/**
* Test Case for the In Circle Test!
double pa[3] = {1,0,0};
double pb[3] = {0,0,1};
double pc[3] = {0,1,0};
double pp[3] = {0.25,0.25,0.5};
double ppout1[3] = {-5,0.25,0.5};
double ppout2[3] = {5.0,0.25,0.5};
double ppout3[3] = {0.25,5.0,0.5};
bool isIn1 = IsInPlanarTriangle(pa,pb,pc,ppout1);
bool isIn2 = IsInPlanarTriangle(pa,pb,pc,ppout2);
bool isIn3 = IsInPlanarTriangle(pa,pb,pc,ppout3);
bool isIn = IsInPlanarTriangle(pa,pb,pc,pp);
*/
bool IsInPlanarTriangle(double *pa, double *pb, double *pc, double *pp)
{
if ( orient2d(pa,pb,pp)<0&& orient2d(pb,pc,pp)<0 && orient2d(pc,pa,pp)<0) {
return false;
}
return true;
}
bool pointIntersectsTriangle(const P2 &p, const P2vec &tri) {
int orient = isAnticlockwise(tri) ? +1 : -1;
if (orient2d(tri[0], tri[1], p) * orient < 0) return false;
if (orient2d(tri[1], tri[2], p) * orient < 0) return false;
if (orient2d(tri[2], tri[0], p) * orient < 0) return false;
return true;
}
void DepthBuffer::drawTriangle(BinnedTriangle& tri,vec2i tilePos) {
vec2i v0(tri.v[0].x,tri.v[0].y);
vec2i v1(tri.v[1].x,tri.v[1].y);
vec2i v2(tri.v[2].x,tri.v[2].y);
float zz[3] = { tri.z[0],tri.z[1],tri.z[2] };
int32 minx = std::min(v0.x,std::min(v1.x,v2.x));
int32 miny = std::min(v0.y,std::min(v1.y,v2.y));
int32 maxx = std::max(v0.x,std::max(v1.x,v2.x));
int32 maxy = std::max(v0.y,std::max(v1.y,v2.y));
minx = std::max(minx,tilePos.x); miny = std::max(miny,tilePos.y);
maxx = std::min(maxx,tilePos.x+tileSize_.x-1); maxy = std::min(maxy,tilePos.y+tileSize_.y-1);
int32 a01 = v0.y - v1.y; int32 b01 = v1.x - v0.x;
int32 a12 = v1.y - v2.y; int32 b12 = v2.x - v1.x;
int32 a20 = v2.y - v0.y; int32 b20 = v0.x - v2.x;
vec2i p(minx,miny);
auto w0_row = orient2d(v1,v2,p);
auto w1_row = orient2d(v2,v0,p);
auto w2_row = orient2d(v0,v1,p);
float* tilePixels = data_ + tilePos.x*tileSize_.y + (tilePos.y*tileSize_.x)*tileCount_.x;
int32 idx2 = minx-tilePos.x + (miny - tilePos.y)*tileSize_.x;
int32 spanx = maxx-minx;
for(int32 endIdx2 = idx2+(tileSize_.x)*(maxy-miny);idx2<=endIdx2;idx2+=tileSize_.x){
auto w0 = w0_row;
auto w1 = w1_row;
auto w2 = w2_row;
//float betaf = float(w1);
//float gamaf = float(w2);
//float depth = zz[0] + betaf*zz[1] + gamaf*zz[2];
//float depthInc = float(a20)*zz[1] + float(a01)*zz[2];
auto idx = idx2;
for(int32 endIdx = idx+spanx;idx<=endIdx;++idx){
if((w0|w1|w2) >= 0){
float betaf = float(w1);
float gamaf = float(w2);
float depth = zz[0] + betaf*zz[1] + gamaf*zz[2];
auto d = tilePixels[idx];
d = depth<d?depth:d;
tilePixels[idx] = d;
}
w0+=a12;
w1+=a20;
w2+=a01;
//depth+=depthInc;
}
w0_row += b12;
w1_row += b20;
w2_row += b01;
}
}
/*!
* The polylines must be different.
*
* \param globalverts global vertices vector
* \param v1 the first polyline
* \param v2
* \param p1 the second polyline
* \param p2
*
* \return 0 if they don't intersect <BR>
* 1 if they do <BR>
*/
int SimplePolygon::doIntersect( DCTPVec2dvector &globalverts, int v1, int v2, int p1, int p2 ) const
{
// check if they share vertices
if ( v1 == p1 || v1 == p2 || v2 == p1 || v2 == p2 ) return 0;
double pa[ 2 ];
double pb[ 2 ];
double pc[ 2 ];
double pd[ 2 ];
const int vv1 = vertices[ v1 ];
const int vv2 = vertices[ v2 ];
const int vp1 = vertices[ p1 ];
const int vp2 = vertices[ p2 ];
pa[ 0 ] = globalverts[ vv1 ][0];
pa[ 1 ] = globalverts[ vv1 ][1];
pb[ 0 ] = globalverts[ vv2 ][0];
pb[ 1 ] = globalverts[ vv2 ][1];
pc[ 0 ] = globalverts[ vp1 ][0];
pc[ 1 ] = globalverts[ vp1 ][1];
pd[ 0 ] = globalverts[ vp2 ][0];
pd[ 1 ] = globalverts[ vp2 ][1];
const double r1 = orient2d(pa, pc, pd);
const double r2 = orient2d(pb, pc, pd);
if( ( r1 < 0.0 ) && ( r2 < 0.0 ) )
{
return 0;
}
if( ( r1 > 0.0 ) && ( r2 > 0.0 ) )
{
return 0;
}
const double r3 = orient2d(pc, pa, pb);
const double r4 = orient2d(pd, pa, pb);
if( ( r3 < 0.0 ) && ( r4 < 0.0 ) )
{
return 0;
}
if( ( r3 > 0.0 ) && ( r4 > 0.0 ) )
{
return 0;
}
return 1;
// do intersect??
/*
* r1 and r2 must have different signs ( <0, >0, =0 ) AND
* r3 and r4 must also have different signs in suffice intersection of
* the two lines.
*/
/* bool s1 = ( !(( r1 < 0 && r2 < 0 ) || ( r1 > 0 && r2 > 0 )) );
bool s2 = ( !(( r3 < 0 && r4 < 0 ) || ( r3 > 0 && r4 > 0 )) );
if ( s1 && s2 ) return 1;
else return 0;*/
}
int triangleLineOrientation(const P2 &p1, const P2 &p2, const P2vec &tri) {
double lo, hi, tmp;
lo = hi = orient2d(p1, p2, tri[0]);
tmp = orient2d(p1, p2, tri[1]); lo = std::min(lo, tmp); hi = std::max(hi, tmp);
tmp = orient2d(p1, p2, tri[2]); lo = std::min(lo, tmp); hi = std::max(hi, tmp);
if (hi < 0.0) return -1;
if (lo > 0.0) return +1;
return 0;
}
void tricircumcenter3d(double*a, double*b, double*c, double*circumcenter,double*cond)
{
double xba, yba, zba, xca, yca, zca;
double balength, calength;
double xcrossbc, ycrossbc, zcrossbc;
double denominator;
double xcirca, ycirca, zcirca;
#ifdef EXACT
double ta[2],tb[2],tc[2];
#endif
/* Use coordinates relative to point `a' of the triangle. */
xba = b[0] - a[0];
yba = b[1] - a[1];
zba = b[2] - a[2];
xca = c[0] - a[0];
yca = c[1] - a[1];
zca = c[2] - a[2];
/* Squares of lengths of the edges incident to `a'. */
balength = xba * xba + yba * yba + zba * zba;
calength = xca * xca + yca * yca + zca * zca;
/* Cross product of these edges. */
#ifdef EXACT
/* Use orient2d() from http://www.cs.cmu.edu/~quake/robust.html */
/* to ensure a correctly signed (and reasonably accurate) result, */
/* avoiding any possibility of division by zero. */
ta[0]=b[1];ta[1]=b[2];tb[0]=c[1];tb[1]=c[2];tc[0]=a[1];tc[1]=a[2];
xcrossbc = orient2d(ta,tb,tc);
ta[0]=b[2];ta[1]=b[0];tb[0]=c[2];tb[1]=c[0];tc[0]=a[2];tc[1]=a[0];
ycrossbc = orient2d(ta,tb,tc);
ta[0]=b[0];ta[1]=b[1];tb[0]=c[0];tb[1]=c[1];tc[0]=a[0];tc[1]=a[1];
zcrossbc = orient2d(ta,tb,tc);
#else
/* Take your chances with floating-point roundoff. */
xcrossbc = yba * zca - yca * zba;
ycrossbc = zba * xca - zca * xba;
zcrossbc = xba * yca - xca * yba;
#endif
/* Calculate the denominator of the formulae. */
denominator = 0.5 / (xcrossbc * xcrossbc + ycrossbc * ycrossbc +
zcrossbc * zcrossbc);
/* Calculate offset (from `a') of circumcenter. */
xcirca = ((balength * yca - calength * yba) * zcrossbc -
(balength * zca - calength * zba) * ycrossbc) * denominator;
ycirca = ((balength * zca - calength * zba) * xcrossbc -
(balength * xca - calength * xba) * zcrossbc) * denominator;
zcirca = ((balength * xca - calength * xba) * ycrossbc -
(balength * yca - calength * yba) * xcrossbc) * denominator;
circumcenter[0] = xcirca;
circumcenter[1] = ycirca;
circumcenter[2] = zcirca;
}
/**
* \brief Determine whether p is internal to the anticlockwise
* angle abc, where b is the apex of the angle.
