//! Implements <a href="http://qsar.sourceforge.net/dicts/blue-obelisk/index.xhtml#calculateOrthogonalisationMatrix">blue-obelisk:calculateOrthogonalisationMatrix</a>
void OBUnitCell::SetData(const vector3 v1, const vector3 v2, const vector3 v3)
{
matrix3x3 m (v1, v2, v3);
_mOrtho.FillOrth(vectorAngle(v2,v3), // alpha
vectorAngle(v1,v3), // beta
vectorAngle(v1,v2), // gamma
v1.length(), // a
v2.length(), // b
v3.length()); // c
_mOrient = m.transpose() * _mOrtho.inverse();
_spaceGroup = NULL;
_spaceGroupName = "";
_lattice = OBUnitCell::Undefined;
}
void WriteAngles(ostream &ofs,OBMol &mol)
{
// Alas, we still need to sort these to only list unique entries...
vector3 v1, v2;
OBAtom *a, *b, *c, *d;
OBBond *bond1, *bond2, *bond3;
vector<OBEdgeBase*>::iterator i, j, k;
char buffer[BUFF_SIZE];
for (bond1 = mol.BeginBond(i); bond1; bond1 = mol.NextBond(i))
{
b = bond1->GetBeginAtom();
c = bond1->GetEndAtom();
for (bond2 = b->BeginBond(j); bond2; bond2 = b->NextBond(j))
{
if (bond2->GetEndAtomIdx() != c->GetIdx()
&& bond2->GetEndAtomIdx() != b->GetIdx())
{
a = bond2->GetEndAtom();
v1 = a->GetVector() - b->GetVector();
v2 = c->GetVector() - b->GetVector();
sprintf(buffer,"%4d %4d %4d %4s %4s %4s %10.3f",
a->GetIdx(),b->GetIdx(),c->GetIdx(),
a->GetType(),b->GetType(),c->GetType(),
vectorAngle(v1, v2));
ofs << buffer << endl;
for (bond3 = c->BeginBond(k); bond3; bond3 = c->NextBond(k))
if (bond3->GetEndAtomIdx() != b->GetIdx()
&& bond3->GetEndAtomIdx() != c->GetIdx())
{
d = bond3->GetEndAtom();
v1 = b->GetVector() - c->GetVector();
v2 = d->GetVector() - c->GetVector();
sprintf(buffer,"%4d %4d %4d %4s %4s %4s %10.3f",
b->GetIdx(),c->GetIdx(),d->GetIdx(),
b->GetType(),c->GetType(),d->GetType(),
vectorAngle(v1, v2));
ofs << buffer << endl;
}
}
}
}
}
inline static qreal signedAngle( const vec2 &v1, const vec2 &v2 )
{
//assuming v1,v2 are normalized
qreal a = vectorAngle( v1, v2 );
vec3 c = vec3::crossProduct( vec3(v1), vec3(v2) );
return c.z() > 0.0 ? a : -a;
}
vector vectorCartesianToPolar(vector v)
{
double vAng = vectorAngle(v), vLength = vectorLength(v);
v.x = vLength;
v.y = vAng;
return v;
}
vector vectorLengthSet(vector v, double length)
{
double vAng;
vAng = vectorAngle(v);
v.x = length * cos(vAng);
v.y = length * sin(vAng);
return v;
}
double
CoordinateFrame::roll() const
{
// roll is the angle between the plane (world_up, cf_fwd) and the plane (cf_up, cf_fwd)
// the angle between two planes is the angle between their normals
// the normals are gotten with cross products
// the vectorAngle function uses acos and dot product
double roll = vectorAngle(cross(Vector3(0, 0, 1), fwd_), cross(up_, fwd_));
if(left_.z() < 0) roll = -roll;
return roll;
}
double OBUnitCell::GetGamma() const
{
return vectorAngle(_mOrtho.GetColumn(0), _mOrtho.GetColumn(1));
}
double OBUnitCell::GetAlpha() const
{
return vectorAngle(_mOrtho.GetColumn(1), _mOrtho.GetColumn(2));
}
vector vectorRotate(vector v, double ang)
{
double vAng;
vAng = vectorAngle(v);
return vectorAngleSet(v, ang + vAng);
}
double vectorAngle(const GPoint & pt) {
return vectorAngle(pt.getX(), pt.getY());
}
esvg::render::PointList esvg::render::Path::generateListPoints(int32_t _level, int32_t _recurtionMax, float _threshold) {
ESVG_VERBOSE(spacingDist(_level) << "Generate List Points ... from a path");
esvg::render::PointList out;
std::vector<esvg::render::Point> tmpListPoint;
vec2 lastPosition(0.0f, 0.0f);
vec2 lastAngle(0.0f, 0.0f);
int32_t lastPointId = -1;
bool PathStart = false;
// Foreach element, we move in the path:
for(auto &it : m_listElement) {
if (it == nullptr) {
continue;
}
ESVG_VERBOSE(spacingDist(_level+1) << " Draw : " << *it);
switch (it->getType()) {
case esvg::render::path_stop:
if (tmpListPoint.size() != 0) {
if (tmpListPoint.size() == 0) {
ESVG_WARNING(spacingDist(_level+1) << " Request path stop of not starting path ...");
} else {
tmpListPoint.back().setEndPath();
out.addList(tmpListPoint);
tmpListPoint.clear();
}
}
lastAngle = vec2(0.0f, 0.0f);
// nothing alse to do ...
