2008-04-25 07:04:09 +00:00
|
|
|
#include "solvespace.h"
|
|
|
|
|
2008-05-23 10:05:07 +00:00
|
|
|
Vector STriangle::Normal(void) {
|
|
|
|
Vector ab = b.Minus(a), bc = c.Minus(b);
|
|
|
|
return ab.Cross(bc);
|
|
|
|
}
|
|
|
|
|
2008-07-02 04:32:24 +00:00
|
|
|
double STriangle::MinAltitude(void) {
|
|
|
|
double altA = a.DistanceToLine(b, c.Minus(b)),
|
|
|
|
altB = b.DistanceToLine(c, a.Minus(c)),
|
|
|
|
altC = c.DistanceToLine(a, b.Minus(a));
|
|
|
|
|
|
|
|
return min(altA, min(altB, altC));
|
|
|
|
}
|
|
|
|
|
2008-05-24 10:34:06 +00:00
|
|
|
bool STriangle::ContainsPoint(Vector p) {
|
2008-06-02 03:31:37 +00:00
|
|
|
Vector n = Normal();
|
2008-07-02 04:32:24 +00:00
|
|
|
if(MinAltitude() < LENGTH_EPS) {
|
2008-06-03 18:48:47 +00:00
|
|
|
// shouldn't happen; zero-area triangle
|
|
|
|
return false;
|
|
|
|
}
|
2008-06-02 03:31:37 +00:00
|
|
|
return ContainsPointProjd(n.WithMagnitude(1), p);
|
|
|
|
}
|
|
|
|
|
|
|
|
bool STriangle::ContainsPointProjd(Vector n, Vector p) {
|
2008-05-24 10:34:06 +00:00
|
|
|
Vector ab = b.Minus(a), bc = c.Minus(b), ca = a.Minus(c);
|
|
|
|
|
|
|
|
Vector no_ab = n.Cross(ab);
|
|
|
|
if(no_ab.Dot(p) < no_ab.Dot(a) - LENGTH_EPS) return false;
|
|
|
|
|
|
|
|
Vector no_bc = n.Cross(bc);
|
|
|
|
if(no_bc.Dot(p) < no_bc.Dot(b) - LENGTH_EPS) return false;
|
|
|
|
|
|
|
|
Vector no_ca = n.Cross(ca);
|
|
|
|
if(no_ca.Dot(p) < no_ca.Dot(c) - LENGTH_EPS) return false;
|
|
|
|
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
|
2008-06-06 11:35:28 +00:00
|
|
|
void STriangle::FlipNormal(void) {
|
|
|
|
SWAP(Vector, a, b);
|
2009-01-19 10:37:10 +00:00
|
|
|
SWAP(Vector, an, bn);
|
2008-06-06 11:35:28 +00:00
|
|
|
}
|
|
|
|
|
2008-05-30 06:09:41 +00:00
|
|
|
STriangle STriangle::From(STriMeta meta, Vector a, Vector b, Vector c) {
|
2009-01-19 10:37:10 +00:00
|
|
|
STriangle tr;
|
|
|
|
ZERO(&tr);
|
|
|
|
tr.meta = meta;
|
|
|
|
tr.a = a;
|
|
|
|
tr.b = b;
|
|
|
|
tr.c = c;
|
2008-05-30 06:09:41 +00:00
|
|
|
return tr;
|
|
|
|
}
|
|
|
|
|
2008-05-30 08:01:19 +00:00
|
|
|
SEdge SEdge::From(Vector a, Vector b) {
|
2009-01-25 11:52:29 +00:00
|
|
|
SEdge se = { 0, 0, 0, a, b };
|
2008-05-30 08:01:19 +00:00
|
|
|
return se;
|
|
|
|
}
|
|
|
|
|
2008-05-22 10:28:28 +00:00
|
|
|
void SEdgeList::Clear(void) {
|
|
|
|
l.Clear();
|
|
|
|
}
|
|
|
|
|
2009-01-25 11:52:29 +00:00
|
|
|
void SEdgeList::AddEdge(Vector a, Vector b, int auxA, int auxB) {
|
2008-05-22 10:28:28 +00:00
|
|
|
SEdge e; ZERO(&e);
|
|
|
|
e.a = a;
|
|
|
|
e.b = b;
|
2009-01-25 11:52:29 +00:00
|
|
|
e.auxA = auxA;
|
|
|
|
e.auxB = auxB;
|
2008-05-22 10:28:28 +00:00
|
|
|
l.Add(&e);
|
|
|
|
}
|
|
|
|
|
2009-01-25 09:19:59 +00:00
|
|
|
bool SEdgeList::AssembleContour(Vector first, Vector last, SContour *dest,
|
|
|
|
SEdge *errorAt, bool keepDir)
|
2008-06-21 10:18:20 +00:00
|
|
|
{
|
|
|
|
int i;
|
|
|
|
|
|
|
|
dest->AddPoint(first);
|
|
|
|
dest->AddPoint(last);
|
|
|
|
|
|
|
|
do {
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
SEdge *se = &(l.elem[i]);
|
|
|
|
if(se->tag) continue;
|
|
|
|
|
|
|
|
if(se->a.Equals(last)) {
|
|
|
|
dest->AddPoint(se->b);
|
|
|
|
last = se->b;
|
|
|
|
se->tag = 1;
|
|
|
|
break;
|
|
|
|
}
|
2009-01-25 09:19:59 +00:00
|
|
|
// Don't allow backwards edges if keepDir is true.
