void SSurface::TriangulateInto(SShell *shell, SMesh *sm) {
SEdgeList el = {};
MakeEdgesInto(shell, &el, AS_UV);
SPolygon poly = {};
if(el.AssemblePolygon(&poly, NULL, true)) {
int i, start = sm->l.n;
if(degm == 1 && degn == 1) {
// A surface with curvature along one direction only; so
// choose the triangulation with chords that lie as much
// as possible within the surface. And since the trim curves
// have been pwl'd to within the desired chord tol, that will
// produce a surface good to within roughly that tol.
//
// If this is just a plane (degree (1, 1)) then the triangulation
// code will notice that, and not bother checking chord tols.
poly.UvTriangulateInto(sm, this);
} else {
// A surface with compound curvature. So we must overlay a
// two-dimensional grid, and triangulate around that.
poly.UvGridTriangulateInto(sm, this);
}
STriMeta meta = { face, color };
for(i = start; i < sm->l.n; i++) {
STriangle *st = &(sm->l.elem[i]);
st->meta = meta;
st->an = NormalAt(st->a.x, st->a.y);
st->bn = NormalAt(st->b.x, st->b.y);
st->cn = NormalAt(st->c.x, st->c.y);
st->a = PointAt(st->a.x, st->a.y);
st->b = PointAt(st->b.x, st->b.y);
st->c = PointAt(st->c.x, st->c.y);
// Works out that my chosen contour direction is inconsistent with
// the triangle direction, sigh.
st->FlipNormal();
}
} else {
dbp("failed to assemble polygon to trim nurbs surface in uv space");
}
el.Clear();
poly.Clear();
}
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();
}
}
void SPolygon::UvGridTriangulateInto(SMesh *mesh, SSurface *srf) {
SEdgeList orig;
ZERO(&orig);
MakeEdgesInto(&orig);
SEdgeList holes;
ZERO(&holes);
normal = Vector::From(0, 0, 1);
FixContourDirections();
// Build a rectangular grid, with horizontal and vertical lines in the
// uv plane. The spacing of these lines is adaptive, so calculate that.
List<double> li, lj;
ZERO(&li);
ZERO(&lj);
double v = 0;
li.Add(&v);
srf->MakeTriangulationGridInto(&li, 0, 1, true);
lj.Add(&v);
srf->MakeTriangulationGridInto(&lj, 0, 1, false);
// Now iterate over each quad in the grid. If it's outside the polygon,
// or if it intersects the polygon, then we discard it. Otherwise we
// generate two triangles in the mesh, and cut it out of our polygon.
int i, j;
for(i = 0; i < (li.n - 1); i++) {
for(j = 0; j < (lj.n - 1); j++) {
double us = li.elem[i], uf = li.elem[i+1],
vs = lj.elem[j], vf = lj.elem[j+1];
Vector a = Vector::From(us, vs, 0),
b = Vector::From(us, vf, 0),
c = Vector::From(uf, vf, 0),
d = Vector::From(uf, vs, 0);
if(orig.AnyEdgeCrossings(a, b, NULL) ||
orig.AnyEdgeCrossings(b, c, NULL) ||
orig.AnyEdgeCrossings(c, d, NULL) ||
orig.AnyEdgeCrossings(d, a, NULL))
{
continue;
}
// There's no intersections, so it doesn't matter which point
// we decide to test.
if(!this->ContainsPoint(a)) {
continue;
}
// Add the quad to our mesh
STriangle tr;
ZERO(&tr);
tr.a = a;
tr.b = b;
tr.c = c;
mesh->AddTriangle(&tr);
tr.a = a;
tr.b = c;
tr.c = d;
mesh->AddTriangle(&tr);
holes.AddEdge(a, b);
holes.AddEdge(b, c);
holes.AddEdge(c, d);
holes.AddEdge(d, a);
}
}
holes.CullExtraneousEdges();
SPolygon hp;
ZERO(&hp);
holes.AssemblePolygon(&hp, NULL, true);
SContour *sc;
for(sc = hp.l.First(); sc; sc = hp.l.NextAfter(sc)) {
l.Add(sc);
}
orig.Clear();
holes.Clear();
li.Clear();
lj.Clear();
hp.l.Clear();
UvTriangulateInto(mesh, srf);
}