*
* @param[in] a
* @param[in] b
* @param[in] c
* @param[in] p
*
* @return true, if p is contained in the anticlockwise angle from
* b->a to b->c. Reflex angles contain p if p lies
* on b->a or on b->c. Acute angles do not contain p
* if p lies on b->a or on b->c. This is so that
* internalToAngle(a,b,c,p) = !internalToAngle(c,b,a,p)
*/
inline bool internalToAngle(const P2 &a,
const P2 &b,
const P2 &c,
const P2 &p) {
bool reflex = (a < c) ? orient2d(b, a, c) <= 0.0 : orient2d(b, c, a) > 0.0;
double d1 = orient2d(b, a, p);
double d2 = orient2d(b, c, p);
if (reflex) {
return d1 >= 0.0 || d2 <= 0.0;
} else {
return d1 > 0.0 && d2 < 0.0;
}
}
/*!
* \param globalverts global vertices vector
* \param v1 first vertex
* \param v2 second vertex
* \param v3 third vertex
* \param p the point
* \return 0 if not inside <BR>
* 1 if inside <BR>
*/
int SimplePolygon::isInsideCircumCircle( DCTPVec2dvector &globalverts, int v1, int v2, int v3, int p ) const
{
double pa[2], pb[2], pc[2], pd[2];
pa [ 0 ] = globalverts[ vertices[ v1 ] ][0];
pa [ 1 ] = globalverts[ vertices[ v1 ] ][1];
pb [ 0 ] = globalverts[ vertices[ v2 ] ][0];
pb [ 1 ] = globalverts[ vertices[ v2 ] ][1];
pc [ 0 ] = globalverts[ vertices[ v3 ] ][0];
pc [ 1 ] = globalverts[ vertices[ v3 ] ][1];
pd [ 0 ] = globalverts[ vertices[ p ] ][0];
pd [ 1 ] = globalverts[ vertices[ p ] ][1];
// check for order of (pa, pb, pc) they must be in counterclockwise order
double order = orient2d( pa, pb, pc );
double dres;
if ( order < 0.0 ) // clockwise order -> change order
dres = incircle( pa, pc, pb, pd );
else
dres = incircle( pa, pb, pc, pd );
//std::cerr << pa[ 0 ] << "," << pa[ 1 ] << " ";
//std::cerr << pb[ 0 ] << "," << pb[ 1 ] << " ";
//std::cerr << pc[ 0 ] << "," << pc[ 1 ] << " ";
//std::cerr << pd[ 0 ] << "," << pd[ 1 ] << std::endl;
//std::cerr << "Inside Circumcircle: " << dres << std::endl; // >0 if inside
if ( dres <= 0 ) return 0;
else return 1;
}
bool SimplePolygon::isReversed( DCTPVec2dvector &globalverts )
{
unsigned int ui_vertex;
unsigned int ui_upperleft;
const unsigned int cui_vertex_cnt = vertices.size( );
double ad_p[ 2 ];
double ad_v[ 2 ];
double ad_n[ 2 ];
ui_upperleft = 0;
for( ui_vertex = 1; ui_vertex < cui_vertex_cnt; ++ui_vertex )
{
if( globalverts[ vertices[ ui_vertex ] ][1] < globalverts[ vertices[ ui_upperleft ] ][1] )
{
ui_upperleft = ui_vertex;
}
else if( ( globalverts[ vertices[ ui_vertex ] ][1] == globalverts[ vertices[ ui_upperleft ] ][1] ) &&
( globalverts[ vertices[ ui_vertex ] ][0] < globalverts[ vertices[ ui_upperleft ] ][0] ) )
{
ui_upperleft = ui_vertex;
}
}
ad_p[ 0 ] = globalverts[ vertices[ ( ui_upperleft + cui_vertex_cnt - 1 ) % cui_vertex_cnt ] ][0];
ad_p[ 1 ] = globalverts[ vertices[ ( ui_upperleft + cui_vertex_cnt - 1 ) % cui_vertex_cnt ] ][1];
ad_v[ 0 ] = globalverts[ vertices[ ui_upperleft ] ][0];
ad_v[ 1 ] = globalverts[ vertices[ ui_upperleft ] ][1];
ad_n[ 0 ] = globalverts[ vertices[ ( ui_upperleft + 1 ) % cui_vertex_cnt ] ][0];
ad_n[ 1 ] = globalverts[ vertices[ ( ui_upperleft + 1 ) % cui_vertex_cnt ] ][1];
return ( orient2d( ad_p, ad_v, ad_n ) <= 0.0 );
}
Exact_adaptive_kernel::Oriented_side Exact_adaptive_kernel::oriented_side (Point2 const& pa, Point2 const& pb, Point2 const& test)
{
double r = orient2d(pa.coord(), pb.coord(), test.coord());
if (r > 0.0)
return ON_POSITIVE_SIDE;
else if (r < 0.0)
return ON_NEGATIVE_SIDE;
else
return ON_ORIENTED_BOUNDARY;
}
bool lineIntersectsTriangle(const P2 &p1, const P2 &p2, const P2vec &tri) {
double s[3];
// does tri lie on one side or the other of p1-p2?
s[0] = orient2d(p1, p2, tri[0]);
s[1] = orient2d(p1, p2, tri[1]);
s[2] = orient2d(p1, p2, tri[2]);
if (*std::max_element(s, s+3) < 0) return false;
if (*std::min_element(s, s+3) > 0) return false;
// does line lie entirely to the right of a triangle edge?
