C++ RS_VectorSolutions::move方法代码示例

/**
  *find the tangential points from a given point, i.e., the tangent lines should pass
  * the given point and tangential points
  *
  *Author: Dongxu Li
  */
RS_VectorSolutions RS_Ellipse::getTangentPoint(const RS_Vector& point) const {
    RS_Vector point2(point);
    point2.move(-getCenter());
    RS_Vector aV(-getAngle());
    point2.rotate(aV);
    RS_VectorSolutions sol;
    double a=getMajorRadius();
    if(a<RS_TOLERANCE || getRatio()<RS_TOLERANCE) return sol;
    RS_Circle c(NULL, RS_CircleData(RS_Vector(0.,0.),a));
    point2.y /=getRatio();
    sol=c.getTangentPoint(point2);
    sol.scale(RS_Vector(1.,getRatio()));
    aV.y *= -1.;
    sol.rotate(aV);
    sol.move(getCenter());
    return sol;
}

RS_VectorSolutions RS_Information::getIntersectionEllipseEllipse(RS_Ellipse* e1, RS_Ellipse* e2) {
    RS_VectorSolutions ret;

    if (e1==NULL || e2==NULL ) {
        return ret;
    }
    if (
        (e1->getCenter() - e2 -> getCenter() ).magnitude() < RS_TOLERANCE &&
        ( e1->getMajorP() - e2 ->getMajorP()).magnitude() < RS_TOLERANCE &&
        fabs(e1->getMajorRadius() - e2 ->getMajorRadius()) < RS_TOLERANCE &&
        fabs(e1->getMinorRadius() - e2 ->getMinorRadius()) < RS_TOLERANCE
    ) { // overlapped ellipses, do not do overlap
        return ret;
    }

    RS_Ellipse *e01= ( RS_Ellipse *) e1->clone();
    if( e01->getMajorRadius() < e01->getMinorRadius() ) e01->switchMajorMinor();
    RS_Ellipse *e02= ( RS_Ellipse *) e2->clone();
    if( e02->getMajorRadius() < e02->getMinorRadius() ) e02->switchMajorMinor();
    //transform ellipse2 to ellipse1's coordinates
    RS_Vector shiftc1=- e01->getCenter();
    double shifta1=-e01->getAngle();
    e02->move(shiftc1);
    e02->rotate(shifta1);
    RS_Vector majorP2=e02->getMajorP();
    double a1=e01->getMajorRadius();
    double b1=e01->getMinorRadius();
    double x2=e02->getCenter().x,
           y2=e02->getCenter().y;
    double a2=e02->getMajorRadius();
    double b2=e02->getMinorRadius();

    if( e01->getMinorRadius() < RS_TOLERANCE || e01 -> getRatio()< RS_TOLERANCE) {
        // treate e01 as a line
        RS_LineData ldata0(RS_Vector(-a1,0.),RS_Vector(a1,0.));
        RS_Line *l0=new RS_Line(e1->getParent(),ldata0);
        ret= getIntersectionLineEllipse(l0, e02);
        ret.rotate(-shifta1);
        ret.move(-shiftc1);
        return ret;
    }
    if( e02->getMinorRadius() < RS_TOLERANCE || e02 -> getRatio()< RS_TOLERANCE) {
        // treate e02 as a line
        RS_LineData ldata0(RS_Vector(-a2,0.),RS_Vector(a2,0.));
        RS_Line *l0=new RS_Line(e1->getParent(),ldata0);
        l0->rotate(RS_Vector(0.,0.),e02->getAngle());
        l0->move(e02->getCenter());
        ret= getIntersectionLineEllipse(l0, e01);
        ret.rotate(-shifta1);
        ret.move(-shiftc1);
        return ret;
    }

