#include "tgeometry.h"
using namespace std;
const T3DPointD TConsts::nap3d((numeric_limits<double>::max)(),
(numeric_limits<double>::max)(),
(numeric_limits<double>::max)());
const TThickPoint TConsts::natp((numeric_limits<double>::max)(),
(numeric_limits<double>::max)(),
(numeric_limits<double>::max)());
const TPointD TConsts::napd((numeric_limits<double>::max)(),
(numeric_limits<double>::max)());
const TPointI TConsts::nap((numeric_limits<int>::max)(),
(numeric_limits<int>::max)());
const TRectD TConsts::infiniteRectD(-(numeric_limits<double>::max)(),
-(numeric_limits<double>::max)(),
(numeric_limits<double>::max)(),
(numeric_limits<double>::max)());
const TRectI TConsts::infiniteRectI(-(numeric_limits<int>::max)(),
-(numeric_limits<int>::max)(),
(numeric_limits<int>::max)(),
(numeric_limits<int>::max)());
//==================================================================================================
// operazioni fra affini
TAffine &TAffine::operator=(const TAffine &a) {
a11 = a.a11;
a12 = a.a12;
a13 = a.a13;
a21 = a.a21;
a22 = a.a22;
a23 = a.a23;
return *this;
}
//--------------------------------------------------------------------------------------------------
TAffine TAffine::operator*(const TAffine &b) const {
return TAffine(a11 * b.a11 + a12 * b.a21, a11 * b.a12 + a12 * b.a22,
a11 * b.a13 + a12 * b.a23 + a13,
a21 * b.a11 + a22 * b.a21, a21 * b.a12 + a22 * b.a22,
a21 * b.a13 + a22 * b.a23 + a23);
}
//--------------------------------------------------------------------------------------------------
TAffine TAffine::operator*=(const TAffine &b) { return *this = *this * b; }
//--------------------------------------------------------------------------------------------------
TAffine TAffine::inv() const {
if (a12 == 0.0 && a21 == 0.0) {
double inv_a11 =
(a11 == 0.0 ? std::numeric_limits<double>::max() / (1 << 16)
: 1.0 / a11);
double inv_a22 =
(a22 == 0.0 ? std::numeric_limits<double>::max() / (1 << 16)
: 1.0 / a22);
return TAffine(inv_a11, 0, -a13 * inv_a11, 0, inv_a22, -a23 * inv_a22);
} else if (a11 == 0.0 && a22 == 0.0) {
assert(a12 != 0.0);
assert(a21 != 0.0);
double inv_a21 =
(a21 == 0.0 ? std::numeric_limits<double>::max() / (1 << 16)
: 1.0 / a21);
double inv_a12 =
(a12 == 0.0 ? std::numeric_limits<double>::max() / (1 << 16)
: 1.0 / a12);
return TAffine(0, inv_a21, -a23 * inv_a21, inv_a12, 0, -a13 * inv_a12);
} else {
double d = 1. / det();
return TAffine(a22 * d, -a12 * d, (a12 * a23 - a22 * a13) * d, -a21 * d,
a11 * d, (a21 * a13 - a11 * a23) * d);
}
}
//--------------------------------------------------------------------------------------------------
double TAffine::det() const { return a11 * a22 - a12 * a21; }
//--------------------------------------------------------------------------------------------------
// Confronti tra affini
bool TAffine::operator==(const TAffine &a) const {
return a11 == a.a11 && a12 == a.a12 && a13 == a.a13 && a21 == a.a21 &&
a22 == a.a22 && a23 == a.a23;
}
//--------------------------------------------------------------------------------------------------
bool TAffine::operator!=(const TAffine &a) const {
return a11 != a.a11 || a12 != a.a12 || a13 != a.a13 || a21 != a.a21 ||
a22 != a.a22 || a23 != a.a23;
}
//--------------------------------------------------------------------------------------------------
bool TAffine::isIdentity(double err) const {
