void SContour::ClipEarInto(SMesh *m, int bp, double scaledEps) {
int ap = WRAP(bp-1, l.n),
cp = WRAP(bp+1, l.n);
STriangle tr;
ZERO(&tr);
tr.a = l.elem[ap].p;
tr.b = l.elem[bp].p;
tr.c = l.elem[cp].p;
if(tr.Normal().MagSquared() < scaledEps*scaledEps) {
// A vertex with more than two edges will cause us to generate
// zero-area triangles, which must be culled.
} else {
m->AddTriangle(&tr);
}
// By deleting the point at bp, we may change the ear-ness of the points
// on either side.
l.elem[ap].ear = SPoint::UNKNOWN;
l.elem[cp].ear = SPoint::UNKNOWN;
l.ClearTags();
l.elem[bp].tag = 1;
l.RemoveTagged();
}
//-----------------------------------------------------------------------------
// Export the mesh as an STL file; it should always be vertex-to-vertex and
// not self-intersecting, so not much to do.
//-----------------------------------------------------------------------------
void SolveSpace::ExportMeshAsStlTo(FILE *f, SMesh *sm) {
char str[80];
memset(str, 0, sizeof(str));
strcpy(str, "STL exported mesh");
fwrite(str, 1, 80, f);
DWORD n = sm->l.n;
fwrite(&n, 4, 1, f);
double s = SS.exportScale;
int i;
for(i = 0; i < sm->l.n; i++) {
STriangle *tr = &(sm->l.elem[i]);
Vector n = tr->Normal().WithMagnitude(1);
float w;
w = (float)n.x; fwrite(&w, 4, 1, f);
w = (float)n.y; fwrite(&w, 4, 1, f);
w = (float)n.z; fwrite(&w, 4, 1, f);
w = (float)((tr->a.x)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->a.y)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->a.z)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->b.x)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->b.y)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->b.z)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->c.x)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->c.y)/s); fwrite(&w, 4, 1, f);
w = (float)((tr->c.z)/s); fwrite(&w, 4, 1, f);
fputc(0, f);
fputc(0, f);
}
}
bool SContour::IsEar(int bp, double scaledEps) {
int ap = WRAP(bp-1, l.n),
cp = WRAP(bp+1, l.n);
STriangle tr;
ZERO(&tr);
tr.a = l.elem[ap].p;
tr.b = l.elem[bp].p;
tr.c = l.elem[cp].p;
if((tr.a).Equals(tr.c)) {
// This is two coincident and anti-parallel edges. Zero-area, so
// won't generate a real triangle, but we certainly can clip it.
return true;
}
Vector n = Vector::From(0, 0, -1);
if((tr.Normal()).Dot(n) < scaledEps) {
// This vertex is reflex, or between two collinear edges; either way,
// it's not an ear.
return false;
}
// Accelerate with an axis-aligned bounding box test
Vector maxv = tr.a, minv = tr.a;
(tr.b).MakeMaxMin(&maxv, &minv);
(tr.c).MakeMaxMin(&maxv, &minv);
int i;
for(i = 0; i < l.n; i++) {
if(i == ap || i == bp || i == cp) continue;
Vector p = l.elem[i].p;
if(p.OutsideAndNotOn(maxv, minv)) continue;
// A point on the edge of the triangle is considered to be inside,
// and therefore makes it a non-ear; but a point on the vertex is
// "outside", since that's necessary to make bridges work.
if(p.EqualsExactly(tr.a)) continue;
if(p.EqualsExactly(tr.b)) continue;
if(p.EqualsExactly(tr.c)) continue;
if(tr.ContainsPointProjd(n, p)) {
return false;
}
}
return true;
}
void SolveSpaceUI::MenuAnalyze(int id) {
SS.GW.GroupSelection();
#define gs (SS.GW.gs)
switch(id) {
case GraphicsWindow::MNU_STEP_DIM:
if(gs.constraints == 1 && gs.n == 0) {
Constraint *c = SK.GetConstraint(gs.constraint[0]);
if(c->HasLabel() && !c->reference) {
SS.TW.shown.dimFinish = c->valA;
SS.TW.shown.dimSteps = 10;
SS.TW.shown.dimIsDistance =
(c->type != Constraint::ANGLE) &&
(c->type != Constraint::LENGTH_RATIO) &&
(c->type != Constraint::LENGTH_DIFFERENCE);
SS.TW.shown.constraint = c->h;
SS.TW.shown.screen = TextWindow::SCREEN_STEP_DIMENSION;
// The step params are specified in the text window,
// so force that to be shown.