    //ellipse01 equation:
    //	x^2/(a1^2) + y^2/(b1^2) - 1 =0
    double t2= - e02->getAngle();
    //ellipse2 equation:
    // ( (x - u) cos(t) - (y - v) sin(t))^2/a^2 + ( (x - u) sin(t) + (y-v) cos(t))^2/b^2 =1
    // ( cos^2/a^2 + sin^2/b^2) x^2 +
    // ( sin^2/a^2 + cos^2/b^2) y^2 +
    //  2 sin cos (1/b^2 - 1/a^2) x y +
    //  ( ( 2 v sin cos - 2 u cos^2)/a^2 - ( 2v sin cos + 2 u sin^2)/b^2) x +
    //  ( ( 2 u sin cos - 2 v sin^2)/a^2 - ( 2u sin cos + 2 v cos^2)/b^2) y +
    //  (u cos - v sin)^2/a^2 + (u sin + v cos)^2/b^2 -1 =0
    // detect whether any ellipse radius is zero
    double cs=cos(t2),si=sin(t2);
    double ucs=x2*cs,usi=x2*si,
           vcs=y2*cs,vsi=y2*si;
    double cs2=cs*cs,si2=1-cs2;
    double tcssi=2.*cs*si;
    double ia2=1./(a2*a2),ib2=1./(b2*b2);
//    std::cout<<"e1: x^2/("<<a1<<")^2+y^2/("<<b1<<")^2-1 =0\n";
//    std::cout<<"e2: ( (x-("<<x2<<"))*("<<cs<<")-(y-("<<y2<<"))*("<<si<<"))^2/"<<a2<<"^2+( ( x - ("<<x2<<"))*("<<si<<")+(y-("<<y2<<"))*("<<cs<<"))^2/"<<b2<<"^2 -1 =0\n";
    double mc1=(ucs - vsi)*(ucs-vsi)*ia2+(usi+vcs)*(usi+vcs)*ib2 -1.;
    double mb10= ( y2*tcssi - 2.*x2*cs2)*ia2 - ( y2*tcssi+2*x2*si2)*ib2; //x
    double mb11= ( x2*tcssi - 2.*y2*si2)*ia2 - ( x2*tcssi+2*y2*cs2)*ib2; //y
    double ma100= cs2*ia2 + si2*ib2; // x^2
    double ma101= cs*si*(ib2 - ia2); // xy term is 2*ma101*x*y
    double ma111= si2*ia2 + cs2*ib2; // y^2
    double ma000= 1./(a1*a1),ma011=1./(b1*b1);
//    std::cout<<"simplified e1: "<<ma000<<"*x^2 + "<<ma011<<"*y^2 -1 =0\n";
//    std::cout<<"simplified e2: "<<ma100<<"*x^2 + 2*("<<ma101<<")*x*y + "<<ma111<<"*y^2 "<<" + ("<<mb10<<")*x + ("<<mb11<<")*y + ("<<mc1<<") =0\n";
    // construct the Bezout determinant
    double v0=2.*ma000*ma101;
    double v2=ma000*mb10;
    double v3=ma000*mb11;
    double v4=ma000*mc1+ma100;
    //double v5= 2.*ma101*ma011;
    //double v6= ma000*ma111;
    //double v7= 2.*ma101;
    double v8= 2.*ma011*mb10;
    //double v9= ma100*ma011;
    double v1=ma000*ma111-ma100*ma011;
    //double v1= v6 - v9;
    double u0 = v4*v4-v2*mb10;
    double u1 = 2.*(v3*v4-v0*mb10);
    double u2 = 2.*(v4*v1-ma101*v0)+v3*v3+0.5*v2*v8;
    double u3 = v0*v8+2.*v3*v1;
    double u4 = v1*v1+2.*ma101*ma011*v0;
    //std::cout<<"u0="<<u0<<"\tu1="<<u1<<"\tu2="<<u2<<"\tu3="<<u3<<"\tu4="<<u4<<std::endl;
//.........这里部分代码省略.........

RS_VectorSolutions RS_Information::getIntersectionEllipseEllipse(
		RS_Ellipse const* e1, RS_Ellipse const* e2) {
    RS_VectorSolutions ret;

	if (!(e1 && e2) ) {
        return ret;
    }
    if (
        (e1->getCenter() - e2 ->getCenter()).squared() < RS_TOLERANCE2 &&
        (e1->getMajorP() - e2 ->getMajorP()).squared() < RS_TOLERANCE2 &&
        fabs(e1->getRatio() - e2 ->getRatio()) < RS_TOLERANCE
    ) { // overlapped ellipses, do not do overlap
        return ret;
    }
	RS_Ellipse ellipse01(nullptr,e1->getData());

