C++ SSurface::NormalAt方法代码示例

//.........这里部分代码省略.........
                                             ss->ctrl[0][2]);
                    sc.exact.weight[1] = ss->weight[0][1];
                    (sc.exact).MakePwlInto(&(sc.pts));
                    sc.surfA = revs.d[j];
                    sc.surfB = revsp.d[j];

                    hSCurve hcc = curve.AddAndAssignId(&sc);

                    STrimBy stb;
                    stb = STrimBy::EntireCurve(this, hcc, false);
                    (surface.FindById(sc.surfA))->trim.Add(&stb);
                    stb = STrimBy::EntireCurve(this, hcc, true);
                    (surface.FindById(sc.surfB))->trim.Add(&stb);
                }
            }
        }

        hsl.Clear();
    }

    for(i = i0; i < surface.n; i++) {
        SSurface *srf = &(surface.elem[i]);

        // Revolution of a line; this is potentially a plane, which we can
        // rewrite to have degree (1, 1).
        if(srf->degm == 1 && srf->degn == 2) {
            // close start, far start, far finish
            Vector cs, fs, ff;
            double d0, d1;
            d0 = (srf->ctrl[0][0]).DistanceToLine(pt, axis);
            d1 = (srf->ctrl[1][0]).DistanceToLine(pt, axis);

            if(d0 > d1) {
                cs = srf->ctrl[1][0];
                fs = srf->ctrl[0][0];
                ff = srf->ctrl[0][2];
            } else {
                cs = srf->ctrl[0][0];
                fs = srf->ctrl[1][0];
                ff = srf->ctrl[1][2];
            }

            // origin close, origin far
            Vector oc = cs.ClosestPointOnLine(pt, axis),
                   of = fs.ClosestPointOnLine(pt, axis);

            if(oc.Equals(of)) {
                // This is a plane, not a (non-degenerate) cone.
                Vector oldn = srf->NormalAt(0.5, 0.5);

                Vector u = fs.Minus(of), v;

                v = (axis.Cross(u)).WithMagnitude(1);

                double vm = (ff.Minus(of)).Dot(v);
                v = v.ScaledBy(vm);

                srf->degm = 1;
                srf->degn = 1;
                srf->ctrl[0][0] = of;
                srf->ctrl[0][1] = of.Plus(u);
                srf->ctrl[1][0] = of.Plus(v);
                srf->ctrl[1][1] = of.Plus(u).Plus(v);
                srf->weight[0][0] = 1;
                srf->weight[0][1] = 1;
                srf->weight[1][0] = 1;
                srf->weight[1][1] = 1;

                if(oldn.Dot(srf->NormalAt(0.5, 0.5)) < 0) {
                    swap(srf->ctrl[0][0], srf->ctrl[1][0]);
                    swap(srf->ctrl[0][1], srf->ctrl[1][1]);
                }
                continue;
            }

            if(fabs(d0 - d1) < LENGTH_EPS) {
                // This is a cylinder; so transpose it so that we'll recognize
                // it as a surface of extrusion.
                SSurface sn = *srf;

                // Transposing u and v flips the normal, so reverse u to
                // flip it again and put it back where we started.
                sn.degm = 2;
                sn.degn = 1;
                int dm, dn;
                for(dm = 0; dm <= 1; dm++) {
                    for(dn = 0; dn <= 2; dn++) {
                        sn.ctrl  [dn][dm] = srf->ctrl  [1-dm][dn];
                        sn.weight[dn][dm] = srf->weight[1-dm][dn];
                    }
                }

                *srf = sn;
                continue;
            }
        }

    }

}

//-----------------------------------------------------------------------------
// Trim this surface against the specified shell, in the way that's appropriate
// for the specified Boolean operation type (and which operand we are). We
// also need a pointer to the shell that contains our own surface, since that
// contains our original trim curves.
//-----------------------------------------------------------------------------
SSurface SSurface::MakeCopyTrimAgainst(SShell *parent,
                                       SShell *sha, SShell *shb,
                                       SShell *into,
                                       int type)
{
    bool opA = (parent == sha);
    SShell *agnst = opA ? shb : sha;

