C++ Point2d::Plus方法代码示例

void SSurface::EdgeNormalsWithinSurface(Point2d auv, Point2d buv,
                                        Vector *pt,
                                        Vector *enin, Vector *enout,
                                        Vector *surfn,
                                        uint32_t auxA,
                                        SShell *shell, SShell *sha, SShell *shb)
{
    // the midpoint of the edge
    Point2d muv  = (auv.Plus(buv)).ScaledBy(0.5);

    *pt    = PointAt(muv);

    // If this edge just approximates a curve, then refine our midpoint so
    // so that it actually lies on that curve too. Otherwise stuff like
    // point-on-face tests will fail, since the point won't actually lie
    // on the other face.
    hSCurve hc = { auxA };
    SCurve *sc = shell->curve.FindById(hc);
    if(sc->isExact && sc->exact.deg != 1) {
        double t;
        sc->exact.ClosestPointTo(*pt, &t, false);
        *pt = sc->exact.PointAt(t);
        ClosestPointTo(*pt, &muv);
    } else if(!sc->isExact) {
        SSurface *trimmedA = sc->GetSurfaceA(sha, shb),
                 *trimmedB = sc->GetSurfaceB(sha, shb);
        *pt = trimmedA->ClosestPointOnThisAndSurface(trimmedB, *pt);
        ClosestPointTo(*pt, &muv);
    }

    *surfn = NormalAt(muv.x, muv.y);

    // Compute the edge's inner normal in xyz space.
    Vector ab    = (PointAt(auv)).Minus(PointAt(buv)),
           enxyz = (ab.Cross(*surfn)).WithMagnitude(SS.ChordTolMm());
    // And based on that, compute the edge's inner normal in uv space. This
    // vector is perpendicular to the edge in xyz, but not necessarily in uv.
    Vector tu, tv;
    TangentsAt(muv.x, muv.y, &tu, &tv);
    Point2d enuv;
    enuv.x = enxyz.Dot(tu) / tu.MagSquared();
    enuv.y = enxyz.Dot(tv) / tv.MagSquared();

    // Compute the inner and outer normals of this edge (within the srf),
    // in xyz space. These are not necessarily antiparallel, if the
    // surface is curved.
    Vector pin   = PointAt(muv.Minus(enuv)),
           pout  = PointAt(muv.Plus(enuv));
    *enin  = pin.Minus(*pt),
    *enout = pout.Minus(*pt);
}

double Point2d::DistanceToLine(Point2d p0, Point2d dp, bool segment) {
    double m = dp.x*dp.x + dp.y*dp.y;
    if(m < LENGTH_EPS*LENGTH_EPS) return VERY_POSITIVE;
   
    // Let our line be p = p0 + t*dp, for a scalar t from 0 to 1
    double t = (dp.x*(x - p0.x) + dp.y*(y - p0.y))/m;

    if((t < 0 || t > 1) && segment) {
        // The closest point is one of the endpoints; determine which.
        double d0 = DistanceTo(p0);
        double d1 = DistanceTo(p0.Plus(dp));

        return min(d1, d0);
    } else {
        Point2d closest = p0.Plus(dp.ScaledBy(t));
        return DistanceTo(closest);
    }
}

//-----------------------------------------------------------------------------
// Find all points where a line through a and b intersects our surface, and
// add them to the list. If seg is true then report only intersections that
// lie within the finite line segment (not including the endpoints); otherwise
// we work along the infinite line. And we report either just intersections
// inside the trim curve, or any intersection with u, v in [0, 1]. And we
// either disregard or report tangent points.
//-----------------------------------------------------------------------------
void SSurface::AllPointsIntersecting(Vector a, Vector b,
                                     List<SInter> *l,
                                     bool seg, bool trimmed, bool inclTangent)
{
    if(LineEntirelyOutsideBbox(a, b, seg)) return;

