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detria.hpp
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// detria - a delaunay triangulation library
//
// Example usage:
/*
// Create a square, and triangulate it
// List of points (positions)
std::vector<detria::PointD> points =
{
{ 0.0, 0.0 },
{ 1.0, 0.0 },
{ 1.0, 1.0 },
{ 0.0, 1.0 }
};
// List of point indices
std::vector<uint32_t> outline = { 0, 1, 2, 3 };
bool delaunay = true;
detria::Triangulation tri;
tri.setPoints(points);
tri.addOutline(outline);
bool success = tri.triangulate(delaunay);
if (success)
{
bool cwTriangles = true;
tri.forEachTriangle([&](detria::Triangle<uint32_t> triangle)
{
// `triangle` contains the point indices
detria::PointD firstPointOfTriangle = points[triangle.x];
detria::PointD secondPointOfTriangle = points[triangle.y];
detria::PointD thirdPointOfTriangle = points[triangle.z];
}, cwTriangles);
}
*/
// See https://github.com/Kimbatt/detria for more information and full documentation.
// License: WTFPL or MIT, at your choice. You can find the license texts at the bottom of this file.
#ifndef DETRIA_HPP_INCLUDED
#define DETRIA_HPP_INCLUDED
#ifdef DETRIA_CXXMODULE
// Using C++20 modules - headers are included by the module file
// Also define the export macro
#define DETRIA_EXPORT export
#else
#include <vector>
#include <array>
#include <cmath>
#include <cstdint>
#include <type_traits>
#include <optional>
#include <variant>
#include <string>
#include <sstream>
#if !defined(NDEBUG)
#include <iostream>
#include <limits>
#if !defined(_WIN32) || !_WIN32
#include <csignal>
#endif
#endif
// Not using C++20 modules - define an empty export macro
#define DETRIA_EXPORT
#endif
namespace detria
{
template <typename T>
struct Vec2
{
T x;
T y;
};
DETRIA_EXPORT using PointF = Vec2<float>;
DETRIA_EXPORT using PointD = Vec2<double>;
DETRIA_EXPORT template <typename Idx>
struct Triangle
{
Idx x;
Idx y;
Idx z;
};
template <typename Idx>
struct Edge
{
Idx x;
Idx y;
};
#if (defined(_MSVC_LANG) && _MSVC_LANG >= 202002L) || __cplusplus >= 202002L
#define DETRIA_LIKELY [[likely]]
#define DETRIA_UNLIKELY [[unlikely]]
#else
#define DETRIA_LIKELY
#define DETRIA_UNLIKELY
#endif
namespace predicates
{
// http://www.cs.cmu.edu/~quake/robust.html
// Routines for Arbitrary Precision Floating-point Arithmetic and Fast Robust Geometric Predicates
// Placed in the public domain by Jonathan Richard Shewchuk
template <typename Scalar>
struct ErrorBounds
{
Scalar splitter;
Scalar epsilon;
Scalar resulterrbound;
Scalar ccwerrboundA, ccwerrboundB, ccwerrboundC;
Scalar o3derrboundA, o3derrboundB, o3derrboundC;
Scalar iccerrboundA, iccerrboundB, iccerrboundC;
Scalar isperrboundA, isperrboundB, isperrboundC;
};
template <typename Scalar>
constexpr ErrorBounds<Scalar> calculateErrorBounds()
{
Scalar check = Scalar(1);
bool everyOther = true;
Scalar epsilon = Scalar(1);
Scalar splitter = Scalar(1);
Scalar lastcheck{ };
do
{
lastcheck = check;
epsilon *= Scalar(0.5);
if (everyOther)
{
splitter *= Scalar(2);
}
everyOther = !everyOther;
check = Scalar(1) + epsilon;
}
while (check != Scalar(1) && (check != lastcheck));
splitter += Scalar(1);
ErrorBounds<Scalar> bounds{ };
bounds.splitter = splitter;
bounds.epsilon = epsilon;
bounds.resulterrbound = (Scalar(3) + Scalar(8) * epsilon) * epsilon;
bounds.ccwerrboundA = (Scalar(3) + Scalar(16) * epsilon) * epsilon;
bounds.ccwerrboundB = (Scalar(2) + Scalar(12) * epsilon) * epsilon;
bounds.ccwerrboundC = (Scalar(9) + Scalar(64) * epsilon) * epsilon * epsilon;
bounds.o3derrboundA = (Scalar(7) + Scalar(56) * epsilon) * epsilon;
bounds.o3derrboundB = (Scalar(3) + Scalar(28) * epsilon) * epsilon;
bounds.o3derrboundC = (Scalar(26) + Scalar(288) * epsilon) * epsilon * epsilon;
