// outlineApproximation.cpp: implementation of the outlineApproximation class.
//
//////////////////////////////////////////////////////////////////////
#include "tstrokeoutline.h"
#include "tstroke.h"
#include "tcurves.h"
#include "tmathutil.h"
#include "tgl.h"
//#include "tcolorfunctions.h"
typedef std::pair<TQuadratic *, TQuadratic *> outlineEdge;
typedef std::vector<outlineEdge> outlineBoundary;
const double infDouble = (std::numeric_limits<double>::max)();
/*
ONLY FOT TEST
TSegment g_tangEnvelope_1;
TSegment g_tangEnvelope_2;
vector<TQuadratic> g_testOutline;
*/
namespace Outline
{
class infinityCurvature
{
};
class notValidOutline
{
};
}
namespace
{
/*
This formule is derived from Graphic Gems pag. 600
e = h^2 |a|/8
e = pixel size
h = step
a = acceleration of curve (for a quadratic is a costant value)
*/
double localComputeStep(const TQuadratic &quad, double pixelSize)
{
double step = 2;
TPointD A = quad.getP0() - 2.0 * quad.getP1() + quad.getP2(); // 2*A is the acceleration of the curve
double A_len = norm(A);
if (A_len > 0)
step = TConsts::sqrt2 * sqrt(pixelSize / A_len);
return step;
}
//---------------------------------------------------------------------------
// selezionano lo spicchio da calcolare nella costruzione dei tappi
// (semicirconferenze iniziali e finali)
const int QUARTER_BEGIN = 1;
const int QUARTER_END = 0;
// selezionano il pezzo d'outline da calcolare (sopra/sotto)
const int OUTLINE_UP = 1;
const int OUTLINE_DOWN = 0;
// utili
const double ratio_1_3 = 1.0 / 3.0;
const double ratio_2_3 = 2.0 / 3.0;
//---------------------------------------------------------------------------
// torna la curvature per t=0
template <class T>
double curvature_t0(const T *curve)
{
assert(curve);
TPointD v1 = curve->getP1() - curve->getP0();
TPointD v2 = curve->getP2() - curve->getP1();
double v_cross = cross(v1, v2);
if (isAlmostZero(v_cross))
return infDouble;
return ratio_2_3 * v_cross / pow(norm(v1), ratio_1_3);
}
//---------------------------------------------------------------------------
// torna la curvature per t=1
double curvature_t1(const TThickQuadratic *curve)
{
assert(curve);
TThickQuadratic tmp;
tmp.setThickP0(curve->getThickP2());
tmp.setThickP1(curve->getThickP1());
tmp.setThickP2(curve->getThickP0());
return curvature_t0(&tmp);
}
//---------------------------------------------------------------------------
// estrae il punto dell'outline per il parametro specificato
// N.B: e' sbagliata non tiene conto degli inviluppi
TPointD getPointInOutline(const TThickQuadratic *tq, double t, int upOrDown)
{
assert(tq);
const TThickPoint &p = tq->getThickPoint(t);
TPointD n = tq->getSpeed(t);
if (norm2(n)) {
n = normalize(n);
n = upOrDown ? rotate90(n) : rotate270(n);
}
return convert(p) + p.thick * n;
}
//---------------------------------------------------------------------------
bool checkPointInOutline(const TPointD &pointToTest,
const TThickQuadratic *tq,
double t,
double error)
{
assert(tq);
TThickPoint tpnt = tq->getThickPoint(t);
if (fabs(sq(pointToTest.x - tpnt.x) +
sq(pointToTest.y - tpnt.y) -
sq(tpnt.thick)) < error)
return true;
return false;
}