int orient = isAnticlockwise(tri) ? +1 : -1;
if (orient2d(tri[0], tri[1], p1) * orient < 0 && orient2d(tri[0], tri[1], p2) * orient < 0) return false;
if (orient2d(tri[1], tri[2], p1) * orient < 0 && orient2d(tri[1], tri[2], p2) * orient < 0) return false;
if (orient2d(tri[2], tri[0], p1) * orient < 0 && orient2d(tri[2], tri[0], p2) * orient < 0) return false;
return true;
}
bool lineSegmentIntersection_simple(const P2 &l1v1, const P2 &l1v2,
const P2 &l2v1, const P2 &l2v2) {
geom::aabb<2> l1_aabb, l2_aabb;
l1_aabb.fit(l1v1, l1v2);
l2_aabb.fit(l2v1, l2v2);
if (l1_aabb.maxAxisSeparation(l2_aabb) > 0.0) {
return false;
}
double l1v1_side = orient2d(l2v1, l2v2, l1v1);
double l1v2_side = orient2d(l2v1, l2v2, l1v2);
double l2v1_side = orient2d(l1v1, l1v2, l2v1);
double l2v2_side = orient2d(l1v1, l1v2, l2v2);
if (l1v1_side * l1v2_side > 0.0 || l2v1_side * l2v2_side > 0.0) {
return false;
}
return true;
}
// returns true if the ray cast from p along positive z axis hits triangle in
// exactly one spot, with edge cases handled appropriately
static bool
tri_zcast(const Vec3d& p,
const Vec3d& q,
const Vec3d& r,
const Vec3d& s)
{
// robustly find orientation of qrs in 2D xy projection
double qrs=orient2d(q.v, r.v, s.v);
if(qrs>0)
return tri_zcast_inner(p, qrs, q, r, s);
else if(qrs<0)
return tri_zcast_inner(p, -qrs, q, s, r); // flip triangle to reorient
else
return false; // triangle is degenerate in 2D projection - ignore
}
Oriented_side Exact_adaptive_kernel::oriented_side( Point2 const& pa, Point2 const& pb, Point2 const& test )
{
double r = orient2d( pa.data(), pb.data(), test.data() );
if ( r > 0.0 )
{
return ON_POSITIVE_SIDE;
}
if ( r < 0.0 )
{
return ON_NEGATIVE_SIDE;
}
return ON_ORIENTED_BOUNDARY;
}
void triorthocenter(double a[], double b[], double c[],
double orthocenter[], double* cnum)
{
double xba, yba, wba, xca, yca, wca;
double balength, calength;
double denominator;
double xcirca, ycirca;
/* Use coordinates relative to point `a' of the triangle. */
xba = b[0] - a[0];
yba = b[1] - a[1];
wba = b[2] - a[2];
xca = c[0] - a[0];
yca = c[1] - a[1];
wca = b[2] - a[2];
/* Squares of lengths of the edges incident to `a'. */
balength = xba * xba + yba * yba - wba;
calength = xca * xca + yca * yca - wca;
/* Calculate the denominator of the formulae. */
#ifdef EXACT
/* Use orient2d() from http://www.cs.cmu.edu/~quake/robust.html */
/* to ensure a correctly signed (and reasonably accurate) result, */
/* avoiding any possibility of division by zero. */
*cnum = orient2d(b, c, a);
denominator = 0.5 / (*cnum);
#else
/* Take your chances with floating-point roundoff. */
denominator = 0.5 / (xba * yca - yba * xca);
*cnum = 1.0; // a value !=0
#endif
/* Calculate offset (from `a') of circumcenter. */
xcirca = (yca * balength - yba * calength) * denominator;
ycirca = (xba * calength - xca * balength) * denominator;
orthocenter[0] = xcirca;
orthocenter[1] = ycirca;
}
bool SimplePolygon::isConvex( DCTPVec2dvector &globalverts )
{
unsigned int ui_next;
const unsigned int cui_vertex_cnt = vertices.size( );
double ad_p[ 2 ];
double ad_v[ 2 ];
double ad_n[ 2 ];
ad_p[ 0 ] = globalverts[ vertices[ cui_vertex_cnt - 2 ] ][0];
ad_p[ 1 ] = globalverts[ vertices[ cui_vertex_cnt - 2 ] ][1];
ad_v[ 0 ] = globalverts[ vertices[ cui_vertex_cnt - 1 ] ][0];
ad_v[ 1 ] = globalverts[ vertices[ cui_vertex_cnt - 1 ] ][1];
for( ui_next = 0; ui_next < cui_vertex_cnt; ++ui_next )
{
// std::cerr <<"ui_next:" << ui_next << std::endl;
ad_n[ 0 ] = globalverts[ vertices[ ui_next ] ][0];
ad_n[ 1 ] = globalverts[ vertices[ ui_next ] ][1];
// previous, current, and next vertices must be in
// counterclockwise order for the polygon to be convex
// (because our tessellator always gives CCW polygons)
if( orient2d( ad_p, ad_v, ad_n ) < 0.0 )
{
// std::cerr << ad_p[ 0 ] << " " << ad_p[ 1 ] << std::endl;
// std::cerr << ad_v[ 0 ] << " " << ad_v[ 1 ] << std::endl;
// std::cerr << ad_n[ 0 ] << " " << ad_n[ 1 ] << std::endl << std::endl;
// not convex
return false;
}
ad_p[ 0 ] = ad_v[ 0 ];
ad_p[ 1 ] = ad_v[ 1 ];
ad_v[ 0 ] = ad_n[ 0 ];
ad_v[ 1 ] = ad_n[ 1 ];
}
// std::cerr << "convex" << std::endl;
return true;
}
double Exact_adaptive_kernel::signed_area( Point2 const& pa, Point2 const& pb, Point2 const& pc )
{
return 0.5 * orient2d( pa.data(), pb.data(), pc.data() );
}
inline double LeftTurn(const double a[2], const double b[2], const double c[2]){
extern double orient2d(double*, double*, double*);
return orient2d((double*)a, (double*)b, (double*)c);
}
bool n3d_prepare(
n3d_rasterizer_t::triangle_t& tri,
const n3d_vertex_t& v0,
const n3d_vertex_t& v1,
const n3d_vertex_t& v2,
const uint32_t flags)
{
const vec4f_t& vp0 = v0.p_;
const vec4f_t& vp1 = v1.p_;
const vec4f_t& vp2 = v2.p_;
// the signed triangle area
const float t_area = (vp1.x - vp0.x) * (vp2.y - vp0.y) -
(vp2.x - vp0.x) * (vp1.y - vp0.y);
// check for back face
if (t_area <= 0.f)
return false;
// reciprocal of area for normalization
const float rt_area = 1.f / t_area;
// find normalized barycentric coordinates
tri.v_ [e_attr_b0] = orient2d(vp1, vp2) * rt_area;
tri.sx_[e_attr_b0] = (vp1.y - vp2.y) * rt_area;
tri.sy_[e_attr_b0] = (vp2.x - vp1.x) * rt_area;
tri.v_ [e_attr_b1] = orient2d(vp2, vp0) * rt_area;
tri.sx_[e_attr_b1] = (vp2.y - vp0.y) * rt_area;
tri.sy_[e_attr_b1] = (vp0.x - vp2.x) * rt_area;
tri.v_ [e_attr_b2] = orient2d(vp0, vp1) * rt_area;
tri.sx_[e_attr_b2] = (vp0.y - vp1.y) * rt_area;
tri.sy_[e_attr_b2] = (vp1.x - vp0.x) * rt_area;
// calculate 1 / w for vertices
const float v0w = 1.f / v0.p_.w;
const float v1w = 1.f / v1.p_.w;
const float v2w = 1.f / v2.p_.w;
//(todo) update all of this to use SSE
// find triangle bounds
tri.min_.x = min3(vp0.x, vp1.x, vp2.x);
tri.min_.y = min3(vp0.y, vp1.y, vp2.y);
tri.max_.x = max3(vp0.x, vp1.x, vp2.x) + 1.f;
tri.max_.y = max3(vp0.y, vp1.y, vp2.y) + 1.f;
// barycenteric interpolate 1 param
#define BLERPW(B) ((tri.B[0] * v0w) + \
(tri.B[1] * v1w) + \
(tri.B[2] * v2w))
// barycentric interpolate 3 param
#define BLERPA(B, A) ((tri.B[0] * v0.attr_[A] * v0w) + \
(tri.B[1] * v1.attr_[A] * v1w) + \
(tri.B[2] * v2.attr_[A] * v2w))
// interplate 1 / w
tri.v_ [e_attr_w] = BLERPW(v_);
tri.sx_[e_attr_w] = BLERPW(sx_);
tri.sy_[e_attr_w] = BLERPW(sy_);
#if 0
for (uint32_t i = 0; i < v0.attr_.size(); ++i) {
tri.v_ [e_attr_custom + i] = BLERPA(v_, i);
tri.sx_[e_attr_custom + i] = BLERPA(sx_, i);
tri.sy_[e_attr_custom + i] = BLERPA(sy_, i);
}
#endif
#undef BLERPW
#undef BLERPA
return true;
}
// helper function for tri_zcast below...