    Vector ba = b.Minus(a);
    double bam = ba.Magnitude();

    List<Inter> inters;
    ZERO(&inters);

    // All the intersections between the line and the surface; either special
    // cases that we can quickly solve in closed form, or general numerical.
    Vector center, axis, start, finish;
    double radius;
    if(degm == 1 && degn == 1) {
        // Against a plane, easy.
        Vector n = NormalAt(0, 0).WithMagnitude(1);
        double d = n.Dot(PointAt(0, 0));
        // Trim to line segment now if requested, don't generate points that
        // would just get discarded later.
        if(!seg ||
           (n.Dot(a) > d + LENGTH_EPS && n.Dot(b) < d - LENGTH_EPS) ||
           (n.Dot(b) > d + LENGTH_EPS && n.Dot(a) < d - LENGTH_EPS))
        {
            Vector p = Vector::AtIntersectionOfPlaneAndLine(n, d, a, b, NULL);
            Inter inter;
            ClosestPointTo(p, &(inter.p.x), &(inter.p.y));
            inters.Add(&inter);
        }
    } else if(IsCylinder(&axis, &center, &radius, &start, &finish)) {
        // This one can be solved in closed form too.
        Vector ab = b.Minus(a);
        if(axis.Cross(ab).Magnitude() < LENGTH_EPS) {
            // edge is parallel to axis of cylinder, no intersection points
            return;
        }
        // A coordinate system centered at the center of the circle, with
        // the edge under test horizontal
        Vector u, v, n = axis.WithMagnitude(1);
        u = (ab.Minus(n.ScaledBy(ab.Dot(n)))).WithMagnitude(1);
        v = n.Cross(u);
        Point2d ap = (a.Minus(center)).DotInToCsys(u, v, n).ProjectXy(),
                bp = (b.Minus(center)).DotInToCsys(u, v, n).ProjectXy(),
                sp = (start. Minus(center)).DotInToCsys(u, v, n).ProjectXy(),
                fp = (finish.Minus(center)).DotInToCsys(u, v, n).ProjectXy();

        double thetas = atan2(sp.y, sp.x), thetaf = atan2(fp.y, fp.x);

        Point2d ip[2];
        int ip_n = 0;
        if(fabs(fabs(ap.y) - radius) < LENGTH_EPS) {
            // tangent
            if(inclTangent) {
                ip[0] = Point2d::From(0, ap.y);
                ip_n = 1;
            }
        } else if(fabs(ap.y) < radius) {
            // two intersections
            double xint = sqrt(radius*radius - ap.y*ap.y);
            ip[0] = Point2d::From(-xint, ap.y);
            ip[1] = Point2d::From( xint, ap.y);
            ip_n = 2;
        }
        int i;
        for(i = 0; i < ip_n; i++) {
            double t = (ip[i].Minus(ap)).DivPivoting(bp.Minus(ap));
            // This is a point on the circle; but is it on the arc?
            Point2d pp = ap.Plus((bp.Minus(ap)).ScaledBy(t));
            double theta = atan2(pp.y, pp.x);
            double dp = WRAP_SYMMETRIC(theta  - thetas, 2*PI),
                   df = WRAP_SYMMETRIC(thetaf - thetas, 2*PI);
            double tol = LENGTH_EPS/radius;

            if((df > 0 && ((dp < -tol) || (dp > df + tol))) ||
               (df < 0 && ((dp >  tol) || (dp < df - tol))))
            {
                continue;
            }

            Vector p = a.Plus((b.Minus(a)).ScaledBy(t));

            Inter inter;
            ClosestPointTo(p, &(inter.p.x), &(inter.p.y));
            inters.Add(&inter);
        }
    } else {
        // General numerical solution by subdivision, fallback
        int cnt = 0, level = 0;
        AllPointsIntersectingUntrimmed(a, b, &cnt, &level, &inters, seg, this);
    }
//.........这里部分代码省略.........