|
|
|
|
if(!keepDir && se->b.Equals(last)) {
|
2008-06-21 10:18:20 +00:00
|
|
|
dest->AddPoint(se->a);
|
|
|
|
last = se->a;
|
|
|
|
se->tag = 1;
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if(i >= l.n) {
|
|
|
|
// Couldn't assemble a closed contour; mark where.
|
|
|
|
if(errorAt) {
|
|
|
|
errorAt->a = first;
|
|
|
|
errorAt->b = last;
|
|
|
|
}
|
|
|
|
return false;
|
|
|
|
}
|
|
|
|
|
|
|
|
} while(!last.Equals(first));
|
|
|
|
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
|
2009-01-25 09:19:59 +00:00
|
|
|
bool SEdgeList::AssemblePolygon(SPolygon *dest, SEdge *errorAt, bool keepDir) {
|
2008-04-25 07:04:09 +00:00
|
|
|
dest->Clear();
|
|
|
|
|
2008-07-13 09:57:46 +00:00
|
|
|
bool allClosed = true;
|
2008-04-25 07:04:09 +00:00
|
|
|
for(;;) {
|
|
|
|
Vector first, last;
|
|
|
|
int i;
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
if(!l.elem[i].tag) {
|
|
|
|
first = l.elem[i].a;
|
|
|
|
last = l.elem[i].b;
|
|
|
|
l.elem[i].tag = 1;
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if(i >= l.n) {
|
2008-07-13 09:57:46 +00:00
|
|
|
return allClosed;
|
2008-04-25 07:04:09 +00:00
|
|
|
}
|
|
|
|
|
2008-06-21 10:18:20 +00:00
|
|
|
// Create a new empty contour in our polygon, and finish assembling
|
|
|
|
// into that contour.
|
2008-04-25 07:04:09 +00:00
|
|
|
dest->AddEmptyContour();
|
2009-01-25 09:19:59 +00:00
|
|
|
if(!AssembleContour(first, last, &(dest->l.elem[dest->l.n-1]),
|
|
|
|
errorAt, keepDir))
|
|
|
|
{
|
2008-07-13 09:57:46 +00:00
|
|
|
allClosed = false;
|
2009-01-25 09:19:59 +00:00
|
|
|
}
|
2008-07-13 09:57:46 +00:00
|
|
|
// But continue assembling, even if some of the contours are open
|
2008-04-25 07:04:09 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2009-01-21 05:04:38 +00:00
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// Test if the specified edge crosses any of the edges in our list. Two edges
|
|
|
|
// are not considered to cross if they share an endpoint (within LENGTH_EPS),
|
|
|
|
// but they are considered to cross if they are coincident and overlapping.
|
2009-01-23 03:30:30 +00:00
|
|
|
// If pi is not NULL, then a crossing is returned in that.
|
2009-01-21 05:04:38 +00:00
|
|
|
//-----------------------------------------------------------------------------
|
2009-01-23 03:30:30 +00:00
|
|
|
int SEdgeList::AnyEdgeCrossings(Vector a, Vector b, Vector *ppi) {
|
2009-01-21 05:04:38 +00:00
|
|
|
Vector d = b.Minus(a);
|
|
|
|
double t_eps = LENGTH_EPS/d.Magnitude();
|
|
|
|
|
2009-01-23 03:30:30 +00:00
|
|
|
int cnt = 0;
|
2009-01-21 05:04:38 +00:00
|
|
|
SEdge *se;
|
|
|
|
for(se = l.First(); se; se = l.NextAfter(se)) {
|
2009-01-23 03:30:30 +00:00
|
|
|
double dist_a, dist_b;
|
|
|
|
double t, tse;
|
|
|
|
bool skew;
|
|
|
|
Vector pi;
|
|
|
|
bool inOrEdge0, inOrEdge1;
|
2009-01-21 05:04:38 +00:00
|
|
|
|
|
|
|
Vector dse = (se->b).Minus(se->a);
|
|
|
|
double tse_eps = LENGTH_EPS/dse.Magnitude();
|
|
|
|
|
2009-01-23 03:30:30 +00:00
|
|
|
if(a.Equals(se->a) && b.Equals(se->b)) goto intersects;
|
|
|
|
if(b.Equals(se->a) && a.Equals(se->b)) goto intersects;
|
2009-01-21 05:04:38 +00:00
|
|
|
|
2009-01-23 03:30:30 +00:00
|
|
|
dist_a = (se->a).DistanceToLine(a, d),
|
|
|
|
dist_b = (se->b).DistanceToLine(a, d);
|
2009-01-21 05:04:38 +00:00
|
|
|
|
2009-05-08 08:33:04 +00:00
|
|
|
// Can't just test if dist_a equals dist_b; they could be on opposite
|
|
|
|
// sides, since it's unsigned.