SS.GW.ForceTextWindowShown();
SS.ScheduleShowTW();
SS.GW.ClearSelection();
} else {
Error("Constraint must have a label, and must not be "
"a reference dimension.");
}
} else {
Error("Bad selection for step dimension; select a constraint.");
}
break;
case GraphicsWindow::MNU_NAKED_EDGES: {
SS.nakedEdges.Clear();
Group *g = SK.GetGroup(SS.GW.activeGroup);
SMesh *m = &(g->displayMesh);
SKdNode *root = SKdNode::From(m);
bool inters, leaks;
root->MakeCertainEdgesInto(&(SS.nakedEdges),
SKdNode::NAKED_OR_SELF_INTER_EDGES, true, &inters, &leaks);
InvalidateGraphics();
const char *intersMsg = inters ?
"The mesh is self-intersecting (NOT okay, invalid)." :
"The mesh is not self-intersecting (okay, valid).";
const char *leaksMsg = leaks ?
"The mesh has naked edges (NOT okay, invalid)." :
"The mesh is watertight (okay, valid).";
std::string cntMsg = ssprintf("\n\nThe model contains %d triangles, from "
"%d surfaces.", g->displayMesh.l.n, g->runningShell.surface.n);
if(SS.nakedEdges.l.n == 0) {
Message("%s\n\n%s\n\nZero problematic edges, good.%s",
intersMsg, leaksMsg, cntMsg.c_str());
} else {
Error("%s\n\n%s\n\n%d problematic edges, bad.%s",
intersMsg, leaksMsg, SS.nakedEdges.l.n, cntMsg.c_str());
}
break;
}
case GraphicsWindow::MNU_INTERFERENCE: {
SS.nakedEdges.Clear();
SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh);
SKdNode *root = SKdNode::From(m);
bool inters, leaks;
root->MakeCertainEdgesInto(&(SS.nakedEdges),
SKdNode::SELF_INTER_EDGES, false, &inters, &leaks);
InvalidateGraphics();
if(inters) {
Error("%d edges interfere with other triangles, bad.",
SS.nakedEdges.l.n);
} else {
Message("The assembly does not interfere, good.");
}
break;
}
case GraphicsWindow::MNU_VOLUME: {
SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh);
double vol = 0;
int i;
for(i = 0; i < m->l.n; i++) {
STriangle tr = m->l.elem[i];
// Translate to place vertex A at (x, y, 0)
Vector trans = Vector::From(tr.a.x, tr.a.y, 0);
tr.a = (tr.a).Minus(trans);
tr.b = (tr.b).Minus(trans);
tr.c = (tr.c).Minus(trans);
// Rotate to place vertex B on the y-axis. Depending on
// whether the triangle is CW or CCW, C is either to the
// right or to the left of the y-axis. This handles the
// sign of our normal.