break;
case esvg::render::path_close:
if (tmpListPoint.size() != 0) {
if (tmpListPoint.size() == 0) {
ESVG_WARNING(spacingDist(_level+1) << " Request path close of not starting path ...");
} else {
// find the previous tart of the path ...
tmpListPoint.front().m_type = esvg::render::Point::type::join;
// Remove the last point if it is the same position...
vec2 delta = (tmpListPoint.front().m_pos - tmpListPoint.back().m_pos).absolute();
if ( delta.x() <= 0.00001
&& delta.y() <= 0.00001) {
tmpListPoint.pop_back();
ESVG_VERBOSE(" Remove point Z property : " << tmpListPoint.back().m_pos << " with delta=" << delta);
}
out.addList(tmpListPoint);
tmpListPoint.clear();
}
}
lastAngle = vec2(0.0f, 0.0f);
// nothing alse to do ...
break;
case esvg::render::path_moveTo:
// stop last path
if (tmpListPoint.size() != 0) {
tmpListPoint.back().setEndPath();
out.addList(tmpListPoint);
tmpListPoint.clear();
}
// create a new one
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
lastPosition += it->getPos();
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::start));
lastAngle = lastPosition;
break;
case esvg::render::path_lineTo:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::start));
}
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
lastPosition += it->getPos();
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
lastAngle = lastPosition;
break;
case esvg::render::path_lineToH:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::start));
}
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
lastPosition += it->getPos();
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
lastAngle = lastPosition;
break;
case esvg::render::path_lineToV:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::start));
}
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
lastPosition += it->getPos();
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
lastAngle = lastPosition;
break;
case esvg::render::path_curveTo:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
}
{
vec2 lastPosStore(lastPosition);
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
vec2 pos1 = lastPosition + it->getPos1();
vec2 pos2 = lastPosition + it->getPos2();
vec2 pos = lastPosition + it->getPos();
interpolateCubicBezier(tmpListPoint,
_recurtionMax,
_threshold,
lastPosStore,
pos1,
pos2,
pos,
0,
esvg::render::Point::type::join);
lastPosition = pos;
lastAngle = pos2;
}
break;
case esvg::render::path_smoothCurveTo:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
}
{
vec2 lastPosStore(lastPosition);
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
vec2 pos2 = lastPosition + it->getPos2();
vec2 pos = lastPosition + it->getPos();
// generate Pos 1
vec2 pos1 = lastPosStore*2.0f - lastAngle;
interpolateCubicBezier(tmpListPoint,
_recurtionMax,
_threshold,
lastPosStore,
pos1,
pos2,
pos,
0,
esvg::render::Point::type::join);
lastPosition = pos;
lastAngle = pos2;
}
break;
case esvg::render::path_bezierCurveTo:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
}
{
vec2 lastPosStore(lastPosition);
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
vec2 pos = lastPosition + it->getPos();
vec2 tmp1 = lastPosition + it->getPos1();
// generate pos1 and pos2
vec2 pos1 = lastPosStore + (tmp1 - lastPosStore)*0.666666666f;
vec2 pos2 = pos + (tmp1 - pos)*0.666666666f;
interpolateCubicBezier(tmpListPoint,
_recurtionMax,
_threshold,
lastPosStore,
pos1,
pos2,
pos,
0,
esvg::render::Point::type::join);
lastPosition = pos;
lastAngle = tmp1;
}
break;
case esvg::render::path_bezierSmoothCurveTo:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
}
{
vec2 lastPosStore(lastPosition);
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
vec2 pos = lastPosition + it->getPos();
vec2 tmp1 = lastPosStore*2.0f - lastAngle;
// generate pos1 and pos2
vec2 pos1 = lastPosStore + (tmp1 - lastPosStore)*0.666666666f;
vec2 pos2 = pos + (tmp1 - pos)*0.66666666f;
interpolateCubicBezier(tmpListPoint,
_recurtionMax,
_threshold,
lastPosStore,
pos1,
pos2,
pos,
0,
esvg::render::Point::type::join);
lastPosition = pos;
lastAngle = tmp1;
}
break;
case esvg::render::path_elliptic:
// If no previous point, we need to create the last point has start ...