|
|
|
|
double m = sqrt(d.Magnitude()*dse.Magnitude());
|
|
|
|
if(sqrt(fabs(d.Dot(dse))) > (m - LENGTH_EPS)) {
|
2009-01-21 05:04:38 +00:00
|
|
|
// The edges are parallel.
|
|
|
|
if(fabs(dist_a) > LENGTH_EPS) {
|
|
|
|
// and not coincident, so can't be interesecting
|
|
|
|
continue;
|
|
|
|
}
|
|
|
|
// The edges are coincident. Make sure that neither endpoint lies
|
|
|
|
// on the other
|
|
|
|
double t;
|
|
|
|
t = ((se->a).Minus(a)).DivPivoting(d);
|
2009-01-23 03:30:30 +00:00
|
|
|
if(t > t_eps && t < (1 - t_eps)) goto intersects;
|
2009-01-21 05:04:38 +00:00
|
|
|
t = ((se->b).Minus(a)).DivPivoting(d);
|
2009-01-23 03:30:30 +00:00
|
|
|
if(t > t_eps && t < (1 - t_eps)) goto intersects;
|
2009-01-21 05:04:38 +00:00
|
|
|
t = a.Minus(se->a).DivPivoting(dse);
|
2009-01-23 03:30:30 +00:00
|
|
|
if(t > tse_eps && t < (1 - tse_eps)) goto intersects;
|
2009-01-21 05:04:38 +00:00
|
|
|
t = b.Minus(se->a).DivPivoting(dse);
|
2009-01-23 03:30:30 +00:00
|
|
|
if(t > tse_eps && t < (1 - tse_eps)) goto intersects;
|
2009-01-21 05:04:38 +00:00
|
|
|
// So coincident but disjoint, okay.
|
|
|
|
continue;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Lines are not parallel, so look for an intersection.
|
2009-01-23 03:30:30 +00:00
|
|
|
pi = Vector::AtIntersectionOfLines(a, b, se->a, se->b,
|
|
|
|
&skew,
|
|
|
|
&t, &tse);
|
2009-01-21 05:04:38 +00:00
|
|
|
if(skew) continue;
|
|
|
|
|
2009-01-23 03:30:30 +00:00
|
|
|
inOrEdge0 = (t > -t_eps) && (t < (1 + t_eps));
|
|
|
|
inOrEdge1 = (tse > -tse_eps) && (tse < (1 + tse_eps));
|
2009-01-22 10:02:46 +00:00
|
|
|
|
|
|
|
if(inOrEdge0 && inOrEdge1) {
|
|
|
|
if((se->a).Equals(a) || (se->b).Equals(a) ||
|
|
|
|
(se->a).Equals(b) || (se->b).Equals(b))
|
|
|
|
{
|
|
|
|
// Not an intersection if we share an endpoint with an edge
|
|
|
|
continue;
|
|
|
|
}
|
|
|
|
// But it's an intersection if a vertex of one edge lies on the
|
|
|
|
// inside of the other (or if they cross away from either's
|
|
|
|
// vertex).
|
2009-01-23 03:30:30 +00:00
|
|
|
if(ppi) *ppi = pi;
|
|
|
|
goto intersects;
|
2009-01-21 05:04:38 +00:00
|
|
|
}
|
2009-01-23 03:30:30 +00:00
|
|
|
continue;
|
|
|
|
|
|
|
|
intersects:
|
|
|
|
cnt++;
|
|
|
|
// and continue with the loop
|
2009-01-21 05:04:38 +00:00
|
|
|
}
|
2009-01-23 03:30:30 +00:00
|
|
|
return cnt;
|
2009-01-21 05:04:38 +00:00
|
|
|
}
|
|
|
|
|
2009-03-15 23:04:45 +00:00
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// Remove unnecessary edges: if two are anti-parallel then remove both, and if
|
|
|
|
// two are parallel then remove one.
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void SEdgeList::CullExtraneousEdges(void) {
|
|
|
|
l.ClearTags();
|
|
|
|
int i, j;
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
SEdge *se = &(l.elem[i]);
|
|
|
|
for(j = i+1; j < l.n; j++) {
|
|
|
|
SEdge *set = &(l.elem[j]);
|
|
|
|
if((set->a).Equals(se->a) && (set->b).Equals(se->b)) {
|
|
|
|
// Two parallel edges exist; so keep only the first one.
|
|
|
|
set->tag = 1;
|
|
|
|
}
|
|
|
|
if((set->a).Equals(se->b) && (set->b).Equals(se->a)) {
|
|
|
|
// Two anti-parallel edges exist; so keep neither.
|
|
|
|
se->tag = 1;
|
|
|
|
set->tag = 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
l.RemoveTagged();
|
|
|
|
}
|
|
|
|
|
2009-04-08 04:54:07 +00:00
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// We have an edge list that contains only collinear edges, maybe with more
|
|
|
|
// splits than necessary. Merge any collinear segments that join.