// Here we are given a robust 2d orientation of qrs in xy projection, which
// must be positive.
static bool
tri_zcast_inner(const Vec3d& p,
double qrs,
const Vec3d& q,
const Vec3d& r,
const Vec3d& s)
{
assert(qrs>0);
// first check if point is above or below triangle in z
double pqrs=orient3d(p.v, q.v, r.v, s.v);
if(pqrs>=0) return false; // point is on or above triangle - no intersection
// then check if point lies outside triangle in 2D xy projection
double pqr=orient2d(p.v, q.v, r.v);
if(pqr<0) return false;
double prs=orient2d(p.v, r.v, s.v);
if(prs<0) return false;
double psq=orient2d(p.v, s.v, q.v);
if(psq<0) return false;
// note: the following tests are somewhat redundant, but it's a pretty
// tiny optimization to eliminate the redundancy compared to the loss in
// clarity.
// check if point is strictly inside the triangle in xy
if(pqr>0 && prs>0 && psq>0) return true;
// check if point is strictly on edge qr
if(pqr==0 && prs>0 && psq>0){
if(q[1]<r[1]) return false;
if(q[1]>r[1]) return true;
if(q[0]<r[0]) return true;
assert(q[0]>r[0]); // q!=r because triangle is not degenerate
return false;
}
// check if point is strictly on edge rs
if(prs==0 && pqr>0 && psq>0){
if(r[1]<s[1]) return false;
if(r[1]>s[1]) return true;
if(r[0]<s[0]) return true;
assert(r[0]>s[0]); // r!=s because triangle is not degenerate
return false;
}
// check if point is strictly on edge sq
if(psq==0 && pqr>0 && prs>0){
if(s[1]<q[1]) return false;
if(s[1]>q[1]) return true;
if(s[0]<q[0]) return true;
assert(s[0]>q[0]); // r!=s because triangle is not degenerate
return false;
}
// check if point is on vertex q
if(p[0]==q[0] && p[1]==q[1]){
return q[1]>=r[1] && q[1]<s[1];
}
// check if point is on vertex r
if(p[0]==r[0] && p[1]==r[1]){
return r[1]>=s[1] && r[1]<q[1];
}
// check if point is on vertex s
if(p[0]==s[0] && p[1]==s[1]){
return s[1]>=q[1] && s[1]<r[1];
}
assert(false); // we should have covered all cases at this point
return false; // just to quiet compiler warnings
}
bool isAnticlockwise(const P2vec &tri) {
return orient2d(tri[0], tri[1], tri[2]) > 0.0;
}
/*Type of Cut Strategy is defined as:
* (useAltCut, useVertical) = (true, true) => Alternating Cuts
* (useAltCut, useVertical) = (true, false) => Horizontal Cuts*
* (useAltCut, useVertical) = (false, true) => Vertical Cuts
* */
void delaunay(Vertex **ppVertices, long numVertices, Edge **ppLe, Edge **ppRe,
bool useAltCuts, bool useVertical) {
NOT_NULL(ppVertices);
if(numVertices == 2) {
Edge *pA = Edge::makeEdge();
if(*ppVertices[0] > *ppVertices[1]) {
ELEM_SWAP(ppVertices[0], ppVertices[1]);
}
pA->setOrg(ppVertices[0]);
pA->setDest(ppVertices[1]);
*ppLe = pA;
*ppRe = pA->Sym();
}
else if(numVertices == 3) {
Edge *pA = Edge::makeEdge(),
*pB = Edge::makeEdge(),
*pC = 0;
if(*ppVertices[0] > *ppVertices[1]) {
ELEM_SWAP(ppVertices[0], ppVertices[1]);
}
if(*ppVertices[1] > *ppVertices[2]) {
ELEM_SWAP(ppVertices[1], ppVertices[2]);
}
Edge::splice(pA->Sym(), pB);
pA->setOrg(ppVertices[0]);
pA->setDest(ppVertices[1]);
pB->setOrg(ppVertices[1]);
pB->setDest(ppVertices[2]);
REAL ccw = orient2d(ppVertices[0]->Pos(), ppVertices[1]->Pos(), ppVertices[2]->Pos());
if(ccw > 0) {
pC = Edge::connect(pB, pA);
*ppLe = pA;
*ppRe = pB->Sym();
}
else if(ccw < 0) {
pC = Edge::connect(pB, pA);
*ppLe = pC->Sym();
*ppRe = pC;
}
else {
*ppLe = pA;
*ppRe = pB->Sym();
}
}
else {
long middle = std::floor(numVertices/2);
Edge *pLdo = 0,
*pLdi = 0,
*pRdi = 0,
*pRdo = 0;
//These vertices are used for merging a horizontal cut
Vertex *pBotMax = 0, //highest vertex of bottom half
*pTopMin = 0, //lowest vertex of top half
*pMin = 0, //Lexicographically max vertex
*pMax = 0; //Lexicographically min vertex
//Find median partition by X or Y, depending on whether we're using a vertical cut
std::nth_element(ppVertices, ppVertices+middle, ppVertices+numVertices, useVertical ? Vertex::lessX : Vertex::lessY);
//Recursive calls
delaunay(ppVertices, middle, &pLdo, &pLdi, useAltCuts, useAltCuts ? !useVertical : useVertical);
delaunay(ppVertices+middle, numVertices - middle, &pRdi, &pRdo, useAltCuts, useAltCuts ? !useVertical : useVertical);
//Modify ldi be highest in bottom half and rdi to be lowest in top half
if(!useVertical) {
pBotMax = ppVertices[0];
pTopMin = ppVertices[middle];
pMin = (*ppVertices[0] < *ppVertices[middle]) ? ppVertices[0] : ppVertices[middle];
pMax = (*ppVertices[0] > *ppVertices[middle]) ? ppVertices[0] : ppVertices[middle];;
for(long i=1; i < middle; i++) {
if(*ppVertices[i] < *pMin) {
pMin = ppVertices[i];
}
else if(*ppVertices[i] > *pMax) {
pMax = ppVertices[i];
}
if(ppVertices[i]->gtY(*pBotMax)) {
pBotMax = ppVertices[i];
}
}
for(long i=middle+1; i < numVertices; i++) {
if(*ppVertices[i] < *pMin) {
pMin = ppVertices[i];
}
else if(*ppVertices[i] > *pMax) {
pMax = ppVertices[i];
}
if(ppVertices[i]->ltY(*pTopMin)) {
pTopMin = ppVertices[i];
}
}
pLdi = pBotMax->getCWHullEdge();
pRdi = pTopMin->getCCWHullEdge();
}
//Compute the lower common tangent of two sets of vertices
while (1) {
if(pLdi->leftOf(pRdi->Org())) {
pLdi = pLdi->Lnext();
}
else if(pRdi->rightOf(pLdi->Org())) {
pRdi = pRdi->Rprev();
}
else {
break;
}
}
// Create a first cross edge pBasel from pRdi.origin to pLdi.origin
Edge *pBasel = Edge::connect(pRdi->Sym(), pLdi);
if(pLdi->Org() == pLdo->Org()) {
pLdo = pBasel->Sym();
}
if(pRdi->Org() == pRdo->Org()) {
pRdo = pBasel;
}
//Merging two halves
while(1) {
//Locate the first Left point pLcand to be encou
Edge *pLcand = pBasel->Sym()->Onext();