//---------------------------------------------------------------------------
// costruisce un ramo di outline (sopra o sotto) per una quadratica cicciona
TQuadratic *makeOutlineForThickQuadratic(const TThickQuadratic *tq, int upOrDown)
{
assert(tq);
// if(!outline) return 0;
TThickPoint
p0 = tq->getThickP0(),
//p1 = tq->getThickP0(),
p2 = tq->getThickP2();
TPointD t0 = tq->getP1() - tq->getP0();
TPointD t1 = tq->getP2() - tq->getP1();
if (t0 == t1)
return 0;
TPointD
N0 = tq->getSpeed(0.0),
N2 = tq->getSpeed(1.0);
if (!norm2(N0) && !norm2(N2))
throw Outline::notValidOutline();
if (norm2(N0)) {
N0 = normalize(N0);
N0 = upOrDown ? rotate90(N0) : rotate270(N0);
}
if (norm2(N2)) {
N2 = normalize(N2);
N2 = upOrDown ? rotate90(N2) : rotate270(N2);
}
TPointD p0aux = (convert(p0) + p0.thick * N0);
TPointD p2aux = (convert(p2) + p2.thick * N2);
TQuadratic
radius(TPointD(tq->getThickP0().thick, 0.0),
TPointD(tq->getThickP1().thick, 0.0),
TPointD(tq->getThickP2().thick, 0.0));
TPointD r0 = radius.getSpeed(0.0);
TPointD r1 = radius.getSpeed(1.0);
TPointD
v0,
v2;
double ct0 = curvature_t0(tq);
if (ct0 != infDouble)
v0 = (1 + p0.thick * ct0) * t0 + 0.5 * r0.x * N0;
else
v0 = r0.x * N0;
double ct1 = curvature_t1(tq);
if (ct1 != infDouble)
v2 = (1 + p2.thick * ct1) * t1 + 0.5 * r1.x * N2;
else
v2 = r1.x * N2;
/*
try {
v0 = (1 + p0.thick * curvature_t0( tq )) * t0 + 0.5 * r0.x * N0;
}
catch( Outline::infinityCurvature& ) {
}
try {
v2 = (1 + p2.thick * curvature_t1( tq )) * t1 + 0.5 * r1.x * N2;
}
catch( Outline::infinityCurvature& ) {
}
*/
// g_tangEnvelope_1.setP0( outline.getP0() );
// g_tangEnvelope_1.setP1( outline.getP0() + v0 );
// g_tangEnvelope_2.setP0( outline.getP2() );
// g_tangEnvelope_2.setP1( outline.getP2() + v2 );
// solve sistem p1 = p0 + k * v1 = p2 + m * v2 to find
double det = v0.x * v0.y - v2.x * v2.y;
if (areAlmostEqual(det, 0.0))
return 0;
double xsol;
try {
xsol = ((p0aux.x - p2aux.x) * v2.y - (p0aux.y - p2aux.y) * v2.x) / det;
//tsolveSistem( A, 2, b );
} catch (TMathException &) {
return new TQuadratic((upOrDown) ? p0aux : p2aux, (p0aux + p2aux) * 0.5, (upOrDown) ? p2aux : p0aux);
} catch (std::exception &e) {
std::string s(e.what());
abort();
} catch (...) {
abort();
}
return new TQuadratic((upOrDown) ? p0aux : p2aux, p0aux + xsol * v0, (upOrDown) ? p2aux : p0aux);
}
//---------------------------------------------------------------------------
/*
costruisce l'outline per una singola quadratica senza
inserire le semicirconferenze iniziali e finali
*/
void makeOutline(/*std::ofstream& cout,*/
outlineBoundary &outl,
const TThickQuadratic &t,
double error)
{
outlineEdge edge;
const TThickQuadratic *tq = &t;
edge.first = edge.second = 0;
try {
edge.first = makeOutlineForThickQuadratic(tq, OUTLINE_UP);
edge.second = makeOutlineForThickQuadratic(tq, OUTLINE_DOWN);
} catch (Outline::notValidOutline &) {
delete edge.first;
delete edge.second;
return;
}
const TQuadratic *q_up = edge.first;
const TQuadratic *q_down = edge.second;
const double parameterTest = 0.5;
// forza l'uscita per valori troppo piccoli
bool isAlmostAPoint =
areAlmostEqual(tq->getThickP0(), tq->getThickP1(), 1e-2) &&
areAlmostEqual(tq->getThickP1(), tq->getThickP2(), 1e-2) /*&&