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
}
{
ememory::SharedPtr<esvg::render::ElementElliptic> tmpIt(ememory::dynamicPointerCast<esvg::render::ElementElliptic>(it));
float angle = tmpIt->m_angle * (M_PI / 180.0);
ESVG_TODO(spacingDist(_level+1) << " Elliptic arc: radius=" << tmpIt->getPos1());
ESVG_TODO(spacingDist(_level+1) << " angle=" << tmpIt->m_angle);
ESVG_TODO(spacingDist(_level+1) << " m_largeArcFlag=" << tmpIt->m_largeArcFlag);
ESVG_TODO(spacingDist(_level+1) << " m_sweepFlag=" << tmpIt->m_sweepFlag);
vec2 lastPosStore(lastPosition);
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
vec2 pos = lastPosition + it->getPos();
float rotationX = tmpIt->m_angle * (M_PI / 180.0);
vec2 radius = tmpIt->getPos1();
#ifdef DEBUG
m_debugInformation.addSegment(lastPosStore, pos);
#endif
vec2 delta = lastPosStore - pos;
float ddd = delta.length();
if ( ddd < 1e-6f
|| radius.x() < 1e-6f
|| radius.y() < 1e-6f) {
ESVG_WARNING("Degenerate arc in Line");
if (tmpListPoint.size() == 0) {
tmpListPoint.push_back(esvg::render::Point(lastPosition, esvg::render::Point::type::join));
}
tmpListPoint.push_back(esvg::render::Point(pos, esvg::render::Point::type::join));
} else {
// Convert to center point parameterization.
// http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes
// procedure describe here : http://www.w3.org/TR/SVG11/implnote.html#ArcConversionCenterToEndpoint
// Compute delta'
mat2 matrixRotationCenter = etk::mat2Rotate(-rotationX);
vec2 deltaPrim = matrixRotationCenter * (delta*0.5f);
ddd = (deltaPrim.x()*deltaPrim.x())/(radius.x()*radius.x())
+ (deltaPrim.y()*deltaPrim.y())/(radius.y()*radius.y());
if (ddd > 1.0f) {
#ifndef __STDCPP_LLVM__
ddd = std::sqrt(ddd);
#else
ddd = sqrtf(ddd);
#endif
radius *= ddd;
}
// Compute center'
float sss = 0.0f;
float ssa = radius.x()*radius.x()*radius.y()*radius.y()
- radius.x()*radius.x()*deltaPrim.y()*deltaPrim.y()
- radius.y()*radius.y()*deltaPrim.x()*deltaPrim.x();
float ssb = radius.x()*radius.x()*deltaPrim.y()*deltaPrim.y()
+ radius.y()*radius.y()*deltaPrim.x()*deltaPrim.x();
if (ssa < 0.0f) {
ssa = 0.0f;
}
if (ssb > 0.0f) {
#ifndef __STDCPP_LLVM__
sss = std::sqrt(ssa / ssb);
#else
sss = sqrtf(ssa / ssb);
#endif
}
if (tmpIt->m_largeArcFlag == tmpIt->m_sweepFlag) {
sss *= -1.0f;
}
vec2 centerPrime(sss * radius.x() * deltaPrim.y() / radius.y(),
sss * -radius.y() * deltaPrim.x() / radius.x());
// Compute center from center'
mat2 matrix = etk::mat2Rotate(rotationX);
vec2 center = (lastPosStore + pos)*0.5f + matrix*centerPrime;
#ifdef DEBUG
m_debugInformation.addSegment(center-vec2(3.0,3.0), center+vec2(3.0,3.0));
m_debugInformation.addSegment(center-vec2(3.0,-3.0), center+vec2(3.0,-3.0));
#endif
// Calculate theta1, and delta theta.
vec2 vectorA = (deltaPrim - centerPrime) / radius;
vec2 vectorB = (deltaPrim + centerPrime) / radius * -1.0f;
#ifdef DEBUG
m_debugInformation.addSegment(center, center+vectorA*radius.x());
m_debugInformation.addSegment(center, center+vectorB*radius.y());
#endif
// Initial angle
float theta1 = vectorAngle(vec2(1.0f,0.0f), vectorA);
// Delta angle
float deltaTheta = vectorAngle(vectorA, vectorB);
// special case of invert angle...
if ( ( deltaTheta == float(M_PI)
|| deltaTheta == -float(M_PI))
&& tmpIt->m_sweepFlag == false) {
deltaTheta *= -1.0f;
}
if (tmpIt->m_largeArcFlag == true) {
// Choose large arc
if (deltaTheta > 0.0f) {
deltaTheta -= 2.0f*M_PI;
} else {
deltaTheta += 2.0f*M_PI;
}
}
// Approximate the arc using cubic spline segments.
matrix.translate(center);
// Split arc into max 90 degree segments.