bool leftFinished = !pLcand->valid(pBasel);
if(!leftFinished) {
while(incircle(pBasel->Dest()->Pos(),
pBasel->Org()->Pos(),
pLcand->Dest()->Pos(),
pLcand->Onext()->Dest()->Pos()) > 0) {
Edge *pT = pLcand->Onext();
Edge::deleteEdge(pLcand);
pLcand = pT;
}
}
//Symmetrically locate the first R point to be hit
Edge *pRcand = pBasel->Oprev();
bool rightFinished = !pRcand->valid(pBasel);
if(!rightFinished) {
while(incircle(pBasel->Dest()->Pos(),
pBasel->Org()->Pos(),
pRcand->Dest()->Pos(),
pRcand->Oprev()->Dest()->Pos()) > 0) {
Edge *pT = pRcand->Oprev();
Edge::deleteEdge(pRcand);
pRcand = pT;
}
}
//both are invalid, pBasel is upper common tangent
if(leftFinished && rightFinished) {
break;
}
//the next cross edge is to be connected to either pLcand.dest or pRcand.dest
if(leftFinished ||
(!rightFinished && incircle(pLcand->Dest()->Pos(),
pLcand->Org()->Pos(),
pRcand->Org()->Pos(),
pRcand->Dest()->Pos()) > 0)) {
pBasel = Edge::connect(pRcand, pBasel->Sym());
}
else {
pBasel = Edge::connect(pBasel->Sym(), pLcand->Sym());
}
}
//Modify pLdo and pRdo if we merging a horizontal cut
if(!useVertical) {
pLdo = pMin->getCCWHullEdge();
pRdo = pMax->getCWHullEdge();
}
*ppLe = pLdo;
*ppRe = pRdo;
}
return;
}
int SimplePolygon::intersectPolygon( DCTPVec2dvector &globalverts, simplepolygonvector &polylist )
{
int oldNum = vertices.size();
int i1, i2;
Vec2d min, max;
Vec2d p3, p4;
unsigned char test, ptest;
// std::cerr << "Removing intersections... " << oldNum << std::endl;
for( i2 = 2; i2 < oldNum; ++i2 )
{
const Vec2d &p1 = globalverts[ vertices[ i2 ] ];
const Vec2d &p2 = globalverts[ vertices[ ( i2 + 1 ) % oldNum ] ];
min = max = p1;
if( min[0] > p2[0] )
min[0] = p2[0];
else if( max[0] < p2[0] )
max[0] = p2[0];
if( min[1] > p2[1] )
min[1] = p2[1];
else if( max[1] < p2[1] )
max[1] = p2[1];
const unsigned int start = ( i2 == oldNum - 1 ) ? 1 : 0;
p4 = globalverts[ vertices[ start ] ];
test = 0;
if( p4[0] - max[0] > DCTP_EPS ) test |= 0x01;
if( min[0] - p4[0] > DCTP_EPS ) test |= 0x02;
if( p4[1] - max[1] > DCTP_EPS ) test |= 0x04;
if( min[1] - p4[1] > DCTP_EPS ) test |= 0x08;
for( i1 = start; i1 < i2 - 1; ++i1 )
{
p3 = p4;
p4 = globalverts[ vertices[ i1 + 1 ] ];
ptest = test;
test = 0;
if( p4[0] - max[0] > DCTP_EPS ) test |= 0x01;
if( min[0] - p4[0] > DCTP_EPS ) test |= 0x02;
if( p4[1] - max[1] > DCTP_EPS ) test |= 0x04;
if( min[1] - p4[1] > DCTP_EPS ) test |= 0x08;
if( ( test & ptest ) == 0 )
{
// std::cerr << i1 << "," << i1 + 1 << " overlaps " << i2 << "," << i2 + 1 << std::endl;
// the bounding boxes overlap
int iip = -1;
bool intersect = false;
double d1[ 2 ] = { p1[0], p1[1] };
double d2[ 2 ] = { p2[0], p2[1] };
double d3[ 2 ] = { p3[0], p3[1] };
double d4[ 2 ] = { p4[0], p4[1] };
if( ( orient2d( d1, d2, d3 ) == 0.0 ) &&
( orient2d( d1, d2, d4 ) == 0.0 ) )
{
// the lines are colinear => ... p1 p4 ... ; p2 ... p3
intersect = true;
}
else
{
if( doIntersect( globalverts, i1, i1 + 1, i2, ( i2 + 1 ) % oldNum ) )
{
// the lines intersect => ... p1 ip p4 ... ; ip p2 ... p3
Vec2d v1 = p2 - p1;
Vec2d v2 = p4 - p3;
Vec2d pp = p3 - p1;
double a = pp[0] * v2[1] - pp[1] * v2[0];
double b = v1[0] * v2[1] - v1[1] * v2[0];
Vec2d ip = p1 + v1 * ( a / b );
if( DCTPVecIsEqual( ip , p1 ) )
{
iip = vertices[ i1 ];
}
else if( DCTPVecIsEqual( ip , p2 ) )
{
iip = vertices[ i1 + 1 ];
}
else if( DCTPVecIsEqual( ip , p3 ) )
{
iip = vertices[ i2 ];
}
else if( DCTPVecIsEqual( ip , p4 ) )
{
iip = vertices[ ( i2 + 1 ) % oldNum ];
}
else
{
iip = globalverts.size();
globalverts.resize( iip + 1 );
globalverts[ iip ] = ip;
}
// std::cerr << p1[0] << "," << p1[1] << " - " << p2[0] << "," << p2[1] << std::endl;
// std::cerr << p3[0] << "," << p3[1] << " - " << p4[0] << "," << p4[1] << std::endl;
// std::cerr << globalverts[ iip ][0] << "," << globalverts[ iip ][1] << " - " << std::endl;
intersect = true;
}
}
if( intersect )
{
int i;
int newNum;
DCTPivector newPoints( oldNum );
SimplePolygon poly;
// std::cerr << i1 << "," << i1 + 1 << " intersects " << i2 << "," << i2 + 1 << std::endl;
// copy points 0 ... i1
for( i = 0; i <= i1; ++i )
{
newPoints[ i ] = vertices[ i ];
}
newNum = i;
// copy iip's
if( iip >= 0 )
{
if( ( iip != vertices[ i1 ] ) &&
( iip != vertices[ ( i2 + 1 ) % oldNum ] ) )
{
newPoints[ newNum ] = iip;
++newNum;
}
if( ( iip != vertices[ i2 ] ) &&
( iip != vertices[ i1 + 1 ] ) )
{
poly.vertices.resize( i2 + 1 - i1 );
poly.vertices[ i2 - i1 ] = iip;
}
else
{
poly.vertices.resize( i2 - i1 );
}
}
else
{
poly.vertices.resize( i2 - i1 );
}
// copy i1+1 ... i2
for( i = 0; i < i2 - i1; ++i )
{
poly.vertices[ i ] = vertices[ i1 + i + 1 ];
}
// copy i2+1 ... n
for( i = i2 + 1; i < oldNum; ++i )
{
newPoints[ newNum ] = vertices[ i ];
++newNum;
}
// copy new points back to polygon
vertices.resize( newNum );
for( i2 = 0; i2 < newNum; ++i2 )
{
vertices[ i2 ] = newPoints[ i2 ];
}
// std::cerr << "split in " << newNum << "," << poly.vertices.size() << std::endl;
// triangulate the new polygon
while( poly.intersectPolygon( globalverts, polylist ) ) { }
if( poly.isReversed( globalverts ) )
{
// std::cerr << "Ignoring reversed polygon." << std::endl;
}
else
{
// Ok, we have a valid polygon, so triangulate it.
poly.triangulate( globalverts, polylist );
}
// check if there are other intersections
return 1;
}
}
}
}
// polygon had no intersections so we are finished
return 0;
}
/*!
* Note that this has complexity O(n).
*
* \param globalverts the global vertices vector
* \return zero on success, and a negative integer if some error occured.