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
static Vector LineStart, LineDirection;
|
|
|
|
static int ByTAlongLine(const void *av, const void *bv)
|
|
|
|
{
|
|
|
|
SEdge *a = (SEdge *)av,
|
|
|
|
*b = (SEdge *)bv;
|
|
|
|
|
|
|
|
double ta = (a->a.Minus(LineStart)).DivPivoting(LineDirection),
|
|
|
|
tb = (b->a.Minus(LineStart)).DivPivoting(LineDirection);
|
|
|
|
|
|
|
|
return (ta > tb) ? 1 : -1;
|
|
|
|
}
|
|
|
|
void SEdgeList::MergeCollinearSegments(Vector a, Vector b) {
|
|
|
|
LineStart = a;
|
|
|
|
LineDirection = b.Minus(a);
|
|
|
|
qsort(l.elem, l.n, sizeof(l.elem[0]), ByTAlongLine);
|
|
|
|
|
|
|
|
l.ClearTags();
|
|
|
|
int i;
|
|
|
|
for(i = 1; i < l.n; i++) {
|
|
|
|
SEdge *prev = &(l.elem[i-1]),
|
|
|
|
*now = &(l.elem[i]);
|
|
|
|
|
|
|
|
if((prev->b).Equals(now->a)) {
|
|
|
|
// The previous segment joins up to us; so merge it into us.
|
|
|
|
prev->tag = 1;
|
|
|
|
now->a = prev->a;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
l.RemoveTagged();
|
|
|
|
}
|
|
|
|
|
2009-06-19 07:56:33 +00:00
|
|
|
void SPointList::Clear(void) {
|
|
|
|
l.Clear();
|
|
|
|
}
|
|
|
|
|
|
|
|
bool SPointList::ContainsPoint(Vector pt) {
|
|
|
|
SPoint *p;
|
|
|
|
for(p = l.First(); p; p = l.NextAfter(p)) {
|
|
|
|
if(pt.Equals(p->p)) {
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return false;
|
|
|
|
}
|
|
|
|
|
|
|
|
void SPointList::Add(Vector pt) {
|
|
|
|
SPoint p;
|
|
|
|
ZERO(&p);
|
|
|
|
p.p = pt;
|
|
|
|
l.Add(&p);
|
|
|
|
}
|
|
|
|
|
2008-06-21 10:18:20 +00:00
|
|
|
void SContour::AddPoint(Vector p) {
|
|
|
|
SPoint sp;
|
|
|
|
sp.tag = 0;
|
|
|
|
sp.p = p;
|
|
|
|
|
|
|
|
l.Add(&sp);
|
|
|
|
}
|
|
|
|
|
2008-05-02 10:54:22 +00:00
|
|
|
void SContour::MakeEdgesInto(SEdgeList *el) {
|
|
|
|
int i;
|
|
|
|
for(i = 0; i < (l.n-1); i++) {
|
|
|
|
SEdge e;
|
2008-05-19 09:23:49 +00:00
|
|
|
e.tag = 0;
|
2008-05-02 10:54:22 +00:00
|
|
|
e.a = l.elem[i].p;
|
|
|
|
e.b = l.elem[i+1].p;
|
|
|
|
el->l.Add(&e);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2009-01-21 05:04:38 +00:00
|
|
|
void SContour::CopyInto(SContour *dest) {
|
|
|
|
SPoint *sp;
|
|
|
|
for(sp = l.First(); sp; sp = l.NextAfter(sp)) {
|
|
|
|
dest->AddPoint(sp->p);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2009-01-22 10:02:46 +00:00
|
|
|
void SContour::FindPointWithMinX(void) {
|
|
|
|
SPoint *sp;
|
|
|
|
xminPt = Vector::From(1e10, 1e10, 1e10);
|
|
|
|
for(sp = l.First(); sp; sp = l.NextAfter(sp)) {
|
|
|
|
if(sp->p.x < xminPt.x) {
|
|
|
|
xminPt = sp->p;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2008-05-05 09:47:23 +00:00
|
|
|
Vector SContour::ComputeNormal(void) {
|
2008-06-01 08:45:11 +00:00
|
|
|
Vector n = Vector::From(0, 0, 0);
|
2008-05-05 09:47:23 +00:00
|
|
|
|
|
|
|
for(int i = 0; i < l.n - 2; i++) {
|
|
|
|
Vector u = (l.elem[i+1].p).Minus(l.elem[i+0].p).WithMagnitude(1);
|
|
|
|
Vector v = (l.elem[i+2].p).Minus(l.elem[i+1].p).WithMagnitude(1);
|
|
|
|
Vector nt = u.Cross(v);
|
|
|
|
if(nt.Magnitude() > n.Magnitude()) {
|
|
|
|
n = nt;
|
|
|
|
}
|
|
|
|
}
|
2008-05-19 09:23:49 +00:00
|
|
|
return n.WithMagnitude(1);
|
2008-05-05 09:47:23 +00:00
|
|
|
}
|
|
|
|
|
2009-06-08 16:21:33 +00:00
|
|
|
Vector SContour::AnyEdgeMidpoint(void) {
|
|
|
|
if(l.n < 2) oops();
|
|
|
|
return ((l.elem[0].p).Plus(l.elem[1].p)).ScaledBy(0.5);
|
|
|
|
}
|
|
|
|
|
2008-05-05 09:47:23 +00:00
|
|
|
bool SContour::IsClockwiseProjdToNormal(Vector n) {
|
2008-05-17 06:04:55 +00:00
|
|
|
// Degenerate things might happen as we draw; doesn't really matter
|
|
|
|
// what we do then.