bounds.iccerrboundA = (Scalar(10) + Scalar(96) * epsilon) * epsilon;
bounds.iccerrboundB = (Scalar(4) + Scalar(48) * epsilon) * epsilon;
bounds.iccerrboundC = (Scalar(44) + Scalar(576) * epsilon) * epsilon * epsilon;
bounds.isperrboundA = (Scalar(16) + Scalar(224) * epsilon) * epsilon;
bounds.isperrboundB = (Scalar(5) + Scalar(72) * epsilon) * epsilon;
bounds.isperrboundC = (Scalar(71) + Scalar(1408) * epsilon) * epsilon * epsilon;
return bounds;
}
template <typename Scalar>
static constexpr predicates::ErrorBounds<Scalar> errorBounds = predicates::calculateErrorBounds<Scalar>();
#define DETRIA_INEXACT
#define DETRIA_Fast_Two_Sum_Tail(a, b, x, y) \
bvirt = x - a; \
y = b - bvirt
#define DETRIA_Fast_Two_Sum(a, b, x, y) \
x = Scalar(a + b); \
DETRIA_Fast_Two_Sum_Tail(a, b, x, y)
#define DETRIA_Two_Sum_Tail(a, b, x, y) \
bvirt = Scalar(x - a); \
avirt = x - bvirt; \
bround = b - bvirt; \
around = a - avirt; \
y = around + bround
#define DETRIA_Two_Sum(a, b, x, y) \
x = Scalar(a + b); \
DETRIA_Two_Sum_Tail(a, b, x, y)
#define DETRIA_Two_Diff_Tail(a, b, x, y) \
bvirt = Scalar(a - x); \
avirt = x + bvirt; \
bround = bvirt - b; \
around = a - avirt; \
y = around + bround
#define DETRIA_Two_Diff(a, b, x, y) \
x = Scalar(a - b); \
DETRIA_Two_Diff_Tail(a, b, x, y)
#define DETRIA_Split(a, ahi, alo) \
c = Scalar(errorBounds<Scalar>.splitter * a); \
abig = Scalar(c - a); \
ahi = c - abig; \
alo = a - ahi
#define DETRIA_Two_Product_Tail(a, b, x, y) \
DETRIA_Split(a, ahi, alo); \
DETRIA_Split(b, bhi, blo); \
err1 = x - (ahi * bhi); \
err2 = err1 - (alo * bhi); \
err3 = err2 - (ahi * blo); \
y = (alo * blo) - err3
#define DETRIA_Two_Product(a, b, x, y) \
x = Scalar(a * b); \
DETRIA_Two_Product_Tail(a, b, x, y)
#define DETRIA_Two_Product_Presplit(a, b, bhi, blo, x, y) \
x = Scalar(a * b); \
DETRIA_Split(a, ahi, alo); \
err1 = x - (ahi * bhi); \
err2 = err1 - (alo * bhi); \
err3 = err2 - (ahi * blo); \
y = (alo * blo) - err3
#define DETRIA_Square_Tail(a, x, y) \
DETRIA_Split(a, ahi, alo); \
err1 = x - (ahi * ahi); \
err3 = err1 - ((ahi + ahi) * alo); \
y = (alo * alo) - err3
#define DETRIA_Square(a, x, y) \
x = Scalar(a * a); \
DETRIA_Square_Tail(a, x, y)
#define DETRIA_Two_One_Sum(a1, a0, b, x2, x1, x0) \
DETRIA_Two_Sum(a0, b , _i, x0); \
DETRIA_Two_Sum(a1, _i, x2, x1)
#define DETRIA_Two_One_Diff(a1, a0, b, x2, x1, x0) \
DETRIA_Two_Diff(a0, b , _i, x0); \
DETRIA_Two_Sum( a1, _i, x2, x1)
#define DETRIA_Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
DETRIA_Two_One_Sum(a1, a0, b0, _j, _0, x0); \
DETRIA_Two_One_Sum(_j, _0, b1, x3, x2, x1)
#define DETRIA_Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
DETRIA_Two_One_Diff(a1, a0, b0, _j, _0, x0); \
DETRIA_Two_One_Diff(_j, _0, b1, x3, x2, x1)
template <typename Scalar>
inline Scalar estimate(int elen, const Scalar* e)
{
Scalar Q = e[0];
for (int eindex = 1; eindex < elen; eindex++)
{
Q += e[eindex];
}
return Q;
}
template <typename Scalar>
inline constexpr Scalar Absolute(Scalar a)
{
return a >= Scalar(0) ? a : -a;
}
template <typename Scalar>
int fast_expansion_sum_zeroelim(int elen, const Scalar* e, int flen, const Scalar* f, Scalar* h)
{
Scalar Q;
DETRIA_INEXACT Scalar Qnew;
DETRIA_INEXACT Scalar hh;
DETRIA_INEXACT Scalar bvirt;
Scalar avirt, bround, around;
int eindex, findex, hindex;
Scalar enow, fnow;
enow = e[0];
fnow = f[0];
eindex = findex = 0;
if ((fnow > enow) == (fnow > -enow))
{
Q = enow;
enow = e[++eindex];
}
else
{
Q = fnow;
fnow = f[++findex];
}
hindex = 0;
if ((eindex < elen) && (findex < flen))
{
if ((fnow > enow) == (fnow > -enow))
{
DETRIA_Fast_Two_Sum(enow, Q, Qnew, hh);
enow = e[++eindex];
}
else
{
DETRIA_Fast_Two_Sum(fnow, Q, Qnew, hh);
fnow = f[++findex];