return ((a11 - 1.0) * (a11 - 1.0) + (a22 - 1.0) * (a22 - 1.0) + a12 * a12 +
a13 * a13 + a21 * a21 + a23 * a23) <+ err;
}
//--------------------------------------------------------------------------------------------------
bool TAffine::isZero(double err) const {
return ( a11*a11 + a12*a12 + a13*a13 +
a21*a21 + a22*a22 + a23*a23 ) <= err;
}
//--------------------------------------------------------------------------------------------------
bool TAffine::isTranslation(double err) const {
return ((a11 - 1.0) * (a11 - 1.0) + (a22 - 1.0) * (a22 - 1.0) + a12 * a12 +
a21 * a21) <= err;
}
//--------------------------------------------------------------------------------------------------
bool TAffine::isIsotropic(double err) const {
return areAlmostEqual(a11, a22, err) && areAlmostEqual(a12, -a21, err);
}
//--------------------------------------------------------------------------------------------------
// applicazione
TPointD TAffine::operator*(const TPointD &p) const {
return TPointD(p.x * a11 + p.y * a12 + a13, p.x * a21 + p.y * a22 + a23);
}
//--------------------------------------------------------------------------------------------------
TPointD TAffine::transformDirection(const TPointD &p) const {
return TPointD(p.x * a11 + p.y * a12, p.x * a21 + p.y * a22);
}
//--------------------------------------------------------------------------------------------------
TRectD TAffine::operator*(const TRectD &rect) const {
if (rect != TConsts::infiniteRectD) {
TPointD p1 = *this * rect.getP00(), p2 = *this * rect.getP01(),
p3 = *this * rect.getP10(), p4 = *this * rect.getP11();
return TRectD(
std::min({p1.x, p2.x, p3.x, p4.x}), std::min({p1.y, p2.y, p3.y, p4.y}),
std::max({p1.x, p2.x, p3.x, p4.x}), std::max({p1.y, p2.y, p3.y, p4.y}));
} else
return TConsts::infiniteRectD;
}
//--------------------------------------------------------------------------------------------------
TAffine TAffine::place(double u, double v, double x, double y) const {
return TAffine(a11, a12, x - (a11 * u + a12 * v), a21, a22,
y - (a21 * u + a22 * v));
}
//--------------------------------------------------------------------------------------------------
TAffine TAffine::place(const TPointD &pIn, const TPointD &pOut) const {
return TAffine(a11, a12, pOut.x - (a11 * pIn.x + a12 * pIn.y), a21, a22,
pOut.y - (a21 * pIn.x + a22 * pIn.y));
}
//--------------------------------------------------------------------------------------------------
TAffine TAffine::rotation(double angle) {
double s = sin(angle);
double c = cos(angle);
return TAffine(c, -s, 0, s, c, 0);
}
//==================================================================================================
TRotation::TRotation(double degrees) {
double rad, sn, cs;
int idegrees = (int)degrees;
if ((double)idegrees == degrees && idegrees % 90 == 0) {
switch ((idegrees / 90) & 3) {
case 0:
sn = 0;
cs = 1;
break;
case 1:
sn = 1;
cs = 0;
break;
case 2:
sn = 0;
cs = -1;
break;
case 3:
sn = -1;
cs = 0;
break;
default:
sn = 0;
cs = 0;
break;
}
} else {
rad = degrees * M_PI_180;
sn = sin(rad);
cs = cos(rad);
if (sn == 1 || sn == -1) cs = 0;
if (cs == 1 || cs == -1) sn = 0;
}
a11 = cs;
a12 = -sn;
a21 = -a12;
a22 = a11;
}
//--------------------------------------------------------------------------------------------------
TRotation::TRotation(const TPointD ¢er, double degrees) {