|
|
|
|
if(n.Magnitude() < 0.01) return true;
|
|
|
|
|
2008-05-05 09:47:23 +00:00
|
|
|
// An arbitrary 2d coordinate system that has n as its normal
|
|
|
|
Vector u = n.Normal(0);
|
|
|
|
Vector v = n.Normal(1);
|
|
|
|
|
|
|
|
double area = 0;
|
|
|
|
for(int i = 0; i < (l.n - 1); i++) {
|
|
|
|
double u0 = (l.elem[i ].p).Dot(u);
|
|
|
|
double v0 = (l.elem[i ].p).Dot(v);
|
|
|
|
double u1 = (l.elem[i+1].p).Dot(u);
|
|
|
|
double v1 = (l.elem[i+1].p).Dot(v);
|
|
|
|
|
|
|
|
area += ((v0 + v1)/2)*(u1 - u0);
|
|
|
|
}
|
|
|
|
return (area < 0);
|
|
|
|
}
|
|
|
|
|
|
|
|
bool SContour::ContainsPointProjdToNormal(Vector n, Vector p) {
|
|
|
|
Vector u = n.Normal(0);
|
|
|
|
Vector v = n.Normal(1);
|
|
|
|
|
|
|
|
double up = p.Dot(u);
|
|
|
|
double vp = p.Dot(v);
|
|
|
|
|
|
|
|
bool inside = false;
|
|
|
|
for(int i = 0; i < (l.n - 1); i++) {
|
|
|
|
double ua = (l.elem[i ].p).Dot(u);
|
|
|
|
double va = (l.elem[i ].p).Dot(v);
|
2008-05-19 09:23:49 +00:00
|
|
|
// The curve needs to be exactly closed; approximation is death.
|
|
|
|
double ub = (l.elem[(i+1)%(l.n-1)].p).Dot(u);
|
|
|
|
double vb = (l.elem[(i+1)%(l.n-1)].p).Dot(v);
|
|
|
|
|
|
|
|
if ((((va <= vp) && (vp < vb)) ||
|
|
|
|
((vb <= vp) && (vp < va))) &&
|
|
|
|
(up < (ub - ua) * (vp - va) / (vb - va) + ua))
|
|
|
|
{
|
|
|
|
inside = !inside;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
return inside;
|
|
|
|
}
|
|
|
|
|
2008-06-12 04:36:33 +00:00
|
|
|
bool SContour::AllPointsInPlane(Vector n, double d, Vector *notCoplanarAt) {
|
|
|
|
for(int i = 0; i < l.n; i++) {
|
|
|
|
Vector p = l.elem[i].p;
|
|
|
|
double dd = n.Dot(p) - d;
|
|
|
|
if(fabs(dd) > 10*LENGTH_EPS) {
|
|
|
|
*notCoplanarAt = p;
|
|
|
|
return false;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
|
2008-05-05 09:47:23 +00:00
|
|
|
void SContour::Reverse(void) {
|
2009-01-19 03:33:15 +00:00
|
|
|
l.Reverse();
|
2008-05-05 09:47:23 +00:00
|
|
|
}
|
2008-05-19 09:23:49 +00:00
|
|
|
|
2008-05-22 10:28:28 +00:00
|
|
|
|
|
|
|
void SPolygon::Clear(void) {
|
|
|
|
int i;
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
(l.elem[i]).l.Clear();
|
|
|
|
}
|
|
|
|
l.Clear();
|
|
|
|
}
|
|
|
|
|
|
|
|
void SPolygon::AddEmptyContour(void) {
|
|
|
|
SContour c;
|
|
|
|
memset(&c, 0, sizeof(c));
|
|
|
|
l.Add(&c);
|
|
|
|
}
|
|
|
|
|
|
|
|
void SPolygon::MakeEdgesInto(SEdgeList *el) {
|
|
|
|
int i;
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
(l.elem[i]).MakeEdgesInto(el);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
Vector SPolygon::ComputeNormal(void) {
|
2008-06-01 08:45:11 +00:00
|
|
|
if(l.n < 1) return Vector::From(0, 0, 0);
|
2008-05-22 10:28:28 +00:00
|
|
|
return (l.elem[0]).ComputeNormal();
|
|
|
|
}
|
|
|
|
|
|
|
|
bool SPolygon::ContainsPoint(Vector p) {
|
2008-06-21 10:18:20 +00:00
|
|
|
return (WindingNumberForPoint(p) % 2) == 1;
|
|
|
|
}
|
|
|
|
|
|
|
|
int SPolygon::WindingNumberForPoint(Vector p) {
|
|
|
|
int winding = 0;
|
2008-05-22 10:28:28 +00:00
|
|
|
int i;
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
SContour *sc = &(l.elem[i]);
|
|
|
|
if(sc->ContainsPointProjdToNormal(normal, p)) {
|
2008-06-21 10:18:20 +00:00
|
|
|
winding++;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
|
|
|
}
|
2008-06-21 10:18:20 +00:00
|
|
|
return winding;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
void SPolygon::FixContourDirections(void) {
|
2009-01-19 03:33:15 +00:00
|
|
|
// At output, the contour's tag will be 1 if we reversed it, else 0.