*/
int SimplePolygon::removeLinearPoints( DCTPVec2dvector &globalverts, const Vec2d min, const Vec2d max )
{
int oldNum = vertices.size( );
int newNum = 0;
DCTPivector newPoints( oldNum ); // waste some memory to have linear time
int i;
int last = oldNum - 1;
// std::cerr << "Removing linear points... " << oldNum << std::endl;
// insert nonlienaer points in new array
for( i = 0; i < oldNum; ++i )
{
Vec2d p = globalverts[ vertices[ i ] ];
// check for double vertices
if( DCTPVecIsNotEqual( p , globalverts[ vertices[ last ] ] ) )
{
Vec2d pp = globalverts[ vertices[ last ] ];
Vec2d pn = globalverts[ vertices[ ( i + 1 ) % oldNum ] ];
if( ( ( p[0] - min[0] < DCTP_EPS ) && ( pn[0] - min[0] < DCTP_EPS ) ) ||
( ( p[1] - min[1] < DCTP_EPS ) && ( pn[1] - min[1] < DCTP_EPS ) ) ||
( ( max[0] - p[0] < DCTP_EPS ) && ( max[0] - pn[0] < DCTP_EPS ) ) ||
( ( max[1] - p[1] < DCTP_EPS ) && ( max[1] - pn[1] < DCTP_EPS ) ) )
{
newPoints[ newNum ] = vertices[ i ];
++newNum;
last = i;
}
else
{
double d1[ 2 ], d2[ 2 ], d3[ 2 ];
d1[ 0 ] = pp[0];
d1[ 1 ] = pp[1];
d2[ 0 ] = p[0];
d2[ 1 ] = p[1];
d3[ 0 ] = pn[0];
d3[ 1 ] = pn[1];
if( orient2d( d1, d2, d3 ) != 0 )
{
newPoints[ newNum ] = vertices[ i ];
++newNum;
last = i;
}
/* else if( ( pp[1] != pn[1] ) && ( pp[0] != pn[0] ) )
{
std::cerr << "removing point " <<std::endl;
std::cerr << pp[0] << "," << pp[1] << std::endl;
std::cerr << "(" << p[0] << "," << p[1] << ")" << std::endl;
std::cerr << pn[0] << "," << pn[1] << std::endl;
char x[ 256 ];
gets( x );
}*/
}
}
}
// std::cerr << newNum << " points left." << std::endl;
// copy new points
if( newNum != oldNum )
{
vertices.resize( newNum );
for( i = 0; i < newNum; ++i )
{
vertices[ i ] = newPoints[ i ];
}
return 1;
}
return 0;
}
/*!
* Note that the resulting triangulation will not necessarily be complex,
* since it's constrained by the polygon's edges.
*
* Besides triangulating the polygon this method also does:
* - insertion of the new polygons (triangles) at the end of
* the polygon list.
* - setting up marking information for the new polygons.
*
* \param polylist the global list of polygons
* \param selfindex the index of this polygon in the global list
* \return zero on success, and a negative integer if some error occured.
*/
int SimplePolygon::triangulate( DCTPVec2dvector &globalverts, simplepolygonvector &polylist)
{
#ifdef OSG_TRIANGULATE_CONVEX
if( ( !is_marked ) && ( m_bConvex ) )
{
// std::cerr <<"triangulating convex: " <<vertices.size() << std::endl;
switch( vertices.size( ) )
{
case 0:
case 1:
case 2:
return 0;
case 3:
{
polylist.push_back( *this );
}
return 0;
}
unsigned int ui_prev;
unsigned int ui_mid;
unsigned int ui_next;
const unsigned int cui_vertex_cnt = vertices.size( );
SimplePolygon cl_poly;
ui_mid = 0;
for( ui_prev = 1; ui_prev < cui_vertex_cnt; ++ui_prev )
{
if( globalverts[ vertices[ ui_prev ] ][1] < globalverts[ vertices[ ui_mid ] ][1] )
{
ui_mid = ui_prev;
}
else if( ( globalverts[ vertices[ ui_prev ] ][1] == globalverts[ vertices[ ui_mid ] ][1] ) &&
( globalverts[ vertices[ ui_prev ] ][0] < globalverts[ vertices[ ui_mid ] ][0] ) )
{
ui_mid = ui_prev;
}
}
ui_prev = ( ui_mid + cui_vertex_cnt - 1 ) % cui_vertex_cnt;
ui_next = ( ui_mid + 1 ) % cui_vertex_cnt;
cl_poly.vertices.resize( 3 );
cl_poly.is_marked = is_marked;
cl_poly.vertices[ 0 ] = vertices[ ui_mid ];
cl_poly.vertices[ 1 ] = vertices[ ui_next ];
cl_poly.vertices[ 2 ] = vertices[ ui_prev ];
ui_prev = ( ui_prev + cui_vertex_cnt - 1 ) % cui_vertex_cnt;
ui_next = ( ui_next + 1 ) % cui_vertex_cnt;
while( cl_poly.vertices[ 1 ] != cl_poly.vertices[ 2 ] )
{
polylist.push_back( cl_poly );
if( globalverts[ vertices[ ui_prev ] ][1] < globalverts[ vertices[ ui_next ] ][1] )
{
cl_poly.vertices[ 0 ] = cl_poly.vertices[ 2 ];
cl_poly.vertices[ 2 ] = vertices[ ui_prev ];
ui_prev = ( ui_prev + cui_vertex_cnt - 1 ) % cui_vertex_cnt;
}
else if( ( globalverts[ vertices[ ui_prev ] ][1] == globalverts[ vertices[ ui_next ] ][1] ) &&
( globalverts[ vertices[ ui_prev ] ][0] < globalverts[ vertices[ ui_next ] ][0] ) )
{
cl_poly.vertices[ 0 ] = cl_poly.vertices[ 2 ];
cl_poly.vertices[ 2 ] = vertices[ ui_prev ];
ui_prev = ( ui_prev + cui_vertex_cnt - 1 ) % cui_vertex_cnt;
}
else
{
cl_poly.vertices[ 0 ] = cl_poly.vertices[ 1 ];
cl_poly.vertices[ 1 ] = vertices[ ui_next ];
ui_next = ( ui_next + 1 ) % cui_vertex_cnt;
}
}
return 0;
}
#endif
// std::cerr << " triangulate in, size: " << vertices.size() << std::endl;
switch( vertices.size( ) )
{
case 0:
case 1:
case 2:
return 0;
case 3:
{
polylist.push_back( *this );
// SimplePolygon p;
// p.vertices = vertices;
// p.is_marked = is_marked;
// std::cerr << "adding polygon of 3 vertices into the list..." << std::endl;
// polylist.push_back( p ); // FIXME, this is not too elegant
// std::cerr << "triangulate out!!!" << std::endl;
}
return 0;
case 4:
{
const int ci_v1 = vertices[ 0 ];
const int ci_v2 = vertices[ 1 ];
const int ci_v3 = vertices[ 2 ];
const int ci_v4 = vertices[ 3 ];
const double cd_sdist1 = ( globalverts[ ci_v1 ] - globalverts[ ci_v3 ] ).squareLength( );
const double cd_sdist2 = ( globalverts[ ci_v2 ] - globalverts[ ci_v4 ] ).squareLength( );
double ad_pa[ 2 ];
double ad_pb[ 2 ];
double ad_pc[ 2 ];
double ad_pd[ 2 ];
SimplePolygon p;
p.vertices.resize( 3 );
p.is_marked = is_marked;
ad_pa[ 0 ] = globalverts[ ci_v1 ][0];
ad_pa[ 1 ] = globalverts[ ci_v1 ][1];
ad_pb[ 0 ] = globalverts[ ci_v2 ][0];
ad_pb[ 1 ] = globalverts[ ci_v2 ][1];
ad_pc[ 0 ] = globalverts[ ci_v3 ][0];
ad_pc[ 1 ] = globalverts[ ci_v3 ][1];
ad_pd[ 0 ] = globalverts[ ci_v4 ][0];
ad_pd[ 1 ] = globalverts[ ci_v4 ][1];
if( cd_sdist1 - cd_sdist2 < DCTP_EPS )
{
/* const double cd_r1 = orient2d( ad_pa, ad_pb, ad_pc );
const double cd_r2 = orient2d( ad_pa, ad_pb, ad_pd );
if( ( ( cd_r1 <= 0.0 ) && ( cd_r2 <= 0.0 ) ) ||
( ( cd_r1 >= 0.0 ) && ( cd_r2 >= 0.0 ) ) )*/
if( ( orient2d( ad_pa, ad_pb, ad_pc ) <= 0.0 ) ||
( orient2d( ad_pa, ad_pd, ad_pc ) >= 0.0 ) ||