TAffine a = TTranslation(center) * TRotation(degrees) * TTranslation(-center);
a11 = a.a11;
a12 = a.a12;
a13 = a.a13;
a21 = a.a21;
a22 = a.a22;
a23 = a.a23;
}
//==================================================================================================
TScale::TScale(const TPointD ¢er, double sx, double sy) {
TAffine a = TTranslation(center) * TScale(sx, sy) * TTranslation(-center);
a11 = a.a11;
a12 = a.a12;
a13 = a.a13;
a21 = a.a21;
a22 = a.a22;
a23 = a.a23;
}
//--------------------------------------------------------------------------------------------------
TScale::TScale(const TPointD ¢er, double s) {
TAffine a = TTranslation(center) * TScale(s) * TTranslation(-center);
a11 = a.a11;
a12 = a.a12;
a13 = a.a13;
a21 = a.a21;
a22 = a.a22;
a23 = a.a23;
}
//==================================================================================================
T3DPointD TAffine3::operator*(const T3DPointD &b) const {
return T3DPointD(
b.x*a11 + b.y*a21 + b.z*a31,
b.x*a12 + b.y*a22 + b.z*a32,
b.x*a13 + b.y*a23 + b.z*a33 );
}
TAffine3 TAffine3::operator*(const TAffine3 &b) const {
return TAffine3(
*this * b.rowX(),
*this * b.rowY(),
*this * b.rowZ() );
}
TAffine3 TAffine3::operator*=(const TAffine3 &b)
{ return *this = *this * b; }
TAffine3 TAffine3::inv() const {
TAffine3 r;
r.a11 = a22*a33 - a32*a23;
r.a12 = a32*a13 - a12*a33;
r.a13 = a12*a23 - a22*a13;
double det = r.a11*a11 + r.a12*a21 + r.a12*a31;
det = fabs(det) > TConsts::epsilon ? 1.0/det : 0.0;
r.a11 *= det;
r.a12 *= det;
r.a13 *= det;
r.a21 = (a31*a23 - a21*a33)*det;
r.a22 = (a11*a33 - a31*a13)*det;
r.a23 = (a21*a13 - a11*a23)*det;
r.a31 = (a21*a32 - a31*a22)*det;
r.a32 = (a31*a12 - a11*a32)*det;
r.a33 = (a11*a22 - a21*a12)*det;
return r;
}
TAffine TAffine3::get2d() const {
return TAffine(
a11, a21, a31,
a12, a22, a32 );
}
TAffine3 TAffine3::translation2d(double x, double y) {
TAffine3 r;
r.rowZ().x = x;
r.rowZ().y = y;
return r;
}
TAffine3 TAffine3::scale2d(double x, double y) {
TAffine3 r;
r.a11 = x;
r.a22 = y;
return r;
}
TAffine3 TAffine3::rotation2d(double angle) {
TAffine3 r;
double s = sin(angle);
double c = cos(angle);
r.a11 = c;
r.a12 = s;
r.a21 = -s;
r.a22 = c;
return r;
}
//==================================================================================================
T4DPointD TAffine4::operator*(const T4DPointD &b) const {
return T4DPointD(
b.x*a11 + b.y*a21 + b.z*a31 + b.w*a41,
b.x*a12 + b.y*a22 + b.z*a32 + b.w*a42,
b.x*a13 + b.y*a23 + b.z*a33 + b.w*a43,
b.x*a14 + b.y*a24 + b.z*a34 + b.w*a44 );
}
TAffine4 TAffine4::operator*(const TAffine4 &b) const {
return TAffine4(
*this * b.rowX(),
*this * b.rowY(),
*this * b.rowZ(),
*this * b.rowW() );
}
TAffine4 TAffine4::operator*=(const TAffine4 &b)
{ return *this = *this * b; }
TAffine4 TAffine4::inv() const {
TAffine4 r;
r.a11 = a22*(a33*a44 - a34*a43) + a23*(a34*a42 - a32*a44) + a24*(a32*a43 - a33*a42);
r.a12 = a21*(a34*a43 - a33*a44) + a23*(a31*a44 - a34*a41) + a24*(a33*a41 - a31*a43);
r.a13 = a21*(a32*a44 - a34*a42) + a22*(a34*a41 - a31*a44) + a24*(a31*a42 - a32*a41);
r.a14 = a21*(a33*a42 - a32*a43) + a22*(a31*a43 - a33*a41) + a23*(a32*a41 - a31*a42);
double det = a11*r.a11 + a12*r.a21 + a13*r.a31 + a14*r.a41;
if (fabs(det) > TConsts::epsilon) det = 1.0/det;
r.a11 *= det;
r.a12 *= det;
r.a13 *= det;
r.a14 *= det;