|
|
|
|
l.ClearTags();
|
|
|
|
|
2008-05-22 10:28:28 +00:00
|
|
|
// Outside curve looks counterclockwise, projected against our normal.
|
|
|
|
int i, j;
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
SContour *sc = &(l.elem[i]);
|
2009-02-18 11:15:33 +00:00
|
|
|
if(sc->l.n < 2) continue;
|
|
|
|
// The contours may not intersect, but they may share vertices; so
|
|
|
|
// testing a vertex for point-in-polygon may fail, but the midpoint
|
|
|
|
// of an edge is okay.
|
|
|
|
Vector pt = (((sc->l.elem[0]).p).Plus(sc->l.elem[1].p)).ScaledBy(0.5);
|
2008-05-22 10:28:28 +00:00
|
|
|
|
2009-01-21 05:04:38 +00:00
|
|
|
sc->timesEnclosed = 0;
|
2008-05-22 10:28:28 +00:00
|
|
|
bool outer = true;
|
|
|
|
for(j = 0; j < l.n; j++) {
|
|
|
|
if(i == j) continue;
|
|
|
|
SContour *sct = &(l.elem[j]);
|
|
|
|
if(sct->ContainsPointProjdToNormal(normal, pt)) {
|
|
|
|
outer = !outer;
|
2009-01-21 05:04:38 +00:00
|
|
|
(sc->timesEnclosed)++;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
bool clockwise = sc->IsClockwiseProjdToNormal(normal);
|
|
|
|
if(clockwise && outer || (!clockwise && !outer)) {
|
|
|
|
sc->Reverse();
|
2009-01-19 03:33:15 +00:00
|
|
|
sc->tag = 1;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2008-06-21 10:18:20 +00:00
|
|
|
bool SPolygon::IsEmpty(void) {
|
2008-06-12 04:36:33 +00:00
|
|
|
if(l.n == 0 || l.elem[0].l.n == 0) return true;
|
2008-06-21 10:18:20 +00:00
|
|
|
return false;
|
|
|
|
}
|
|
|
|
|
|
|
|
Vector SPolygon::AnyPoint(void) {
|
|
|
|
if(IsEmpty()) oops();
|
|
|
|
return l.elem[0].l.elem[0].p;
|
|
|
|
}
|
2008-06-12 04:36:33 +00:00
|
|
|
|
2008-06-21 10:18:20 +00:00
|
|
|
bool SPolygon::AllPointsInPlane(Vector *notCoplanarAt) {
|
|
|
|
if(IsEmpty()) return true;
|
|
|
|
|
|
|
|
Vector p0 = AnyPoint();
|
2008-06-12 04:36:33 +00:00
|
|
|
double d = normal.Dot(p0);
|
|
|
|
|
|
|
|
for(int i = 0; i < l.n; i++) {
|
|
|
|
if(!(l.elem[i]).AllPointsInPlane(normal, d, notCoplanarAt)) {
|
|
|
|
return false;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
|
2009-01-23 03:30:30 +00:00
|
|
|
bool SPolygon::SelfIntersecting(Vector *intersectsAt) {
|
|
|
|
SEdgeList el;
|
|
|
|
ZERO(&el);
|
|
|
|
MakeEdgesInto(&el);
|
|
|
|
|
|
|
|
SEdge *se;
|
|
|
|
for(se = el.l.First(); se; se = el.l.NextAfter(se)) {
|
|
|
|
int inters = el.AnyEdgeCrossings(se->a, se->b, intersectsAt);
|
|
|
|
if(inters != 1) return true;
|
|
|
|
}
|
|
|
|
return false;
|
|
|
|
}
|
|
|
|
|
2008-06-26 07:28:29 +00:00
|
|
|
static int TriMode, TriVertexCount;
|
|
|
|
static Vector Tri1, TriNMinus1, TriNMinus2;
|
|
|
|
static Vector TriNormal;
|
|
|
|
static SMesh *TriMesh;
|
|
|
|
static STriMeta TriMeta;
|
|
|
|
static void GLX_CALLBACK TriBegin(int mode)
|
|
|
|
{
|
|
|
|
TriMode = mode;
|
|
|
|
TriVertexCount = 0;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
2008-06-26 07:28:29 +00:00
|
|
|
static void GLX_CALLBACK TriEnd(void)
|
2008-05-22 10:28:28 +00:00
|
|
|
{
|
|
|
|
}
|
2008-06-26 07:28:29 +00:00
|
|
|
static void GLX_CALLBACK TriVertex(Vector *triN)
|
|
|
|
{
|
|
|
|
if(TriVertexCount == 0) {
|
|
|
|
Tri1 = *triN;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
2008-06-26 07:28:29 +00:00
|
|
|
if(TriMode == GL_TRIANGLES) {
|
|
|
|
if((TriVertexCount % 3) == 2) {
|
|
|
|
TriMesh->AddTriangle(
|
|
|
|
TriMeta, TriNormal, TriNMinus2, TriNMinus1, *triN);
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