}
Q = Qnew;
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
while ((eindex < elen) && (findex < flen))
{
if ((fnow > enow) == (fnow > -enow))
{
DETRIA_Two_Sum(Q, enow, Qnew, hh);
if (++eindex < elen)
{
enow = e[eindex];
}
}
else
{
DETRIA_Two_Sum(Q, fnow, Qnew, hh);
if (++findex < flen)
{
fnow = f[findex];
}
}
Q = Qnew;
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
}
}
while (eindex < elen)
{
DETRIA_Two_Sum(Q, enow, Qnew, hh);
if (++eindex < elen)
{
enow = e[eindex];
}
Q = Qnew;
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
}
while (findex < flen)
{
DETRIA_Two_Sum(Q, fnow, Qnew, hh);
if (++findex < flen)
{
fnow = f[findex];
}
Q = Qnew;
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
}
if ((Q != Scalar(0)) || (hindex == 0))
{
h[hindex++] = Q;
}
return hindex;
}
template <typename Scalar>
Scalar orient2dadapt(Scalar pa[2], Scalar pb[2], Scalar pc[2], Scalar detsum)
{
DETRIA_INEXACT Scalar acx, acy, bcx, bcy;
Scalar acxtail, acytail, bcxtail, bcytail;
DETRIA_INEXACT Scalar detleft, detright;
Scalar detlefttail, detrighttail;
Scalar det, errbound;
Scalar B[4]{ }, C1[8]{ }, C2[12]{ }, D[16]{ };
DETRIA_INEXACT Scalar B3;
int C1length, C2length, Dlength;
Scalar u[4]{ };
DETRIA_INEXACT Scalar u3;
DETRIA_INEXACT Scalar s1, t1;
Scalar s0, t0;
DETRIA_INEXACT Scalar bvirt;
Scalar avirt, bround, around;
DETRIA_INEXACT Scalar c;
DETRIA_INEXACT Scalar abig;
Scalar ahi, alo, bhi, blo;
Scalar err1, err2, err3;
DETRIA_INEXACT Scalar _i, _j;
Scalar _0;
acx = pa[0] - pc[0];
bcx = pb[0] - pc[0];
acy = pa[1] - pc[1];
bcy = pb[1] - pc[1];
DETRIA_Two_Product(acx, bcy, detleft, detlefttail);
DETRIA_Two_Product(acy, bcx, detright, detrighttail);
DETRIA_Two_Two_Diff(detleft, detlefttail, detright, detrighttail, B3, B[2], B[1], B[0]);
B[3] = B3;
det = estimate(4, B);
errbound = errorBounds<Scalar>.ccwerrboundB * detsum;
if ((det >= errbound) || (-det >= errbound))
{
return det;
}
DETRIA_Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
DETRIA_Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
DETRIA_Two_Diff_Tail(pa[1], pc[1], acy, acytail);
DETRIA_Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
if ((acxtail == Scalar(0)) && (acytail == Scalar(0)) && (bcxtail == Scalar(0)) && (bcytail == Scalar(0)))
{
return det;
}
errbound = errorBounds<Scalar>.ccwerrboundC * detsum + errorBounds<Scalar>.resulterrbound * Absolute(det);
det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail);
if ((det >= errbound) || (-det >= errbound))
{
return det;
}
DETRIA_Two_Product(acxtail, bcy, s1, s0);
DETRIA_Two_Product(acytail, bcx, t1, t0);
DETRIA_Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
u[3] = u3;
C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
DETRIA_Two_Product(acx, bcytail, s1, s0);
DETRIA_Two_Product(acy, bcxtail, t1, t0);
DETRIA_Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
u[3] = u3;
C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
DETRIA_Two_Product(acxtail, bcytail, s1, s0);
DETRIA_Two_Product(acytail, bcxtail, t1, t0);
DETRIA_Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
u[3] = u3;
Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
return(D[Dlength - 1]);
}
template <typename Scalar>
int scale_expansion_zeroelim(int elen, const Scalar* e, Scalar b, Scalar* h)
{
DETRIA_INEXACT Scalar Q, sum;
Scalar hh;
DETRIA_INEXACT Scalar product1;
Scalar product0;
int eindex, hindex;
Scalar enow;
DETRIA_INEXACT Scalar bvirt;
Scalar avirt, bround, around;
DETRIA_INEXACT Scalar c;
DETRIA_INEXACT Scalar abig;
Scalar ahi, alo, bhi, blo;
Scalar err1, err2, err3;
DETRIA_Split(b, bhi, blo);
DETRIA_Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
hindex = 0;
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