    SSurface ret;
    // The returned surface is identical, just the trim curves change
    ret = *this;
    ret.trim = {};

    // First, build a list of the existing trim curves; update them to use
    // the split curves.
    STrimBy *stb;
    for(stb = trim.First(); stb; stb = trim.NextAfter(stb)) {
        STrimBy stn = *stb;
        stn.curve = (parent->curve.FindById(stn.curve))->newH;
        ret.trim.Add(&stn);
    }

    if(type == SShell::AS_DIFFERENCE && !opA) {
        // The second operand of a Boolean difference gets turned inside out
        ret.Reverse();
    }

    // Build up our original trim polygon; remember the coordinates could
    // be changed if we just flipped the surface normal, and we are using
    // the split curves (not the original curves).
    SEdgeList orig = {};
    ret.MakeEdgesInto(into, &orig, AS_UV);
    ret.trim.Clear();
    // which means that we can't necessarily use the old BSP...
    SBspUv *origBsp = SBspUv::From(&orig, &ret);

    // And now intersect the other shell against us
    SEdgeList inter = {};

    SSurface *ss;
    for(ss = agnst->surface.First(); ss; ss = agnst->surface.NextAfter(ss)) {
        SCurve *sc;
        for(sc = into->curve.First(); sc; sc = into->curve.NextAfter(sc)) {
            if(sc->source != SCurve::FROM_INTERSECTION) continue;
            if(opA) {
                if(sc->surfA.v != h.v || sc->surfB.v != ss->h.v) continue;
            } else {
                if(sc->surfB.v != h.v || sc->surfA.v != ss->h.v) continue;
            }

            int i;
            for(i = 1; i < sc->pts.n; i++) {
                Vector a = sc->pts.elem[i-1].p,
                       b = sc->pts.elem[i].p;

                Point2d auv, buv;
                ss->ClosestPointTo(a, &(auv.x), &(auv.y));
                ss->ClosestPointTo(b, &(buv.x), &(buv.y));

                int c = (ss->bsp) ? ss->bsp->ClassifyEdge(auv, buv, ss) : SBspUv::OUTSIDE;
                if(c != SBspUv::OUTSIDE) {
                    Vector ta = Vector::From(0, 0, 0);
                    Vector tb = Vector::From(0, 0, 0);
                    ret.ClosestPointTo(a, &(ta.x), &(ta.y));
                    ret.ClosestPointTo(b, &(tb.x), &(tb.y));

                    Vector tn = ret.NormalAt(ta.x, ta.y);
                    Vector sn = ss->NormalAt(auv.x, auv.y);

                    // We are subtracting the portion of our surface that
                    // lies in the shell, so the in-plane edge normal should
                    // point opposite to the surface normal.
                    bool bkwds = true;
                    if((tn.Cross(b.Minus(a))).Dot(sn) < 0) bkwds = !bkwds;
                    if(type == SShell::AS_DIFFERENCE && !opA) bkwds = !bkwds;
                    if(bkwds) {
                        inter.AddEdge(tb, ta, sc->h.v, 1);
                    } else {
                        inter.AddEdge(ta, tb, sc->h.v, 0);
                    }
                }
            }
        }
    }

    // Record all the points where more than two edges join, which I will call
    // the choosing points. If two edges join at a non-choosing point, then
    // they must either both be kept or both be discarded (since that would
    // otherwise create an open contour).
    SPointList choosing = {};
    SEdge *se;
    for(se = orig.l.First(); se; se = orig.l.NextAfter(se)) {
        choosing.IncrementTagFor(se->a);
        choosing.IncrementTagFor(se->b);
//.........这里部分代码省略.........

void SSurface::IntersectAgainst(SSurface *b, SShell *agnstA, SShell *agnstB,
                                SShell *into)
{
    Vector amax, amin, bmax, bmin;
    GetAxisAlignedBounding(&amax, &amin);
    b->GetAxisAlignedBounding(&bmax, &bmin);

    if(Vector::BoundingBoxesDisjoint(amax, amin, bmax, bmin)) {
        // They cannot possibly intersect, no curves to generate
        return;
    }

    Vector alongt, alongb;
    SBezier oft, ofb;
    bool isExtdt = this->IsExtrusion(&oft, &alongt),
         isExtdb =    b->IsExtrusion(&ofb, &alongb);

    if(degm == 1 && degn == 1 && b->degm == 1 && b->degn == 1) {
        // Line-line intersection; it's a plane or nothing.
        Vector na = NormalAt(0, 0).WithMagnitude(1),
               nb = b->NormalAt(0, 0).WithMagnitude(1);
        double da = na.Dot(PointAt(0, 0)),
               db = nb.Dot(b->PointAt(0, 0));

        Vector dl = na.Cross(nb);
        if(dl.Magnitude() < LENGTH_EPS) return; // parallel planes
        dl = dl.WithMagnitude(1);
        Vector p = Vector::AtIntersectionOfPlanes(na, da, nb, db);

        // Trim it to the region 0 <= {u,v} <= 1 for each plane; not strictly
        // necessary, since line will be split and excess edges culled, but
        // this improves speed and robustness.
        int i;
        double tmax = VERY_POSITIVE, tmin = VERY_NEGATIVE;
        for(i = 0; i < 2; i++) {
            SSurface *s = (i == 0) ? this : b;
            Vector tu, tv;
            s->TangentsAt(0, 0, &tu, &tv);

            double up, vp, ud, vd;
            s->ClosestPointTo(p, &up, &vp);
            ud = (dl.Dot(tu)) / tu.MagSquared();
            vd = (dl.Dot(tv)) / tv.MagSquared();

            // so u = up + t*ud
            //    v = vp + t*vd
            if(ud > LENGTH_EPS) {
                tmin = max(tmin, -up/ud);
                tmax = min(tmax, (1 - up)/ud);
            } else if(ud < -LENGTH_EPS) {
                tmax = min(tmax, -up/ud);
                tmin = max(tmin, (1 - up)/ud);
            } else {
                if(up < -LENGTH_EPS || up > 1 + LENGTH_EPS) {
                    // u is constant, and outside [0, 1]
                    tmax = VERY_NEGATIVE;
                }
            }
            if(vd > LENGTH_EPS) {
                tmin = max(tmin, -vp/vd);
                tmax = min(tmax, (1 - vp)/vd);
            } else if(vd < -LENGTH_EPS) {
                tmax = min(tmax, -vp/vd);
                tmin = max(tmin, (1 - vp)/vd);
            } else {
                if(vp < -LENGTH_EPS || vp > 1 + LENGTH_EPS) {
                    // v is constant, and outside [0, 1]
                    tmax = VERY_NEGATIVE;
                }
            }
        }

        if(tmax > tmin + LENGTH_EPS) {
            SBezier bezier = SBezier::From(p.Plus(dl.ScaledBy(tmin)),
                                           p.Plus(dl.ScaledBy(tmax)));
            AddExactIntersectionCurve(&bezier, b, agnstA, agnstB, into);
        }
    } else if((degm == 1 && degn == 1 && isExtdb) ||
              (b->degm == 1 && b->degn == 1 && isExtdt))
    {
        // The intersection between a plane and a surface of extrusion
        SSurface *splane, *sext;
        if(degm == 1 && degn == 1) {
            splane = this;
            sext = b;
        } else {
            splane = b;
            sext = this;
        }

        Vector n = splane->NormalAt(0, 0).WithMagnitude(1), along;
        double d = n.Dot(splane->PointAt(0, 0));
        SBezier bezier;
        (void)sext->IsExtrusion(&bezier, &along);

        if(fabs(n.Dot(along)) < LENGTH_EPS) {
            // Direction of extrusion is parallel to plane; so intersection
            // is zero or more lines. Build a line within the plane, and
            // normal to the direction of extrusion, and intersect that line
            // against the surface; each intersection point corresponds to
//.........这里部分代码省略.........

void Group::GenerateShellAndMesh(void) {
    bool prevBooleanFailed = booleanFailed;
    booleanFailed = false;

    Group *srcg = this;

    thisShell.Clear();
    thisMesh.Clear();
    runningShell.Clear();
    runningMesh.Clear();

    // Don't attempt a lathe or extrusion unless the source section is good:
    // planar and not self-intersecting.
    bool haveSrc = true;
    if(type == EXTRUDE || type == LATHE) {
        Group *src = SK.GetGroup(opA);
        if(src->polyError.how != POLY_GOOD) {
            haveSrc = false;
        }
    }

    if(type == TRANSLATE || type == ROTATE) {
        // A step and repeat gets merged against the group's prevous group,
        // not our own previous group.
        srcg = SK.GetGroup(opA);

        GenerateForStepAndRepeat<SShell>(&(srcg->thisShell), &thisShell);
        GenerateForStepAndRepeat<SMesh> (&(srcg->thisMesh),  &thisMesh);
    } else if(type == EXTRUDE && haveSrc) {
        Group *src = SK.GetGroup(opA);
        Vector translate = Vector::From(h.param(0), h.param(1), h.param(2));

        Vector tbot, ttop;
        if(subtype == ONE_SIDED) {
            tbot = Vector::From(0, 0, 0); ttop = translate.ScaledBy(2);
        } else {
            tbot = translate.ScaledBy(-1); ttop = translate.ScaledBy(1);
        }

        SBezierLoopSetSet *sblss = &(src->bezierLoops);
        SBezierLoopSet *sbls;
        for(sbls = sblss->l.First(); sbls; sbls = sblss->l.NextAfter(sbls)) {
            int is = thisShell.surface.n;
            // Extrude this outer contour (plus its inner contours, if present)
            thisShell.MakeFromExtrusionOf(sbls, tbot, ttop, color);

            // And for any plane faces, annotate the model with the entity for
            // that face, so that the user can select them with the mouse.
            Vector onOrig = sbls->point;
            int i;
            for(i = is; i < thisShell.surface.n; i++) {
                SSurface *ss = &(thisShell.surface.elem[i]);
                hEntity face = Entity::NO_ENTITY;

                Vector p = ss->PointAt(0, 0),
                       n = ss->NormalAt(0, 0).WithMagnitude(1);
                double d = n.Dot(p);

                if(i == is || i == (is + 1)) {
                    // These are the top and bottom of the shell.
                    if(fabs((onOrig.Plus(ttop)).Dot(n) - d) < LENGTH_EPS) {
                        face = Remap(Entity::NO_ENTITY, REMAP_TOP);
                        ss->face = face.v;
                    }
                    if(fabs((onOrig.Plus(tbot)).Dot(n) - d) < LENGTH_EPS) {
                        face = Remap(Entity::NO_ENTITY, REMAP_BOTTOM);
                        ss->face = face.v;
                    }
                    continue;
                }

                // So these are the sides
                if(ss->degm != 1 || ss->degn != 1) continue;

                Entity *e;
                for(e = SK.entity.First(); e; e = SK.entity.NextAfter(e)) {
                    if(e->group.v != opA.v) continue;
                    if(e->type != Entity::LINE_SEGMENT) continue;

                    Vector a = SK.GetEntity(e->point[0])->PointGetNum(),
                           b = SK.GetEntity(e->point[1])->PointGetNum();
                    a = a.Plus(ttop);
                    b = b.Plus(ttop);
                    // Could get taken backwards, so check all cases.
                    if((a.Equals(ss->ctrl[0][0]) && b.Equals(ss->ctrl[1][0])) ||
                       (b.Equals(ss->ctrl[0][0]) && a.Equals(ss->ctrl[1][0])) ||
                       (a.Equals(ss->ctrl[0][1]) && b.Equals(ss->ctrl[1][1])) ||
                       (b.Equals(ss->ctrl[0][1]) && a.Equals(ss->ctrl[1][1])))
                    {
                        face = Remap(e->h, REMAP_LINE_TO_FACE);
                        ss->face = face.v;
                        break;
                    }
                }
            }
        }
    } else if(type == LATHE && haveSrc) {
        Group *src = SK.GetGroup(opA);

        Vector pt   = SK.GetEntity(predef.origin)->PointGetNum(),
//.........这里部分代码省略.........