Vector u = Vector::From(-tr.b.y, tr.b.x, 0);
u = u.WithMagnitude(1);
Vector v = Vector::From(tr.b.x, tr.b.y, 0);
v = v.WithMagnitude(1);
Vector n = Vector::From(0, 0, 1);
tr.a = (tr.a).DotInToCsys(u, v, n);
tr.b = (tr.b).DotInToCsys(u, v, n);
tr.c = (tr.c).DotInToCsys(u, v, n);
n = tr.Normal().WithMagnitude(1);
// Triangles on edge don't contribute
if(fabs(n.z) < LENGTH_EPS) continue;
// The plane has equation p dot n = a dot n
double d = (tr.a).Dot(n);
// nx*x + ny*y + nz*z = d
// nz*z = d - nx*x - ny*y
double A = -n.x/n.z, B = -n.y/n.z, C = d/n.z;
double mac = tr.c.y/tr.c.x, mbc = (tr.c.y - tr.b.y)/tr.c.x;
double xc = tr.c.x, yb = tr.b.y;
// I asked Maple for
// int(int(A*x + B*y +C, y=mac*x..(mbc*x + yb)), x=0..xc);
double integral =
(1.0/3)*(
A*(mbc-mac)+
(1.0/2)*B*(mbc*mbc-mac*mac)
)*(xc*xc*xc)+
(1.0/2)*(A*yb+B*yb*mbc+C*(mbc-mac))*xc*xc+
C*yb*xc+
(1.0/2)*B*yb*yb*xc;
vol += integral;
}
std::string msg = ssprintf("The volume of the solid model is:\n\n"" %.3f %s^3",
vol / pow(SS.MmPerUnit(), 3),
SS.UnitName());
if(SS.viewUnits == SolveSpaceUI::UNIT_MM) {
msg += ssprintf("\n %.2f mL", vol/(10*10*10));
}
msg += "\n\nCurved surfaces have been approximated as triangles.\n"
"This introduces error, typically of around 1%.";
Message("%s", msg.c_str());
break;
}
case GraphicsWindow::MNU_AREA: {
Group *g = SK.GetGroup(SS.GW.activeGroup);
if(g->polyError.how != Group::POLY_GOOD) {
Error("This group does not contain a correctly-formed "
"2d closed area. It is open, not coplanar, or self-"
"intersecting.");
break;
}
SEdgeList sel = {};
g->polyLoops.MakeEdgesInto(&sel);
SPolygon sp = {};
sel.AssemblePolygon(&sp, NULL, true);
sp.normal = sp.ComputeNormal();
sp.FixContourDirections();
double area = sp.SignedArea();
double scale = SS.MmPerUnit();
Message("The area of the region sketched in this group is:\n\n"
" %.3f %s^2\n\n"
"Curves have been approximated as piecewise linear.\n"
"This introduces error, typically of around 1%%.",
area / (scale*scale),
SS.UnitName());
sel.Clear();
sp.Clear();
break;
}
case GraphicsWindow::MNU_SHOW_DOF:
// This works like a normal solve, except that it calculates
// which variables are free/bound at the same time.
SS.GenerateAll(SolveSpaceUI::GENERATE_ALL, true);
break;
case GraphicsWindow::MNU_TRACE_PT:
if(gs.points == 1 && gs.n == 1) {
SS.traced.point = gs.point[0];
SS.GW.ClearSelection();
} else {
Error("Bad selection for trace; select a single point.");
}
break;
case GraphicsWindow::MNU_STOP_TRACING: {
std::string exportFile;
if(GetSaveFile(&exportFile, "", CsvFileFilter)) {
FILE *f = ssfopen(exportFile, "wb");
if(f) {
int i;
SContour *sc = &(SS.traced.path);
for(i = 0; i < sc->l.n; i++) {
Vector p = sc->l.elem[i].p;
double s = SS.exportScale;
fprintf(f, "%.10f, %.10f, %.10f\r\n",
p.x/s, p.y/s, p.z/s);
}
fclose(f);
} else {
Error("Couldn't write to '%s'", exportFile.c_str());
}
}
// Clear the trace, and stop tracing
SS.traced.point = Entity::NO_ENTITY;
SS.traced.path.l.Clear();
InvalidateGraphics();
break;
}
default: oops();
}
}
SBsp3 *SBsp3::Insert(STriangle *tr, SMesh *instead) {
if(!this) {
if(instead) {
if(instead->flipNormal) {
instead->atLeastOneDiscarded = true;
} else {
instead->AddTriangle(tr->meta, tr->a, tr->b, tr->c);
}
return NULL;
}
// Brand new node; so allocate for it, and fill us in.