for (eindex = 1; eindex < elen; eindex++)
{
enow = e[eindex];
DETRIA_Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
DETRIA_Two_Sum(Q, product0, sum, hh);
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
DETRIA_Fast_Two_Sum(product1, sum, Q, hh);
if (hh != Scalar(0))
{
h[hindex++] = hh;
}
}
if (Q != Scalar(0) || hindex == 0)
{
h[hindex++] = Q;
}
return hindex;
}
template <typename Scalar>
Scalar incircleadapt(Scalar pa[2], Scalar pb[2], Scalar pc[2], Scalar pd[2], Scalar permanent)
{
DETRIA_INEXACT Scalar adx, bdx, cdx, ady, bdy, cdy;
Scalar det, errbound;
DETRIA_INEXACT Scalar bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
Scalar bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
Scalar bc[4], ca[4], ab[4];
DETRIA_INEXACT Scalar bc3, ca3, ab3;
Scalar axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
int axbclen, axxbclen, aybclen, ayybclen, alen;
Scalar bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
int bxcalen, bxxcalen, bycalen, byycalen, blen;
Scalar cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
int cxablen, cxxablen, cyablen, cyyablen, clen;
Scalar abdet[64];
int ablen;
Scalar fin1[1152], fin2[1152];
Scalar* finnow, * finother, * finswap;
int finlength;
Scalar adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
DETRIA_INEXACT Scalar adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
Scalar adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
Scalar aa[4], bb[4], cc[4];
DETRIA_INEXACT Scalar aa3, bb3, cc3;
DETRIA_INEXACT Scalar ti1, tj1;
Scalar ti0, tj0;
Scalar u[4], v[4];
DETRIA_INEXACT Scalar u3, v3;
Scalar temp8[8], temp16a[16], temp16b[16], temp16c[16];
Scalar temp32a[32], temp32b[32], temp48[48], temp64[64];
int temp8len, temp16alen, temp16blen, temp16clen;
int temp32alen, temp32blen, temp48len, temp64len;
Scalar axtbb[8], axtcc[8], aytbb[8], aytcc[8];
int axtbblen, axtcclen, aytbblen, aytcclen;
Scalar bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
int bxtaalen, bxtcclen, bytaalen, bytcclen;
Scalar cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
int cxtaalen, cxtbblen, cytaalen, cytbblen;
Scalar axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
Scalar axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
Scalar axtbctt[8], aytbctt[8], bxtcatt[8];
Scalar bytcatt[8], cxtabtt[8], cytabtt[8];
int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
Scalar abt[8], bct[8], cat[8];
int abtlen, bctlen, catlen;
Scalar abtt[4], bctt[4], catt[4];
int abttlen, bcttlen, cattlen;
DETRIA_INEXACT Scalar abtt3, bctt3, catt3;
Scalar negate;
DETRIA_INEXACT Scalar bvirt;
Scalar avirt, bround, around;
DETRIA_INEXACT Scalar c;
DETRIA_INEXACT Scalar abig;
Scalar ahi, alo, bhi, blo;
Scalar err1, err2, err3;
DETRIA_INEXACT Scalar _i, _j;
Scalar _0;
axtbclen = 0;
aytbclen = 0;
bxtcalen = 0;
bytcalen = 0;
cxtablen = 0;
cytablen = 0;
adx = Scalar(pa[0] - pd[0]);
bdx = Scalar(pb[0] - pd[0]);
cdx = Scalar(pc[0] - pd[0]);
ady = Scalar(pa[1] - pd[1]);
bdy = Scalar(pb[1] - pd[1]);
cdy = Scalar(pc[1] - pd[1]);
DETRIA_Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
DETRIA_Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
DETRIA_Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
bc[3] = bc3;
axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
DETRIA_Two_Product(cdx, ady, cdxady1, cdxady0);
DETRIA_Two_Product(adx, cdy, adxcdy1, adxcdy0);
DETRIA_Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
ca[3] = ca3;
bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
DETRIA_Two_Product(adx, bdy, adxbdy1, adxbdy0);
DETRIA_Two_Product(bdx, ady, bdxady1, bdxady0);
DETRIA_Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
ab[3] = ab3;
cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
det = estimate(finlength, fin1);
errbound = errorBounds<Scalar>.iccerrboundB * permanent;
if ((det >= errbound) || (-det >= errbound))
{
return det;
}
DETRIA_Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
DETRIA_Two_Diff_Tail(pa[1], pd[1], ady, adytail);
DETRIA_Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
DETRIA_Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
DETRIA_Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
DETRIA_Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
if (adxtail == Scalar(0) && bdxtail == Scalar(0) && cdxtail == Scalar(0) &&
adytail == Scalar(0) && bdytail == Scalar(0) && cdytail == Scalar(0))
{
return det;
}
errbound = errorBounds<Scalar>.iccerrboundC * permanent + errorBounds<Scalar>.resulterrbound * Absolute(det);
det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
- (bdy * cdxtail + cdx * bdytail))
+ Scalar(2) * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
+ ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
- (cdy * adxtail + adx * cdytail))
+ Scalar(2) * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
+ ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
- (ady * bdxtail + bdx * adytail))
+ Scalar(2) * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
if (det >= errbound || -det >= errbound)
{
return det;
}
finnow = fin1;
finother = fin2;
if (bdxtail != Scalar(0) || bdytail != Scalar(0) || cdxtail != Scalar(0) || cdytail != Scalar(0))
{
DETRIA_Square(adx, adxadx1, adxadx0);
DETRIA_Square(ady, adyady1, adyady0);
DETRIA_Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
aa[3] = aa3;
}
if (cdxtail != Scalar(0) || cdytail != Scalar(0) || adxtail != Scalar(0) || adytail != Scalar(0))
{
DETRIA_Square(bdx, bdxbdx1, bdxbdx0);
DETRIA_Square(bdy, bdybdy1, bdybdy0);
DETRIA_Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
bb[3] = bb3;
}
if (adxtail != Scalar(0) || adytail != Scalar(0) || bdxtail != Scalar(0) || bdytail != Scalar(0))
{
DETRIA_Square(cdx, cdxcdx1, cdxcdx0);
DETRIA_Square(cdy, cdycdy1, cdycdy0);
DETRIA_Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
cc[3] = cc3;
}
if (adxtail != Scalar(0))
{
axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, Scalar(2) * adx, temp16a);
axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adytail != Scalar(0))
{
aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, Scalar(2) * ady, temp16a);
aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdxtail != Scalar(0))
{
bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, Scalar(2) * bdx, temp16a);
bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdytail != Scalar(0))
{
bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
temp16alen = scale_expansion_zeroelim(bytcalen, bytca, Scalar(2) * bdy, temp16a);
bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdxtail != Scalar(0))
{
cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, Scalar(2) * cdx, temp16a);
cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdytail != Scalar(0))
{
cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
temp16alen = scale_expansion_zeroelim(cytablen, cytab, Scalar(2) * cdy, temp16a);
cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adxtail != Scalar(0) || adytail != Scalar(0))
{
if (bdxtail != Scalar(0) || bdytail != Scalar(0) || cdxtail != Scalar(0) || cdytail != Scalar(0))
{
DETRIA_Two_Product(bdxtail, cdy, ti1, ti0);
DETRIA_Two_Product(bdx, cdytail, tj1, tj0);
DETRIA_Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
u[3] = u3;
negate = -bdy;
DETRIA_Two_Product(cdxtail, negate, ti1, ti0);
negate = -bdytail;
DETRIA_Two_Product(cdx, negate, tj1, tj0);
DETRIA_Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