( incircle( ad_pa, ad_pb, ad_pc, ad_pd ) > 0.0 ) )
{
p.vertices[ 0 ] = ci_v1;
p.vertices[ 1 ] = ci_v2;
p.vertices[ 2 ] = ci_v4;
polylist.push_back( p );
p.vertices[ 0 ] = ci_v2;
p.vertices[ 1 ] = ci_v3;
p.vertices[ 2 ] = ci_v4;
polylist.push_back( p );
// std::cerr << globalverts[ ci_v1 ] << globalverts[ ci_v2 ] << globalverts[ ci_v3 ] << globalverts[ ci_v4 ] << std::endl;
}
else
{
p.vertices[ 0 ] = ci_v1;
p.vertices[ 1 ] = ci_v2;
p.vertices[ 2 ] = ci_v3;
polylist.push_back( p );
p.vertices[ 0 ] = ci_v1;
p.vertices[ 1 ] = ci_v3;
p.vertices[ 2 ] = ci_v4;
polylist.push_back( p );
}
}
else
{
// const double cd_r1 = orient2d( ad_pc, ad_pd, ad_pa );
// const double cd_r2 = orient2d( ad_pc, ad_pd, ad_pb );
// if( ( ( cd_r1 <= 0.0 ) && ( cd_r2 <= 0.0 ) ) ||
// ( ( cd_r1 >= 0.0 ) && ( cd_r2 >= 0.0 ) ) )
if( ( orient2d( ad_pb, ad_pc, ad_pd ) <= 0.0 ) ||
( orient2d( ad_pb, ad_pa, ad_pd ) >= 0.0 ) ||
( incircle( ad_pa, ad_pb, ad_pd, ad_pc ) > 0.0 ) )
{
p.vertices[ 0 ] = ci_v1;
p.vertices[ 1 ] = ci_v2;
p.vertices[ 2 ] = ci_v3;
polylist.push_back( p );
p.vertices[ 0 ] = ci_v1;
p.vertices[ 1 ] = ci_v3;
p.vertices[ 2 ] = ci_v4;
polylist.push_back( p );
// std::cerr << globalverts[ ci_v1 ] << globalverts[ ci_v2 ] << globalverts[ ci_v3 ] << globalverts[ ci_v4 ] << std::endl;
}
else
{
p.vertices[ 0 ] = ci_v1;
p.vertices[ 1 ] = ci_v2;
p.vertices[ 2 ] = ci_v4;
polylist.push_back( p );
p.vertices[ 0 ] = ci_v2;
p.vertices[ 1 ] = ci_v3;
p.vertices[ 2 ] = ci_v4;
polylist.push_back( p );
}
}
}
return 0;
}
// recalc valid third points!
v1tp = -1;
validThirdPoints.resize( vertices.size( ) );
SimplePolygon poly;
int i2, i3; // this is an index into the vertices[] vector
int err;
DCTPivector verts; //p1verts, p2verts, p3verts;
int i;
int j;
// pseudo random (reproduces same triangulation)
int offs = ( int( globalverts[ vertices[ 0 ] ][0] * vertices.size( ) ) ) % vertices.size( );
/* for( i = 0; i < vertices.size( ); ++i )
{
std::cerr << globalverts[ vertices[ i ] ][0] << ",";
std::cerr << globalverts[ vertices[ i ] ][1] << std::endl;
}*/
for( j = 0; j < int(vertices.size()); j++ ) {
i = ( j + offs ) % vertices.size( );
// v1 = vertices[ i ];
if ( i == int(vertices.size()) - 1 )
i2 = 0; //v2 = vertices [ 0 ];
else
i2 = i + 1; //v2 = vertices[ i + 1 ];
err = findThirdPoint( globalverts, i, i2, i3 );
if ( err ) return err;
if ( i3 >= 0 ) {
// build p1
int k = i2; // !!!
verts.resize( 0 );
while ( k != i3 ) {
// std::cerr << " k: " << k;
verts.push_back( vertices[ k ] );
k++; if ( k == int(vertices.size()) ) k = 0;
} // while k
verts.push_back( vertices[ k ] ); // record the last one aswell
// std::cerr << " k: " << k << std::endl;
poly.vertices = verts;
poly.is_marked = is_marked;
// std::cerr << "calling p1... " << std::endl;
err = poly.triangulate( globalverts, polylist);
if ( err ) return err;
// build p2
verts.resize( 3 );
verts[ 0 ] = vertices[ i ];
verts[ 1 ] = vertices[ i2 ];
verts[ 2 ] = vertices[ i3 ];
poly.vertices = verts;
poly.is_marked = is_marked;
// std::cerr << "adding p2 to the list..." << std::endl;
polylist.push_back( poly );
// build p3
k = i3;
verts.resize( 0 );
while ( k != i ) {
verts.push_back( vertices[ k ] );
k++; if ( k == int(vertices.size()) ) k = 0;
} // while k
verts.push_back( vertices[ k ] ); // record the last one aswell
poly.vertices = verts;
poly.is_marked = is_marked;
// std::cerr << "calling p3... " << std::endl;
err = poly.triangulate( globalverts, polylist );
if ( err ) return err;
// std::cerr << "triangulate out!!!" << std::endl;
return 0;
} // if
} // for i
/* SWARNING << "triangulate out WITH ERROR!!!" << endLog;
for( i = 0; i < vertices.size( ); ++i )
{
std::cerr << globalverts[ vertices[ i ] ][0] << ",";
std::cerr << globalverts[ vertices[ i ] ][1] << std::endl;
}*/
// char x[ 256 ];
// gets( x );
return -1;
}
/*!
* `i1' and `i2' must already be an edge of the polygon, and the third point `i3'
* be a point of the polygon different from `i1' and `i2'. The polygon's lines
* must not cross each other.
*
* \param globalverts global vertices vector
* \param i1 first point
* \param i2 second point (must form an edge with the first point)
* \param i3 third point
* \return 1 if not inside <BR>
* 0 if inside <BR>
* and a negative value if an error happened.
*/
int SimplePolygon::isInsidePolygon( DCTPVec2dvector &globalverts, int i1, int i2, int i3 ) const
{
double dres;
const int size = vertices.size( );
const int vi1 = vertices[ i1 ];
const int vi2 = vertices[ i2 ];
const int vi3 = vertices[ i3 ];
const int prev = vertices[ ( size + i1 - 1 ) % size ];
const int next = vertices[ ( i2 + 1 ) % size ];
// the third (i3) point must lie to the left of the edge (i2, next)
// (NOT! on the edge) to be inside
double p2[ 2 ], p3[ 2 ], pn[ 2 ];
p3 [ 0 ] = globalverts[ vi3 ][0];
p3 [ 1 ] = globalverts[ vi3 ][1];
p2 [ 0 ] = globalverts[ vi2 ][0];
p2 [ 1 ] = globalverts[ vi2 ][1];
pn [ 0 ] = globalverts[ next ][0];
pn [ 1 ] = globalverts[ next ][1];
if( vi3 != next )
{
dres = orient2d( p3, p2, pn );
// std::cerr << "next edge test: " << dres << std::endl;
if ( dres < 0.0 ) return 1;
}
// the third (i3) point must also lie to the left of the edge (prev, i1)
// (NOT! on the edge) to be inside
double p1[ 2 ], pp[ 2 ];
pp [ 0 ] = globalverts[ prev ][0];
pp [ 1 ] = globalverts[ prev ][1];
p1 [ 0 ] = globalverts[ vi1 ][0];
p1 [ 1 ] = globalverts[ vi1 ][1];
if( vi3 != prev )
{
dres = orient2d( p3, pp, p1 );
// std::cerr << "prev edge test: " << dres << std::endl;
if ( dres < 0.0 ) return 1;
}
// the third (i3) point must also lie to the left of the edge (i1, i2)
// (NOT! on the edge) to be inside
dres = orient2d( p3, p1, p2 );
// std::cerr << "actual edge test: " << dres << std::endl;
if ( dres <= 0.0 ) return 1;
// if( m_bConvex ) return 0; // don't need intersection test for convex polygons
// the triangle is not completely outside the polygon, we have to
// go for the intersection test.