SBsp3 *r = Alloc();
r->n = (tr->Normal()).WithMagnitude(1);
r->d = (tr->a).Dot(r->n);
r->tri = *tr;
return r;
}
double dt[3] = { (tr->a).Dot(n), (tr->b).Dot(n), (tr->c).Dot(n) };
int inc = 0, posc = 0, negc = 0;
bool isPos[3], isNeg[3], isOn[3];
ZERO(&isPos); ZERO(&isNeg); ZERO(&isOn);
// Count vertices in the plane
for(int i = 0; i < 3; i++) {
if(fabs(dt[i] - d) < LENGTH_EPS) {
inc++;
isOn[i] = true;
} else if(dt[i] > d) {
posc++;
isPos[i] = true;
} else {
negc++;
isNeg[i] = true;
}
}
// All vertices in-plane
if(inc == 3) {
InsertHow(COPLANAR, tr, instead);
return this;
}
// No split required
if(posc == 0 || negc == 0) {
if(inc == 2) {
Vector a, b;
if (!isOn[0]) { a = tr->b; b = tr->c; }
else if(!isOn[1]) { a = tr->c; b = tr->a; }
else if(!isOn[2]) { a = tr->a; b = tr->b; }
else oops();
if(!instead) {
SEdge se = SEdge::From(a, b);
edges = edges->InsertEdge(&se, n, tr->Normal());
}
}
if(posc > 0) {
InsertHow(POS, tr, instead);
} else {
InsertHow(NEG, tr, instead);
}
return this;
}
// The polygon must be split into two pieces, one above, one below.
Vector a, b, c;
if(posc == 1 && negc == 1 && inc == 1) {
bool bpos;
// Standardize so that a is on the plane
if (isOn[0]) { a = tr->a; b = tr->b; c = tr->c; bpos = isPos[1];
} else if(isOn[1]) { a = tr->b; b = tr->c; c = tr->a; bpos = isPos[2];
} else if(isOn[2]) { a = tr->c; b = tr->a; c = tr->b; bpos = isPos[0];
} else oops();
Vector bPc = IntersectionWith(b, c);
STriangle btri = STriangle::From(tr->meta, a, b, bPc);
STriangle ctri = STriangle::From(tr->meta, c, a, bPc);
if(bpos) {
InsertHow(POS, &btri, instead);
InsertHow(NEG, &ctri, instead);
} else {
InsertHow(POS, &ctri, instead);
InsertHow(NEG, &btri, instead);
}
if(!instead) {
SEdge se = SEdge::From(a, bPc);
edges = edges->InsertEdge(&se, n, tr->Normal());
}
return this;
}
if(posc == 2 && negc == 1) {
// Standardize so that a is on one side, and b and c are on the other.
if (isNeg[0]) { a = tr->a; b = tr->b; c = tr->c;
} else if(isNeg[1]) { a = tr->b; b = tr->c; c = tr->a;
} else if(isNeg[2]) { a = tr->c; b = tr->a; c = tr->b;
} else oops();
} else if(posc == 1 && negc == 2) {
if (isPos[0]) { a = tr->a; b = tr->b; c = tr->c;
} else if(isPos[1]) { a = tr->b; b = tr->c; c = tr->a;
} else if(isPos[2]) { a = tr->c; b = tr->a; c = tr->b;
} else oops();
} else oops();
Vector aPb = IntersectionWith(a, b);
Vector cPa = IntersectionWith(c, a);
STriangle alone = STriangle::From(tr->meta, a, aPb, cPa);
Vector quad[4] = { aPb, b, c, cPa };
if(posc == 2 && negc == 1) {
InsertConvexHow(POS, tr->meta, quad, 4, instead);
InsertHow(NEG, &alone, instead);
} else {
InsertConvexHow(NEG, tr->meta, quad, 4, instead);
InsertHow(POS, &alone, instead);
}
if(!instead) {
SEdge se = SEdge::From(aPb, cPa);
edges = edges->InsertEdge(&se, n, alone.Normal());
}
return this;
}
void Group::GenerateDisplayItems(void) {
// This is potentially slow (since we've got to triangulate a shell, or
// to find the emphasized edges for a mesh), so we will run it only
// if its inputs have changed.
if(displayDirty) {
Group *pg = RunningMeshGroup();
if(pg && thisMesh.IsEmpty() && thisShell.IsEmpty()) {
// We don't contribute any new solid model in this group, so our
// display items are identical to the previous group's; which means
// that we can just display those, and stop ourselves from
// recalculating for those every time we get a change in this group.