v[3] = v3;
bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
DETRIA_Two_Product(bdxtail, cdytail, ti1, ti0);
DETRIA_Two_Product(cdxtail, bdytail, tj1, tj0);
DETRIA_Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
bctt[3] = bctt3;
bcttlen = 4;
}
else
{
bct[0] = Scalar(0);
bctlen = 1;
bctt[0] = Scalar(0);
bcttlen = 1;
}
if (adxtail != Scalar(0))
{
temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, Scalar(2) * adx, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
if (bdytail != Scalar(0))
{
temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdytail != Scalar(0))
{
temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, temp32a);
axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, Scalar(2) * adx, temp16a);
temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adytail != Scalar(0))
{
temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, Scalar(2) * ady, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, temp32a);
aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, Scalar(2) * ady, temp16a);
temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
}
if (bdxtail != Scalar(0) || bdytail != Scalar(0))
{
if (cdxtail != Scalar(0) || cdytail != Scalar(0) || adxtail != Scalar(0) || adytail != Scalar(0))
{
DETRIA_Two_Product(cdxtail, ady, ti1, ti0);
DETRIA_Two_Product(cdx, adytail, tj1, tj0);
DETRIA_Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
u[3] = u3;
negate = -cdy;
DETRIA_Two_Product(adxtail, negate, ti1, ti0);
negate = -cdytail;
DETRIA_Two_Product(adx, negate, tj1, tj0);
DETRIA_Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
v[3] = v3;
catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
DETRIA_Two_Product(cdxtail, adytail, ti1, ti0);
DETRIA_Two_Product(adxtail, cdytail, tj1, tj0);
DETRIA_Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
catt[3] = catt3;
cattlen = 4;
}
else
{
cat[0] = Scalar(0);
catlen = 1;
catt[0] = Scalar(0);
cattlen = 1;
}
if (bdxtail != Scalar(0))
{
temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, Scalar(2) * bdx, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
if (cdytail != Scalar(0))
{
temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adytail != Scalar(0))
{
temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, temp32a);
bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, Scalar(2) * bdx, temp16a);
temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdytail != Scalar(0))
{
temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, Scalar(2) * bdy, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, temp32a);
bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, Scalar(2) * bdy, temp16a);
temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
}
if (cdxtail != Scalar(0) || cdytail != Scalar(0))
{
if (adxtail != Scalar(0) || adytail != Scalar(0) || bdxtail != Scalar(0) || bdytail != Scalar(0))
{
DETRIA_Two_Product(adxtail, bdy, ti1, ti0);
DETRIA_Two_Product(adx, bdytail, tj1, tj0);
DETRIA_Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
u[3] = u3;
negate = -ady;
DETRIA_Two_Product(bdxtail, negate, ti1, ti0);
negate = -adytail;
DETRIA_Two_Product(bdx, negate, tj1, tj0);
DETRIA_Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
v[3] = v3;
abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
DETRIA_Two_Product(adxtail, bdytail, ti1, ti0);
DETRIA_Two_Product(bdxtail, adytail, tj1, tj0);
DETRIA_Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
abtt[3] = abtt3;
abttlen = 4;
}
else
{
abt[0] = Scalar(0);
abtlen = 1;
abtt[0] = Scalar(0);
abttlen = 1;
}
if (cdxtail != Scalar(0))
{
temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, Scalar(2) * cdx, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother);