0;i<sn;i )ta[i]=sa64[i]; bezier_call(ta,sn,ti,bit); xy t(ta[0].x>>bit3,ta[0].y>>bit3); for(int di=0;1;di ){ if(di<dn){ if(t==da[di])break; }else{ da[dn ]=t; break; } } } return dn;}*/void bezier_call(xyf*sa,int sn,float ti_div_tn){ if(sn<=1)return; for(int si=0;(si 1)<sn;si )sa[si]=sa[si] (sa[si 1]-sa[si])*ti_div_tn; bezier_call(sa,sn-1,ti_div_tn);}int bezier(xy*sa,int sn,xy*da){ xyf ta[100]; if(1<=sn&&sn<=nof(ta)){}else return 0; xy tnxy=0; for(int si=0;(si 1)<sn;si ){ tnxy =(sa[si 1]-sa[si]).get_number();// abs() } const int tn=tnxy.x tnxy.y; if(tn==0)return 0; if(sn==2){ return paint_line(sa[0],sa[1],da); } if(sn==3){ xyf a=sa[0]; xyf b=sa[1]; xyf c=sa[2]; xyf a_add=(b-a)/tn; xyf b_add=(c-b)/tn; int dn=0; for(int ti=0;ti<tn;ti ){ xyf tf=a (b-a)*ti/float(tn); a =a_add; b =b_add; xy t(tf.x,tf.y); for(int di=0;1;di ){ if(di<dn){ if(t==da[di])break; }else{ da[dn ]=t; break; } } } return dn; } if(sn==4){ xyf a=sa[0]; xyf b=sa[1]; xyf c=sa[2]; xyf d=sa[3]; xyf a_add=(b-a)/tn; xyf b_add=(c-b)/tn; xyf c_add=(d-c)/tn; int dn=0; for(int ti=0;ti<tn;ti ){ float tt=ti/float(tn); xyf ta=a (b-a)*tt; xyf tb=b (c-b)*tt; xyf tf=ta (tb-ta)*tt; a =a_add; b =b_add; c =c_add; xy t(tf.x,tf.y); for(int di=0;1;di ){ if(di<dn){ if(t==da[di])break; }else{ da[dn ]=t; break; } } } return dn; } int dn=0; for(int ti=0;ti<tn;ti ){ for(int i=0;i<sn;i )ta[i]=sa[i]; bezier_call(ta,sn,ti/float(tn)); xy t(ta[0].x,ta[0].y); for(int di=0;1;di ){ if(di<dn){ if(t==da[di])break; }else{ da[dn ]=t; break; } } } return dn;}const int g=1;void sets(void (*set)(int color,xy*da,int dn,int*wa,xy w),int*wa,int width,int height,xy pos){ xy w(width,height); //for(int n=w.x*w.y,i=0;i<n;i )wa[i]=0; xy wn=w/g; xy wo=wn/2; xy w1=xy(wn.x/4,wn.y/2); xy w2=xy(wn.x*3/4,wn.y/2); xy wr=pos/g; if(wr<wn){ xy da[xymax*xymax]; int dn; //dn=paint_line(wo,wr,da);set(0x008000,da,dn,wa,w); //dn=paint_circle(wo,(wr-wo).sqrt_xx_yy(),da),set(0x008000,da,dn,wa,w); //dn=paint_ellipse(wo,wr,da);set(0x008000,da,dn,wa,w); // dn=fill_line(wo,wr,da,20);set(0x008000,da,dn,wa,w); ////dn=fill_circle(wo,(wr-wo).sqrt_xx_yy(),da),set(0x008000,da,dn,wa,w); // dn=fill_ellipse(wo,wr,da);set(0x008000,da,dn,wa,w); xy sa[]={wo/2,wo,wr}; for(int si=0;(si 1)<=nof(sa);si ){dn=paint_line(sa[si%nof(sa)],sa[(si 1)%nof(sa)],da);set(0x808080,da,dn,wa,w); } dn=bezier(sa,nof(sa),da);set(0x008000,da,dn,wa,w); }}// 妄想扣篮的男人 贝塞尔曲线 知识来源：// 1,九年义务教育// 2,百度百科 贝塞尔曲线// 3,微软文档 PolyBezier struct get_bezier{void get(char(*sa)[1000],int sn){ if(sn<=1)return; for(int si=0;(si 1)<sn;si ){ char a[1000];sprintf(a,"%s",sa[si]); sprintf(sa[si],"(%s (%s-%s)*i_div_n)",a,sa[si 1],a); } get(sa,sn-1);}get_bezier(){ char da[0x1000]; const int sn=4; char sa[sn][1000]; for(int si=0;si<sn;si )sprintf(sa[si],"%c",a si); get(sa,sn); printf("%s\n",*sa);// (a (b-a)*i_div_n)// ((a (b-a)*i_div_n) ((b (c-b)*i_div_n)-(a (b-a)*i_div_n))*i_div_n)// (((a (b-a)*i_div_n) ((b (c-b)*i_div_n)-(a (b-a)*i_div_n))*i_div_n) (((b (c-b)*i_div_n) ((c (d-c)*i_div_n)-(b (c-b)*i_div_n))*i_div_n)-((a (b-a)*i_div_n) ((b (c-b)*i_div_n)-(a (b-a)*i_div_n))*i_div_n))*i_div_n) exit(0);}}//get_bezier;