r.a21 = det*( a12*(a34*a43 - a33*a44) + a13*(a32*a44 - a34*a42) + a14*(a33*a42 - a32*a43) );
r.a22 = det*( a11*(a33*a44 - a34*a43) + a13*(a34*a41 - a31*a44) + a14*(a31*a43 - a33*a41) );
r.a23 = det*( a11*(a34*a42 - a32*a44) + a12*(a31*a44 - a34*a41) + a14*(a32*a41 - a31*a42) );
r.a24 = det*( a11*(a32*a43 - a33*a42) + a12*(a33*a41 - a31*a43) + a13*(a31*a42 - a32*a41) );
r.a31 = det*( a12*(a23*a44 - a24*a43) + a13*(a24*a42 - a22*a44) + a14*(a22*a43 - a23*a42) );
r.a32 = det*( a11*(a24*a43 - a23*a44) + a13*(a21*a44 - a24*a41) + a14*(a23*a41 - a21*a43) );
r.a33 = det*( a11*(a22*a44 - a24*a42) + a12*(a24*a41 - a21*a44) + a14*(a21*a42 - a22*a41) );
r.a34 = det*( a11*(a23*a42 - a22*a43) + a12*(a21*a43 - a23*a41) + a13*(a22*a41 - a21*a42) );
r.a41 = det*( a12*(a24*a33 - a23*a34) + a13*(a22*a34 - a24*a32) + a14*(a23*a32 - a22*a33) );
r.a42 = det*( a11*(a23*a34 - a24*a33) + a13*(a24*a31 - a21*a34) + a14*(a21*a33 - a23*a31) );
r.a43 = det*( a11*(a24*a32 - a22*a34) + a12*(a21*a34 - a24*a31) + a14*(a22*a31 - a21*a32) );
r.a44 = det*( a11*(a22*a33 - a23*a32) + a12*(a23*a31 - a21*a33) + a13*(a21*a32 - a22*a31) );
return r;
}
TAffine TAffine4::get2d(double z) const {
return TAffine(
a11, a21, z*a31 + a41,
a12, a22, z*a32 + a42 );
}
TAffine3 TAffine4::get2dPersp(double z) const {
return TAffine3(
T3DPointD( a11 , a12 , a14 ),
T3DPointD( a21 , a22 , a24 ),
T3DPointD( a31*z+a41 , a32*z+a42 , a34*z+a44 ) );
}
TAffine4 TAffine4::translation(double x, double y, double z) {
TAffine4 r;
r.rowW().x = x;
r.rowW().y = y;
r.rowW().z = z;
return r;
}
TAffine4 TAffine4::scale(double x, double y, double z) {
TAffine4 r;
r.a11 = x;
r.a22 = y;
r.a33 = z;
return r;
}
TAffine4 TAffine4::rotation(double x, double y, double z, double angle) {
TAffine4 r;
double k = x*x + y*y + z*z;
if (k > TConsts::epsilon*TConsts::epsilon) {
k = 1.0 / sqrt(k);
double s = sin(angle);
double c = cos(angle);
double ic = 1.0 - c;
x *= k;
y *= k;
z *= k;
r.a11 = ic*x*x + c;
r.a12 = ic*x*y + s*z;
r.a13 = ic*z*x - s*y;
r.a21 = ic*x*y - s*z;
r.a22 = ic*y*y + c;
r.a23 = ic*y*z + s*x;
r.a31 = ic*z*x + s*y;
r.a32 = ic*y*z - s*x;
r.a33 = ic*z*z + c;
}
return r;
}
TAffine4 TAffine4::rotationX(double angle) {
TAffine4 r;
double s = sin(angle);
double c = cos(angle);
r.a22 = c;
r.a23 = s;
r.a32 = -s;
r.a33 = c;
return r;
}
TAffine4 TAffine4::rotationY(double angle) {
TAffine4 r;
double s = sin(angle);
double c = cos(angle);
r.a11 = c;
r.a13 = -s;
r.a31 = s;
r.a33 = c;
return r;
}
TAffine4 TAffine4::rotationZ(double angle) {
TAffine4 r;
double s = sin(angle);
double c = cos(angle);
r.a11 = c;
r.a12 = s;
r.a21 = -s;
r.a22 = c;
return r;
}
//==================================================================================================
int TAngleRangeSet::find(Type a) const {
assert(!m_angles.empty());
int i0 = 0, i1 = m_angles.size() - 1;
if (a < m_angles[0]) return i1;
if (m_angles[i1] <= a) return i1;
while(true) {
int i = (i1 + i0)/2;
if (i == i0) break;
if (m_angles[i] <= a) i0 = i; else i1 = i;
}
return i0;
}
void TAngleRangeSet::insert(Type a) {
if (m_angles.empty()) {
m_angles.push_back(a);
} else {
int i = find(a);
if (m_angles[i] == a)
m_angles.erase(m_angles.begin() + i);
else if (a < m_angles[0])
m_angles.insert(m_angles.begin(), a);
else
m_angles.insert(m_angles.begin() + i + 1, a);
}
}
void TAngleRangeSet::doAdd(Type a0, Type a1) {
if (m_angles.empty()) {
