14-规则曲线的生成

1规则曲线的绘制内容大纲1曲线的参数方程2点生成曲线3线段生成曲线4

复合曲线案例1曲线的参数方程椭圆的参数式:x=x0+acos

y=y0+bsin∈[0°,360°]绘制曲线大部分都采用参数方程椭圆的代数式:x2/a2+y2/b2=1x或y的范围？

1曲线的参数方程

抛物线：x=2pt

y=2pt2

星开线：x=acos3t

y=asin3t圆的渐开线：x=a(cost+tsint)

y=a(sint-tcost)

心脏线：x=acost(1+cost)

y=asint(1+cost)voidStar1(CDC*pDC,intx0,inty0,inta,floatd,COLORREFcolor){intx,y;for(floatt=0;t<=6.3;t=t+d) {x=x0+a*cos(t)*cos(t)*cos(t); y=y0+a*sin(t)*sin(t)*sin(t); pDC->SetPixel(x,y,color); }}a=100d=0.02

星开线2点生成曲线a=100d=0.02voidHeart1(CDC*pDC,intx0,inty0,inta,

floatd,COLORREFcolor){intx,y;for(floatt=0;t<=6.3;t=t+d) {x=x0+a*cos(t)*(1+cos(t)); y=y0+a*sin(t)*(1+cos(t)); pDC->SetPixel(x,y,color); }}

心脏线2点生成曲线voidParabola1(CDC*pDC,intx0,inty0,intp,floatt1,floatt2,floatd,COLORREFcolor){intx,y;for(floatt=t1;t<=t2;t=t+d) {x=x0+2*p*t; y=y0+2*p*t*t; pDC->SetPixel(x,y,color); }}p=30d=0.01t1=-2t2=2

抛物线2点生成曲线a=5d=0.02t1=0t2=30voidInvolute1(CDC*pDC,intx0,inty0,inta,floatt1,floatt2,floatd,COLORREFcolor){intx,y;for(floatt=t1;t<=t2;t=t+d){x=x0+a*(cos(t)+t*sin(t));y=y0+a*(sin(t)-t*cos(t));pDC->SetPixel(x,y,color);}}圆的渐开线2点生成曲线voidEllipse1(CDC*pDC,intx0,inty0,inta,intb,floatd,COLORREFcolor){intx1,y1,x2,y2;

x1=x0+a*cos(0);y1=y0+b*sin(0);for(floatt=d;t<6.3;t=t+d)

{x2=x0+a*cos(t); y2=y0+b*sin(t); Line_DDA(pDC,x1,y1,x2,y2,color);

x1=x2,y1=y2;

}}3线段生成曲线a=80,b=50d=0.1d=0.25d=0.5d=0.05voidStar2(CDC*pDC,intx0,inty0,inta,intd,COLORREFcolor){intx1,y1,x2,y2;

x=x0+a*cos(0)*cos(0)*cos(0);y=y0+a*sin(0)*sin(0)*sin(0);for(floatt=d;t<6.3;t=t+d)

{x=x0+a*cos(t)*cos(t)*cos(t); y=y0+a*sin(t)*sin(t)*sin(t); Line_DDA(pDC,x1,y1,x2,y2,color);

x1=x2,y1=y2;

}}3线段生成曲线3线段生成曲线voidCure(CDC*p,floatx0,floaty0,void(*f)(float[],float&,float&),

floatT[],floatts,floatte,floatd){floatx,y;T[0]=ts;(*f)(T,x,y);p->MoveTo(x0+x,y0+y);for(floatt=ts+d;t<te;t=t+d) {T[0]=t; (*f)(T,x,y); p->LineTo(x0+x,y0+y); }}voidHeart(floatt[],float&x,float&y){x=t[1]*cos(t[0])*(1+cos(t[0]));y=t[1]*sin(t[0])*(1+cos(t[0]));}voidEllipse(floatt[],float&x,float&y){x=t[1]*cos(t[0]);y=t[2]*sin(t[0]);}floatT[5];T[1]=80,Cure(p,100,100,Heart,T,0,6.2,0.1);T[1]=80,T[2]=50,Cure(p,200,100,Ellipse,T,0,6.2,0.1);4复合曲线案例正弦曲线的生成叶片边缘模拟x=sin(y)xy(x0,y0)x=x0+Asin(6.28t)y=y0+Bt

t∈[0,1]AB4复合曲线案例叶片形状的生成xy(x0,y0)x1=x0+Asin(3.14t)y1=y0+Bt

t∈[0,1]ABx2=x0-Asin(3.14t)y2=y0+Btt∈[0,1]A=40B=2004复合曲线案例叶齿形状的生成x1=x0+Asin(6.28t)+Csin(m*3.14t)y1=y0+Btt∈[0,1]x2=x0-Asin(6.28t)-Csin(m*3.14t)y2=y0+Btt∈[0,1]A=40B=200C=5m=204复合曲线案例叶齿形状的生成x1=x0+Asin(6.28t)+C|sin(m*3.14t)|

y1=y0+Btt∈[0,1]x2=x0-Asin(6.28t)-C|sin(m*3.14t)|

y2=y0+Btt∈[0,1]A=40B=200C=5m=204复合曲线案例A=40,B=200C=5,m=20A=50,B=200C=5,m=20A=50,B=200C=10,m=20A=50,B=200C=5,m=10

4复合曲线案例x1=x0+Asin(6.28t-0.5)+Csinm*3.14t)y1=y0+Btt∈[0,1]x2=x0-Asin(6.28t-0.5)-Csin(m*3.14t)y2=y0+Btt∈[0,1]A=50,B=200C=5,m=104复合曲线案例x1=x0+Asin(6.28t-0.5)+Csinm*3.14t)y1=y0+Btt∈[0.2,1]x2=x0-Asin(6.28t-0.5)-Csin(m*3.14t)y2=y0+Btt∈[0.2,1]A=50,B=200C=5,m=104复合曲线案例x1=x0+Asin(6.28t-0.5)+Csinm*3.14t)y1=y0+Btt∈[0.2,1]x2=x0-Asin(6.28t-0.5)-Csin(m*3.14t)y2=y0+Btt∈[0.2,1]起点（x0,y0+0.1B)A=50,B=200C=5,m=104复合曲线案例x1=x0+Asin(6.28t-0.5)+Csinm*3.14t)y1=y0+Btt∈[0.2,1]x2=x0-Asin(6.28t-0.5)-Csin(m*3.14t)y2=y0+Btt∈[0.2,1]起点（x0,y0+0.1B)终点（x0,y2+5)终点（x0,y1+5)A=50,B=200C=5,m=104复合曲线案例x1=x0+Asin(6.28t-0.5)+Csinm*3.14t)y1=y0+Btt∈[0.2,1]x2=x0-Asin(6.28t-0.5)-Csin(m*3.14t)y2=y0+Btt∈[0.2,1]起点（x0,y0+0.1B)终点（x0,y2-20)终点（x0,y1-20)A=50,B=200C=5,m=104复合曲线案例voidLeafE(CDC*p,floatdx,floatdy,inta,intb,intc,intm,floaty1,floaty2){floatx,y;p->MoveTo(dx,dy+y1*b);for(floatt=0.2;t<1;t=t+0.01) {x=dx+a*sin(3.14*t-0.5)+c*fabs(sin(m*3.14*t));y=dy+b*t;p->LineTo