// FIXME/TODO: use bounding boxes to speed up testing:
// only test with those edges that are at least partially in the
// bounding box of the triangle to be tested
int res;
int j = size - 1;
Vec2d min, max;
unsigned char test, ptest;
min = max = globalverts[ vi1 ];
if( min[0] > globalverts[ vi2 ][0] )
min[0] = globalverts[ vi2 ][0];
else if( max[0] < globalverts[ vi2 ][0] )
max[0] = globalverts[ vi2 ][0];
if( min[1] > globalverts[ vi2 ][1] )
min[1] = globalverts[ vi2 ][1];
else if( max[1] < globalverts[ vi2 ][1] )
max[1] = globalverts[ vi2 ][1];
if( min[0] > globalverts[ vi3 ][0] )
min[0] = globalverts[ vi3 ][0];
else if( max[0] < globalverts[ vi3 ][0] )
max[0] = globalverts[ vi3 ][0];
if( min[1] > globalverts[ vi3 ][1] )
min[1] = globalverts[ vi3 ][1];
else if( max[1] < globalverts[ vi3 ][1] )
max[1] = globalverts[ vi3 ][1];
const Vec2d &pj = globalverts[ vertices[ j ] ];
test = 0;
if( pj[0] - max[0] > DCTP_EPS ) test |= 0x01;
if( min[0] - pj[0] > DCTP_EPS ) test |= 0x02;
if( pj[1] - max[1] > DCTP_EPS ) test |= 0x04;
if( min[1] - pj[1] > DCTP_EPS ) test |= 0x08;
for ( int i = 0; i < size; i++ )
{
ptest = test;
test = 0;
const Vec2d &pi = globalverts[ vertices[ i ] ];
if( pi[0] - max[0] > DCTP_EPS ) test |= 0x01;
if( min[0] - pi[0] > DCTP_EPS ) test |= 0x02;
if( pi[1] - max[1] > DCTP_EPS ) test |= 0x04;
if( min[1] - pi[1] > DCTP_EPS ) test |= 0x08;
if( ( test & ptest ) == 0 )
{
// std::cerr << "checking: " << v1 << " " << v3 << " and i: " << i << std::endl;
res = doIntersect( globalverts, i1, i3, j, i );
if ( res ) return res; // either intersection or error
res = doIntersect( globalverts, i2, i3, j, i );
if ( res ) return res; // see above
}
j = i;
}
return 0;
}
void
CalcPixels2(double Edges[3][2], int **Pixels, int *counter)
{
int i;
double minX=10000000,maxX=-10000000,minY=100000000,maxY=-100000000;
for (i=0;i<3;i++){
Edges[i][0] = round(Edges[i][0]);
Edges[i][1] = round(Edges[i][1]);
}
for (i=0;i<3;i++){
if (Edges[i][0]<minX){
minX = Edges[i][0];
}
if (Edges[i][0]>maxX){
maxX = Edges[i][0];
}
if (Edges[i][1]<minY){
minY = Edges[i][1];
}
if (Edges[i][1]>maxY){
maxY = Edges[i][1];
}
}
*counter = 0;
int A01 = Edges[0][1] - Edges[1][1], B01 = Edges[1][0] - Edges[0][0];
int A12 = Edges[1][1] - Edges[2][1], B12 = Edges[2][0] - Edges[1][0];
int A20 = Edges[2][1] - Edges[0][1], B20 = Edges[0][0] - Edges[2][0];
struct Point2D p = { minX, minY };
struct Point2D v0 = { Edges[0][0], Edges[0][1]};
struct Point2D v1 = { Edges[1][0], Edges[1][1]};
struct Point2D v2 = { Edges[2][0], Edges[2][1]};
int w0_row = orient2d(v1, v2, p);
int w1_row = orient2d(v2, v0, p);
int w2_row = orient2d(v0, v1, p);
for (p.y = minY; p.y <= maxY; p.y++) {
int w0 = w0_row;
int w1 = w1_row;
int w2 = w2_row;
for (p.x = minX; p.x <= maxX; p.x++) {
if (w0 >= 0 && w1 >= 0 && w2 >= 0){
Pixels[*counter][0] = p.x;
Pixels[*counter][1] = p.y;
*counter+=1;
}
else if(len2d(v1,v2,p)<0.99){
Pixels[*counter][0] = p.x;
Pixels[*counter][1] = p.y;
*counter+=1;
}
else if(len2d(v2,v0,p)<0.99){
Pixels[*counter][0] = p.x;
Pixels[*counter][1] = p.y;
*counter+=1;
}
else if(len2d(v0,v1,p)<0.99){
Pixels[*counter][0] = p.x;
Pixels[*counter][1] = p.y;
*counter+=1;
}
w0 += A12;
w1 += A20;
w2 += A01;
}
w0_row += B12;
w1_row += B20;
w2_row += B01;
}
}
Orient PredWrapper::doOrient3DSoSOnly
(
const RealType* p0,
const RealType* p1,
const RealType* p2,
const RealType* p3,
int v0,
int v1,
int v2,
int v3
) const
{
////
// Sort points using vertex as key, also note their sorted order
////
const int DIM = 3;
const int NUM = DIM + 1;
const RealType* p[NUM] = { p0, p1, p2, p3 };
int v[NUM] = { v0, v1, v2, v3 };
int pn = 1;
for ( int i = 0; i < 3; ++i )
{
int minI = i;
for ( int j = i + 1; j < 4; ++j )
if ( v[j] < v[minI] )
minI = j;
if ( minI != i )
{
int tempI = v[minI];
v[minI] = v[i];
v[i] = tempI;
pn = -pn;
//cuSwap( p[minI], p[i] );
std::swap( p[minI], p[i] );
}
}
RealType result = 0;
RealType pa2[2], pb2[2], pc2[2];
int depth;
for ( depth = 0; depth < 14; ++depth )
{
switch ( depth )
{
case 0:
pa2[0] = p[1][0];
pa2[1] = p[1][1];
pb2[0] = p[2][0];
pb2[1] = p[2][1];
pc2[0] = p[3][0];
pc2[1] = p[3][1];
break;
case 1:
pa2[0] = p[1][0];
pa2[1] = p[1][2];
pb2[0] = p[2][0];
pb2[1] = p[2][2];
pc2[0] = p[3][0];
pc2[1] = p[3][2];
break;
case 2:
pa2[0] = p[1][1];
pa2[1] = p[1][2];
pb2[0] = p[2][1];
pb2[1] = p[2][2];
pc2[0] = p[3][1];
pc2[1] = p[3][2];
break;
case 3:
pa2[0] = p[0][0];
pa2[1] = p[0][1];
pb2[0] = p[2][0];
pb2[1] = p[2][1];
pc2[0] = p[3][0];
pc2[1] = p[3][1];
break;
case 4:
result = p[2][0] - p[3][0];
break;
case 5:
result = p[2][1] - p[3][1];
break;
case 6:
pa2[0] = p[0][0];
pa2[1] = p[0][2];
pb2[0] = p[2][0];
pb2[1] = p[2][2];
pc2[0] = p[3][0];
pc2[1] = p[3][2];
break;
case 7:
result = p[2][2] - p[3][2];
break;
case 8:
pa2[0] = p[0][1];
pa2[1] = p[0][2];
pb2[0] = p[2][1];
pb2[1] = p[2][2];
pc2[0] = p[3][1];
pc2[1] = p[3][2];
break;
case 9:
pa2[0] = p[0][0];
pa2[1] = p[0][1];
pb2[0] = p[1][0];
pb2[1] = p[1][1];
pc2[0] = p[3][0];
pc2[1] = p[3][1];
break;
case 10:
result = p[1][0] - p[3][0];
break;
case 11:
result = p[1][1] - p[3][1];
break;
case 12:
result = p[0][0] - p[3][0];
break;
default:
result = 1.0;
break;
}
switch ( depth )
{
case 0:
case 1:
case 2:
case 3:
case 6:
case 8:
case 9:
result = orient2d( pa2, pb2, pc2 );
}
if ( result != 0 )
break;
}
switch ( depth )
{
case 1:
case 3:
case 5:
case 8:
case 10:
result = -result;
}
const RealType det = result * pn;
return ortToOrient( det );
}