if (!m_flip) set(a0, a1);
return;
}
int i0 = find(a0);
int i1 = find(a1);
if (i0 == i1) {
bool visible = (i0%2 != 0) == m_flip;
if (m_angles[i0] != a0 && m_angles[i0] - a0 <= a1 - a0) {
if (visible) fill(); else set(a0, a1);
} else
if (!visible) {
if (a1 < a0) m_flip = true;
insert(a0);
insert(a1);
}
return;
}
bool visible0 = (i0%2 != 0) == m_flip;
bool visible1 = (i1%2 != 0) == m_flip;
// remove range (i0, i1]
i0 = (i0 + 1)%m_angles.size();
if (i1 < i0) {
m_angles.erase(m_angles.begin() + i0, m_angles.end());
m_angles.erase(m_angles.begin(), m_angles.begin() + i1 + 1);
} else {
m_angles.erase(m_angles.begin() + i0, m_angles.begin() + i1 + 1);
}
// insert new angles if need
if (!visible0) insert(a0);
if (!visible1) insert(a1);
if (m_angles.empty() || a1 < a0)
m_flip = true;
}
bool TAngleRangeSet::contains(Type a) const {
if (isEmpty()) return false;
if (isFull()) return true;
return (find(a)%2 != 0) == m_flip;
}
bool TAngleRangeSet::check() const {
if (m_angles.size() % 2 != 0)
return false;
for(int i = 1; i < (int)m_angles.size(); ++i)
if (m_angles[i-1] >= m_angles[i])
return false;
return true;
}
void TAngleRangeSet::set(Type a0, Type a1) {
m_angles.clear();
if (a0 < a1) {
m_flip = false;
m_angles.push_back(a0);
m_angles.push_back(a1);
} else
if (a0 > a1) {
m_flip = true;
m_angles.push_back(a1);
m_angles.push_back(a0);
} else {
m_flip = true;
}
}
void TAngleRangeSet::set(const TAngleRangeSet &x, bool flip) {
if (&x == this) return;
m_flip = (x.isFlipped() != flip);
m_angles = x.angles();
}
void TAngleRangeSet::invert(Type a0, Type a1) {
if (a0 == a1) return;
if (isEmpty()) { set(a0, a1); return; }
if (isFull()) { set(a1, a0); return; }
if (a1 < a0) m_flip = !m_flip;
insert(a0);
insert(a1);
}
void TAngleRangeSet::invert(const TAngleRangeSet &x) {
if (x.isEmpty()) { return; }
if (x.isFull()) { invert(); return; }
if (isEmpty()) { set(x); return; }
if (isFull()) { set(x, true); return; }
m_flip = m_flip != x.isFlipped();
for(List::const_iterator i = x.angles().begin(); i != x.angles().end(); ++i)
insert(*i);
}
void TAngleRangeSet::add(Type a0, Type a1) {
if (!isFull() && a0 != a1)
{ if (isEmpty()) set(a0, a1); else doAdd(a0, a1); }
}
void TAngleRangeSet::add(const TAngleRangeSet &x) {
if (&x == this || isFull() || x.isEmpty()) return;
if (isEmpty()) { set(x); return; }
if (x.isFull()) { fill(); return; }
for (Iterator i(x); i && !isFull(); ++i)
doAdd(i.a0(), i.a1());
}
void TAngleRangeSet::subtract(Type a0, Type a1) {
if (!isEmpty() && a0 != a1) {
if (isFull()) set(a1, a0); else
{ invert(); doAdd(a0, a1); invert(); }
}
}
void TAngleRangeSet::subtract(const TAngleRangeSet &x) {
if (isEmpty() || x.isEmpty()) return;
if (&x == this || x.isFull()) { clear(); return; }
if (isFull()) { set(x); invert(); return; }
// a - b = !(!a + b)
invert();
for (Iterator i(x); i && !isFull(); ++i)
doAdd(i.a0(), i.a1());
invert();
}
void TAngleRangeSet::intersect(Type a0, Type a1) {
if (!isEmpty()) {
if (a0 == a1) clear(); else
if (isFull()) set(a0, a1); else
{ invert(); doAdd(a1, a0); invert(); }
}
}
void TAngleRangeSet::intersect(const TAngleRangeSet &x) {
if (&x == this || isEmpty() || x.isFull()) return;
if (x.isEmpty()) { clear(); return; }
if (isFull()) { set(x); return; }
// a & b = !(!a + !b)
invert();
for (Iterator i(x, true); i && !isFull(); ++i)
doAdd(i.a0(), i.a1());
invert();
}