2008-06-26 07:28:29 +00:00
|
|
|
} else if(TriMode == GL_TRIANGLE_FAN) {
|
|
|
|
if(TriVertexCount >= 2) {
|
|
|
|
TriMesh->AddTriangle(
|
|
|
|
TriMeta, TriNormal, Tri1, TriNMinus1, *triN);
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
2008-06-26 07:28:29 +00:00
|
|
|
} else if(TriMode == GL_TRIANGLE_STRIP) {
|
|
|
|
if(TriVertexCount >= 2) {
|
|
|
|
TriMesh->AddTriangle(
|
|
|
|
TriMeta, TriNormal, TriNMinus2, TriNMinus1, *triN);
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
2008-06-26 07:28:29 +00:00
|
|
|
} else oops();
|
|
|
|
|
|
|
|
TriNMinus2 = TriNMinus1;
|
|
|
|
TriNMinus1 = *triN;
|
|
|
|
TriVertexCount++;
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
|
|
|
void SPolygon::TriangulateInto(SMesh *m) {
|
2008-06-21 10:18:20 +00:00
|
|
|
STriMeta meta;
|
|
|
|
ZERO(&meta);
|
|
|
|
TriangulateInto(m, meta);
|
|
|
|
}
|
|
|
|
void SPolygon::TriangulateInto(SMesh *m, STriMeta meta) {
|
2008-06-26 07:28:29 +00:00
|
|
|
TriMesh = m;
|
|
|
|
TriNormal = normal;
|
|
|
|
TriMeta = meta;
|
2008-05-22 10:28:28 +00:00
|
|
|
|
2008-06-26 07:28:29 +00:00
|
|
|
GLUtesselator *gt = gluNewTess();
|
|
|
|
gluTessCallback(gt, GLU_TESS_BEGIN, (glxCallbackFptr *)TriBegin);
|
|
|
|
gluTessCallback(gt, GLU_TESS_END, (glxCallbackFptr *)TriEnd);
|
|
|
|
gluTessCallback(gt, GLU_TESS_VERTEX, (glxCallbackFptr *)TriVertex);
|
2008-05-22 10:28:28 +00:00
|
|
|
|
2008-06-26 07:28:29 +00:00
|
|
|
glxTesselatePolygon(gt, this);
|
2008-05-22 10:28:28 +00:00
|
|
|
|
2008-06-26 07:28:29 +00:00
|
|
|
gluDeleteTess(gt);
|
2008-05-22 10:28:28 +00:00
|
|
|
}
|
|
|
|
|
2008-08-14 08:28:25 +00:00
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// Low-quality routines to cutter radius compensate a polygon. Assumes the
|
|
|
|
// polygon is in the xy plane, and the contours all go in the right direction
|
|
|
|
// with respect to normal (0, 0, -1).
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void SPolygon::OffsetInto(SPolygon *dest, double r) {
|
|
|
|
int i;
|
|
|
|
dest->Clear();
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
SContour *sc = &(l.elem[i]);
|
|
|
|
dest->AddEmptyContour();
|
|
|
|
sc->OffsetInto(&(dest->l.elem[dest->l.n-1]), r);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// Calculate the intersection point of two lines. Returns true for success,
|
|
|
|
// false if they're parallel.
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
static bool IntersectionOfLines(double x0A, double y0A, double dxA, double dyA,
|
|
|
|
double x0B, double y0B, double dxB, double dyB,
|
|
|
|
double *xi, double *yi)
|
|
|
|
{
|
|
|
|
double A[2][2];
|
|
|
|
double b[2];
|
|
|
|
|
|
|
|
// The line is given to us in the form:
|
|
|
|
// (x(t), y(t)) = (x0, y0) + t*(dx, dy)
|
|
|
|
// so first rewrite it as
|
|
|
|
// (x - x0, y - y0) dot (dy, -dx) = 0
|
|
|
|
// x*dy - x0*dy - y*dx + y0*dx = 0
|
|
|
|
// x*dy - y*dx = (x0*dy - y0*dx)
|
|
|
|
|
|
|
|
// So write the matrix, pre-pivoted.
|
|
|
|
if(fabs(dyA) > fabs(dyB)) {
|
|
|
|
A[0][0] = dyA; A[0][1] = -dxA; b[0] = x0A*dyA - y0A*dxA;
|
|
|
|
A[1][0] = dyB; A[1][1] = -dxB; b[1] = x0B*dyB - y0B*dxB;
|
|
|
|
} else {
|
|
|
|
A[1][0] = dyA; A[1][1] = -dxA; b[1] = x0A*dyA - y0A*dxA;
|
|
|
|
A[0][0] = dyB; A[0][1] = -dxB; b[0] = x0B*dyB - y0B*dxB;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Check the determinant; if it's zero then no solution.