// The loop assumes an iteration per end point (including start and end), this +1.
#ifndef __STDCPP_LLVM__
int32_t ndivs = int32_t(std::abs(deltaTheta) / (M_PI*0.5f)) + 1;
#else
int32_t ndivs = int32_t(fabs(deltaTheta) / (M_PI*0.5f)) + 1;
#endif
float hda = (deltaTheta / float(ndivs)) * 0.5f;
#ifndef __STDCPP_LLVM__
float kappa = std::abs(4.0f / 3.0f * (1.0f - std::cos(hda)) / std::sin(hda));
#else
float kappa = fabs(4.0f / 3.0f * (1.0f - cosf(hda)) / sinf(hda));
#endif
if (deltaTheta < 0.0f) {
kappa = -kappa;
}
vec2 pointPosPrevious(0.0,0.0);
vec2 tangentPrevious(0.0,0.0);
for (int32_t iii=0; iii<=ndivs; ++iii) {
float a = theta1 + deltaTheta * (float(iii)/(float)ndivs);
#ifndef __STDCPP_LLVM__
delta = vec2(std::cos(a), std::sin(a));
#else
delta = vec2(cosf(a), sinf(a));
#endif
// position
vec2 pointPos = matrix * vec2(delta.x()*radius.x(), delta.y()*radius.y());
// tangent
vec2 tangent = matrix.applyScaleRotation(vec2(-delta.y()*radius.x() * kappa, delta.x()*radius.y() * kappa));
if (iii > 0) {
vec2 zlastPosStore(lastPosition);
if (it->getRelative() == false) {
lastPosition = vec2(0.0f, 0.0f);
}
vec2 zpos1 = pointPosPrevious + tangentPrevious;
vec2 zpos2 = pointPos - tangent;
vec2 zpos = pointPos;
interpolateCubicBezier(tmpListPoint,
_recurtionMax,
_threshold,
zlastPosStore,
zpos1,
zpos2,
zpos,
0,
esvg::render::Point::type::join);
lastPosition = zpos;
lastAngle = zpos2;
}
pointPosPrevious = pointPos;
tangentPrevious = tangent;
}
}
lastPosition = pos;
}
break;
default:
ESVG_ERROR(spacingDist(_level+1) << " Unknow PATH commant (internal error)");
break;
}
}
// special case : No request end of path ==> open path:
if (tmpListPoint.size() != 0) {
ESVG_VERBOSE("Auto-end PATH");
tmpListPoint.back().setEndPath();
out.addList(tmpListPoint);
tmpListPoint.clear();
}
out.display();
return out;
}
// calculate height at (x,y) with plane
float Terrain::getHeight (float x_float, float z_float, Angle &a) {
Vector v1, v2, v3, normal, ab, bc;
Plane plane;
bool up;
int res_int = (int) res;
int x = (int) (x_float);
int z = (int) (z_float);
int xs, zs;
xs = (int) ((x+size/2) / res_int) * res_int - (size/2);
zs = (int) ((z+size/2) / res_int) * res_int - (size/2);
// FIND PLANE EQUATION (Ax + By + Cz + D)
// find triangle - START
// mi servono i vertici della diagonale -> 0 e 2
v1.x = xs;
v1.z = zs;
v1.y = getHeightFromMap (v1.x+size/2, v1.z+size/2);
v3.x = xs + res;
v3.z = zs + res;
v3.y = getHeightFromMap (v3.x+size/2, v3.z+size/2);
// calcolo la retta passante per i punti
float rect_z = v3.z * ((xs-v1.x)/(v3.x-v1.x));
if (z_float > rect_z)
up = true;
else
up = false;
// find triangle - END
if (up) {
v2.x = xs;
v2.z = zs + res;
v2.y = getHeightFromMap (v2.x+size/2, v2.z+size/2);
}
else {
v2.x = xs + res;
v2.z = zs;
v2.y = getHeightFromMap (v2.x+size/2, v2.z+size/2);
}
// calculate plane equation
vectorSubtract (v1, v2, ab);
vectorSubtract (v2, v3, bc);
crossProduct (ab, bc, normal);
makePlane (v1, normal, plane);
// calculate height
float height = (plane.d - (plane.a * x_float) - (plane.c * z_float)) / plane.b;
// calculate angle x
Vector temp_vec;
temp_vec.x = 1.0;
temp_vec.y = 0.0;
temp_vec.z = 0.0;
float temp_angle_x = vectorAngle (temp_vec, normal);
a.x = 90.0 - temp_angle_x;
// calculate angle z
temp_vec.x = 0.0;
temp_vec.y = 0.0;
temp_vec.z = 1.0;
float temp_angle_z = vectorAngle (temp_vec, normal);
a.z = 90.0 - temp_angle_z;
// return height
return height;
}