//
// Note that this can end up recursing multiple times (if multiple
// groups that contribute no solid model exist in sequence), but
// that's okay.
pg->GenerateDisplayItems();
displayMesh.Clear();
displayMesh.MakeFromCopyOf(&(pg->displayMesh));
displayEdges.Clear();
displayOutlines.Clear();
if(SS.GW.showEdges) {
SEdge *se;
SEdgeList *src = &(pg->displayEdges);
for(se = src->l.First(); se; se = src->l.NextAfter(se)) {
displayEdges.l.Add(se);
}
displayOutlines.MakeFromCopyOf(&pg->displayOutlines);
}
} else {
// We do contribute new solid model, so we have to triangulate the
// shell, and edge-find the mesh.
displayMesh.Clear();
runningShell.TriangulateInto(&displayMesh);
STriangle *t;
for(t = runningMesh.l.First(); t; t = runningMesh.l.NextAfter(t)) {
STriangle trn = *t;
Vector n = trn.Normal();
trn.an = n;
trn.bn = n;
trn.cn = n;
displayMesh.AddTriangle(&trn);
}
displayEdges.Clear();
displayOutlines.Clear();
if(SS.GW.showEdges) {
if(runningMesh.l.n > 0) {
// Triangle mesh only; no shell or emphasized edges.
runningMesh.MakeCertainEdgesAndOutlinesInto(
&displayEdges, &displayOutlines, SKdNode::EMPHASIZED_EDGES);
} else {
displayMesh.MakeCertainEdgesAndOutlinesInto(
&displayEdges, &displayOutlines, SKdNode::SHARP_EDGES);
}
}
}
displayDirty = false;
}
}
void SolveSpace::ExportLinesAndMesh(SEdgeList *sel, SBezierList *sbl, SMesh *sm,
Vector u, Vector v, Vector n,
Vector origin, double cameraTan,
VectorFileWriter *out)
{
double s = 1.0 / SS.exportScale;
// Project into the export plane; so when we're done, z doesn't matter,
// and x and y are what goes in the DXF.
SEdge *e;
for(e = sel->l.First(); e; e = sel->l.NextAfter(e)) {
// project into the specified csys, and apply export scale
(e->a) = e->a.InPerspective(u, v, n, origin, cameraTan).ScaledBy(s);
(e->b) = e->b.InPerspective(u, v, n, origin, cameraTan).ScaledBy(s);
}
SBezier *b;
if(sbl) {
for(b = sbl->l.First(); b; b = sbl->l.NextAfter(b)) {
*b = b->InPerspective(u, v, n, origin, cameraTan);
int i;
for(i = 0; i <= b->deg; i++) {
b->ctrl[i] = (b->ctrl[i]).ScaledBy(s);
}
}
}
// If cutter radius compensation is requested, then perform it now
if(fabs(SS.exportOffset) > LENGTH_EPS) {
// assemble those edges into a polygon, and clear the edge list
SPolygon sp;
ZERO(&sp);
sel->AssemblePolygon(&sp, NULL);
sel->Clear();
SPolygon compd;
ZERO(&compd);
sp.normal = Vector::From(0, 0, -1);
sp.FixContourDirections();
sp.OffsetInto(&compd, SS.exportOffset*s);
sp.Clear();
compd.MakeEdgesInto(sel);
compd.Clear();
}
// Now the triangle mesh; project, then build a BSP to perform
// occlusion testing and generated the shaded surfaces.