|
|
|
|
if(fabs(A[0][0]*A[1][1] - A[0][1]*A[1][0]) < LENGTH_EPS) {
|
|
|
|
return false;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Solve
|
|
|
|
double v = A[1][0] / A[0][0];
|
|
|
|
A[1][0] -= A[0][0]*v;
|
|
|
|
A[1][1] -= A[0][1]*v;
|
|
|
|
b[1] -= b[0]*v;
|
|
|
|
|
|
|
|
// Back-substitute.
|
|
|
|
*yi = b[1] / A[1][1];
|
|
|
|
*xi = (b[0] - A[0][1]*(*yi)) / A[0][0];
|
|
|
|
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
void SContour::OffsetInto(SContour *dest, double r) {
|
|
|
|
int i;
|
|
|
|
|
|
|
|
for(i = 0; i < l.n; i++) {
|
|
|
|
Vector a, b, c;
|
|
|
|
Vector dp, dn;
|
|
|
|
double thetan, thetap;
|
|
|
|
|
|
|
|
a = l.elem[WRAP(i-1, (l.n-1))].p;
|
|
|
|
b = l.elem[WRAP(i, (l.n-1))].p;
|
|
|
|
c = l.elem[WRAP(i+1, (l.n-1))].p;
|
|
|
|
|
|
|
|
dp = a.Minus(b);
|
|
|
|
thetap = atan2(dp.y, dp.x);
|
|
|
|
|
|
|
|
dn = b.Minus(c);
|
|
|
|
thetan = atan2(dn.y, dn.x);
|
|
|
|
|
|
|
|
// A short line segment in a badly-generated polygon might look
|
|
|
|
// okay but screw up our sense of direction.
|
|
|
|
if(dp.Magnitude() < LENGTH_EPS || dn.Magnitude() < LENGTH_EPS) {
|
|
|
|
continue;
|
|
|
|
}
|
|
|
|
|
|
|
|
if(thetan > thetap && (thetan - thetap) > PI) {
|
|
|
|
thetap += 2*PI;
|
|
|
|
}
|
|
|
|
if(thetan < thetap && (thetap - thetan) > PI) {
|
|
|
|
thetan += 2*PI;
|
|
|
|
}
|
|
|
|
|
|
|
|
if(fabs(thetan - thetap) < (1*PI)/180) {
|
|
|
|
Vector p = { b.x - r*sin(thetap), b.y + r*cos(thetap) };
|
|
|
|
dest->AddPoint(p);
|
|
|
|
} else if(thetan < thetap) {
|
|
|
|
// This is an inside corner. We have two edges, Ep and En. Move
|
|
|
|
// out from their intersection by radius, normal to En, and
|
|
|
|
// then draw a line parallel to En. Move out from their
|
|
|
|
// intersection by radius, normal to Ep, and then draw a second
|
|
|
|
// line parallel to Ep. The point that we want to generate is
|
|
|
|
// the intersection of these two lines--it removes as much
|
|
|
|
// material as we can without removing any that we shouldn't.
|
|
|
|
double px0, py0, pdx, pdy;
|
|
|
|
double nx0, ny0, ndx, ndy;
|
|
|
|
double x, y;
|
|
|
|
|
|
|
|
px0 = b.x - r*sin(thetap);
|
|
|
|
py0 = b.y + r*cos(thetap);
|
|
|
|
pdx = cos(thetap);
|
|
|
|
pdy = sin(thetap);
|
|
|
|
|
|
|
|
nx0 = b.x - r*sin(thetan);
|
|
|
|
ny0 = b.y + r*cos(thetan);
|
|
|
|
ndx = cos(thetan);
|
|
|
|
ndy = sin(thetan);
|
|
|
|
|
|
|
|
IntersectionOfLines(px0, py0, pdx, pdy,
|
|
|
|
nx0, ny0, ndx, ndy,
|
|
|
|
&x, &y);
|
|
|
|
|
|
|
|
dest->AddPoint(Vector::From(x, y, 0));
|
|
|
|
} else {
|
|
|
|
if(fabs(thetap - thetan) < (6*PI)/180) {
|
|
|
|
Vector pp = { b.x - r*sin(thetap),
|
|
|
|
b.y + r*cos(thetap), 0 };
|
|
|
|
dest->AddPoint(pp);
|
|
|
|
|
|
|
|
Vector pn = { b.x - r*sin(thetan),
|
|
|
|
b.y + r*cos(thetan), 0 };
|
|
|
|
dest->AddPoint(pn);
|
|
|
|
} else {
|
|
|
|
double theta;
|
|
|
|
for(theta = thetap; theta <= thetan; theta += (6*PI)/180) {
|
|
|
|
Vector p = { b.x - r*sin(theta),
|
|
|
|
b.y + r*cos(theta), 0 };
|
|
|
|
dest->AddPoint(p);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|