//-----------------------------------------------------------------------------
// Does the given point lie on our shell? There are many cases; inside and
// outside are obvious, but then there's all the edge-on-edge and edge-on-face
// possibilities.
//
// To calculate, we intersect a ray through p with our shell, and classify
// using the closest intersection point. If the ray hits a surface on edge,
// then just reattempt in a different random direction.
//-----------------------------------------------------------------------------
bool SShell::ClassifyEdge(int *indir, int *outdir,
                          Vector ea, Vector eb,
                          Vector p,
                          Vector edge_n_in, Vector edge_n_out, Vector surf_n)
{
    List<SInter> l;
    ZERO(&l);

    srand(0);

    // First, check for edge-on-edge
    int edge_inters = 0;
    Vector inter_surf_n[2], inter_edge_n[2];
    SSurface *srf;
    for(srf = surface.First(); srf; srf = surface.NextAfter(srf)) {
        if(srf->LineEntirelyOutsideBbox(ea, eb, true)) continue;

        SEdgeList *sel = &(srf->edges);
        SEdge *se;
        for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) {
            if((ea.Equals(se->a) && eb.Equals(se->b)) ||
               (eb.Equals(se->a) && ea.Equals(se->b)) ||
                p.OnLineSegment(se->a, se->b))
            {
                if(edge_inters < 2) {
                    // Edge-on-edge case
                    Point2d pm;
                    srf->ClosestPointTo(p,  &pm, false);
                    // A vector normal to the surface, at the intersection point
                    inter_surf_n[edge_inters] = srf->NormalAt(pm);
                    // A vector normal to the intersecting edge (but within the
                    // intersecting surface) at the intersection point, pointing
                    // out.
                    inter_edge_n[edge_inters] =
                      (inter_surf_n[edge_inters]).Cross((se->b).Minus((se->a)));
                }

                edge_inters++;
            }
        }
    }

    if(edge_inters == 2) {
        // TODO, make this use the appropriate curved normals
        double dotp[2];
        for(int i = 0; i < 2; i++) {
            dotp[i] = edge_n_out.DirectionCosineWith(inter_surf_n[i]);
        }

        if(fabs(dotp[1]) < DOTP_TOL) {
            SWAP(double, dotp[0],         dotp[1]);
            SWAP(Vector, inter_surf_n[0], inter_surf_n[1]);
            SWAP(Vector, inter_edge_n[0], inter_edge_n[1]);
        }

        int coinc = (surf_n.Dot(inter_surf_n[0])) > 0 ? COINC_SAME : COINC_OPP;

        if(fabs(dotp[0]) < DOTP_TOL && fabs(dotp[1]) < DOTP_TOL) {
            // This is actually an edge on face case, just that the face
            // is split into two pieces joining at our edge.
            *indir  = coinc;
            *outdir = coinc;
        } else if(fabs(dotp[0]) < DOTP_TOL && dotp[1] > DOTP_TOL) {
            if(edge_n_out.Dot(inter_edge_n[0]) > 0) {
                *indir  = coinc;
                *outdir = OUTSIDE;
            } else {
                *indir  = INSIDE;
                *outdir = coinc;
            }
        } else if(fabs(dotp[0]) < DOTP_TOL && dotp[1] < -DOTP_TOL) {
            if(edge_n_out.Dot(inter_edge_n[0]) > 0) {
                *indir  = coinc;
                *outdir = INSIDE;
            } else {
                *indir  = OUTSIDE;
                *outdir = coinc;
            }
        } else if(dotp[0] > DOTP_TOL && dotp[1] > DOTP_TOL) {
            *indir  = INSIDE;
            *outdir = OUTSIDE;
        } else if(dotp[0] < -DOTP_TOL && dotp[1] < -DOTP_TOL) {
            *indir  = OUTSIDE;
            *outdir = INSIDE;
        } else {
            // Edge is tangent to the shell at shell's edge, so can't be
            // a boundary of the surface.
            return false;
        }
        return true;
    }
//.........这里部分代码省略.........