SMesh smp;
ZERO(&smp);
if(sm) {
Vector l0 = (SS.lightDir[0]).WithMagnitude(1),
l1 = (SS.lightDir[1]).WithMagnitude(1);
STriangle *tr;
for(tr = sm->l.First(); tr; tr = sm->l.NextAfter(tr)) {
STriangle tt = *tr;
tt.a = (tt.a).InPerspective(u, v, n, origin, cameraTan).ScaledBy(s);
tt.b = (tt.b).InPerspective(u, v, n, origin, cameraTan).ScaledBy(s);
tt.c = (tt.c).InPerspective(u, v, n, origin, cameraTan).ScaledBy(s);
// And calculate lighting for the triangle
Vector n = tt.Normal().WithMagnitude(1);
double lighting = SS.ambientIntensity +
max(0, (SS.lightIntensity[0])*(n.Dot(l0))) +
max(0, (SS.lightIntensity[1])*(n.Dot(l1)));
double r = min(1, REDf (tt.meta.color)*lighting),
g = min(1, GREENf(tt.meta.color)*lighting),
b = min(1, BLUEf (tt.meta.color)*lighting);
tt.meta.color = RGBf(r, g, b);
smp.AddTriangle(&tt);
}
}
// Use the BSP routines to generate the split triangles in paint order.
SBsp3 *bsp = SBsp3::FromMesh(&smp);
SMesh sms;
ZERO(&sms);
bsp->GenerateInPaintOrder(&sms);
// And cull the back-facing triangles
STriangle *tr;
sms.l.ClearTags();
for(tr = sms.l.First(); tr; tr = sms.l.NextAfter(tr)) {
Vector n = tr->Normal();
if(n.z < 0) {
tr->tag = 1;
}
}
sms.l.RemoveTagged();
// And now we perform hidden line removal if requested
SEdgeList hlrd;
ZERO(&hlrd);
if(sm && !SS.GW.showHdnLines) {
SKdNode *root = SKdNode::From(&smp);
// Generate the edges where a curved surface turns from front-facing
// to back-facing.
if(SS.GW.showEdges) {
root->MakeCertainEdgesInto(sel, SKdNode::TURNING_EDGES,
false, NULL, NULL);
}
root->ClearTags();
int cnt = 1234;
SEdge *se;
for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) {
if(se->auxA == Style::CONSTRAINT) {
// Constraints should not get hidden line removed; they're
// always on top.
hlrd.AddEdge(se->a, se->b, se->auxA);
continue;
}
SEdgeList out;
ZERO(&out);
// Split the original edge against the mesh
out.AddEdge(se->a, se->b, se->auxA);
root->OcclusionTestLine(*se, &out, cnt);
// the occlusion test splits unnecessarily; so fix those
out.MergeCollinearSegments(se->a, se->b);
cnt++;
// And add the results to our output
SEdge *sen;
for(sen = out.l.First(); sen; sen = out.l.NextAfter(sen)) {
hlrd.AddEdge(sen->a, sen->b, sen->auxA);
}
out.Clear();
}
sel = &hlrd;
}
// We kept the line segments and Beziers separate until now; but put them
// all together, and also project everything into the xy plane, since not
// all export targets ignore the z component of the points.
for(e = sel->l.First(); e; e = sel->l.NextAfter(e)) {
SBezier sb = SBezier::From(e->a, e->b);
sb.auxA = e->auxA;
sbl->l.Add(&sb);
}
for(b = sbl->l.First(); b; b = sbl->l.NextAfter(b)) {
for(int i = 0; i <= b->deg; i++) {
b->ctrl[i].z = 0;
}
}
// If possible, then we will assemble these output curves into loops. They
// will then get exported as closed paths.
SBezierLoopSetSet sblss;
ZERO(&sblss);
SBezierList leftovers;
ZERO(&leftovers);
SSurface srf = SSurface::FromPlane(Vector::From(0, 0, 0),
Vector::From(1, 0, 0),
Vector::From(0, 1, 0));
SPolygon spxyz;
ZERO(&spxyz);
bool allClosed;
SEdge notClosedAt;
sbl->l.ClearTags();
sblss.FindOuterFacesFrom(sbl, &spxyz, &srf,
SS.ChordTolMm()*s,
&allClosed, ¬ClosedAt,
NULL, NULL,
&leftovers);
for(b = leftovers.l.First(); b; b = leftovers.l.NextAfter(b)) {
sblss.AddOpenPath(b);
}
// Now write the lines and triangles to the output file
out->Output(&sblss, &sms);
leftovers.Clear();
spxyz.Clear();
sblss.Clear();
smp.Clear();
sms.Clear();
hlrd.Clear();
}