    RS_Ellipse *e01= & ellipse01;
    if( e01->getMajorRadius() < e01->getMinorRadius() ) e01->switchMajorMinor();
	RS_Ellipse ellipse02(nullptr,e2->getData());
    RS_Ellipse *e02= &ellipse02;
    if( e02->getMajorRadius() < e02->getMinorRadius() ) e02->switchMajorMinor();
    //transform ellipse2 to ellipse1's coordinates
    RS_Vector shiftc1=- e01->getCenter();
    double shifta1=-e01->getAngle();
    e02->move(shiftc1);
    e02->rotate(shifta1);
//    RS_Vector majorP2=e02->getMajorP();
    double a1=e01->getMajorRadius();
    double b1=e01->getMinorRadius();
    double x2=e02->getCenter().x,
           y2=e02->getCenter().y;
    double a2=e02->getMajorRadius();
    double b2=e02->getMinorRadius();

    if( e01->getMinorRadius() < RS_TOLERANCE || e01 -> getRatio()< RS_TOLERANCE) {
        // treate e01 as a line
		RS_Line *l0=new RS_Line{e1->getParent(), {{-a1,0.}, {a1,0.}}};
        ret= getIntersectionEllipseLine(l0, e02);
        ret.rotate(-shifta1);
        ret.move(-shiftc1);
        return ret;
    }
    if( e02->getMinorRadius() < RS_TOLERANCE || e02 -> getRatio()< RS_TOLERANCE) {
        // treate e02 as a line
		RS_Line *l0=new RS_Line{e1->getParent(), {{-a2,0.}, {a2,0.}}};
		l0->rotate({0.,0.}, e02->getAngle());
        l0->move(e02->getCenter());
        ret= getIntersectionEllipseLine(l0, e01);
        ret.rotate(-shifta1);
        ret.move(-shiftc1);
        return ret;
    }

    //ellipse01 equation:
    //	x^2/(a1^2) + y^2/(b1^2) - 1 =0
    double t2= - e02->getAngle();
    //ellipse2 equation:
    // ( (x - u) cos(t) - (y - v) sin(t))^2/a^2 + ( (x - u) sin(t) + (y-v) cos(t))^2/b^2 =1
    // ( cos^2/a^2 + sin^2/b^2) x^2 +
    // ( sin^2/a^2 + cos^2/b^2) y^2 +
    //  2 sin cos (1/b^2 - 1/a^2) x y +
    //  ( ( 2 v sin cos - 2 u cos^2)/a^2 - ( 2v sin cos + 2 u sin^2)/b^2) x +
    //  ( ( 2 u sin cos - 2 v sin^2)/a^2 - ( 2u sin cos + 2 v cos^2)/b^2) y +
    //  (u cos - v sin)^2/a^2 + (u sin + v cos)^2/b^2 -1 =0
    // detect whether any ellipse radius is zero
    double cs=cos(t2),si=sin(t2);
    double ucs=x2*cs,usi=x2*si,
           vcs=y2*cs,vsi=y2*si;
    double cs2=cs*cs,si2=1-cs2;
    double tcssi=2.*cs*si;
    double ia2=1./(a2*a2),ib2=1./(b2*b2);
    std::vector<double> m(0,0.);
    m.push_back( 1./(a1*a1)); //ma000
    m.push_back( 1./(b1*b1)); //ma011
    m.push_back(cs2*ia2 + si2*ib2); //ma100
    m.push_back(cs*si*(ib2 - ia2)); //ma101
    m.push_back(si2*ia2 + cs2*ib2); //ma111
    m.push_back(( y2*tcssi - 2.*x2*cs2)*ia2 - ( y2*tcssi+2*x2*si2)*ib2); //mb10
    m.push_back( ( x2*tcssi - 2.*y2*si2)*ia2 - ( x2*tcssi+2*y2*cs2)*ib2); //mb11
    m.push_back((ucs - vsi)*(ucs-vsi)*ia2+(usi+vcs)*(usi+vcs)*ib2 -1.); //mc1
	auto vs0=RS_Math::simultaneousQuadraticSolver(m);
    shifta1 = - shifta1;
    shiftc1 = - shiftc1;
	for(RS_Vector vp: vs0){
        vp.rotate(shifta1);
        vp.move(shiftc1);
        ret.push_back(vp);
    }
    return ret;
}