areAlmostEqual( tq.getThickP0(), tq.getThickP2(), 1e-2 )*/;
if (isAlmostAPoint ||
q_up && checkPointInOutline(q_up->getPoint(parameterTest), tq, parameterTest, error) &&
q_down && checkPointInOutline(q_down->getPoint(parameterTest), tq, parameterTest, error)) {
/* if (edge.first)
cout << "left: "<< *(edge.first);
else
cout << "left: "<< 0;
if (edge.second)
cout << "right: "<<*(edge.second);
else
cout << "right: "<< 0;
cout<<std::endl;*/
outl.push_back(edge);
return;
} else {
delete edge.first;
delete edge.second;
}
TThickQuadratic
tq_left,
tq_rigth;
tq->split(0.5, tq_left, tq_rigth);
makeOutline(/*out,*/ outl, tq_left, error);
makeOutline(/*cout,*/ outl, tq_rigth, error);
}
//---------------------------------------------------------------------------
void splitCircularArcIntoQuadraticCurves(const TPointD &Center,
const TPointD &Pstart,
const TPointD &Pend,
std::vector<TQuadratic *> &quadArray)
{
// It splits a circular anticlockwise arc into a sequence of quadratic bezier curves
// Every quadratic curve can approximate an arc no TLonger than 45 degrees (or 60).
// It supposes that Pstart and Pend are onto the circumference (so that their lengths
// are equal to tha radius of the circumference), otherwise the resulting curves could
// be unpredictable.
// The last component in quadCurve[] is an ending void curve
/* ---------------------------------------------------------------------------------- */
// If you want to split the arc into arcs no TLonger than 45 degrees (so that the whole
// curve will be splitted into 8 pieces) you have to set these constants as follows:
// cos_ang ==> cos_45 = 0.5 * sqrt(2);
// sin_ang ==> sin_45 = 0.5 * sqrt(2);
// tan_semiang ==> tan_22p5 = 0.4142135623730950488016887242097;
// N_QUAD = 8;
// If you want to split the arc into arcs no TLonger than 60 degrees (so that the whole
// curve will be splitted into 6 pieces) you have to set these constants as follows:
// cos_ang ==> cos_60 = 0.5;
// sin_ang ==> sin_60 = 0.5 * sqrt(3);
// tan_semiang ==> tan_30 = 0.57735026918962576450914878050196;
// N_QUAD = 6;
/* ---------------------------------------------------------------------------------- */
// Defines some useful constant to split the arc into arcs no TLonger than 'ang' degrees
// (the whole circumference will be splitted into 360/ang quadratic curves).
const double cos_ang = 0.5 * sqrt(2.0);
const double sin_ang = 0.5 * sqrt(2.0);
const double tan_semiang = 0.4142135623730950488016887242097;
const int N_QUAD = 8; // it's 360/ang
// First of all, it computes the vectors from the center to the circumference,
// in Pstart and Pend, and their cross and dot products
TPointD Rstart = Pstart - Center; // its length is R (radius of the circle)
TPointD Rend = Pend - Center; // its length is R (radius of the circle)
double cross_prod = cross(Rstart, Rend); // it's Rstart x Rend
double dot_prod = Rstart * Rend;
const double sqr_radius = Rstart * Rstart;
TPointD aliasPstart = Pstart;
TQuadratic *quad;
while ((cross_prod <= 0) || (dot_prod <= cos_ang * sqr_radius)) // the circular arc is TLonger
// than a 'ang' degrees arc
{
if ((int)quadArray.size() == N_QUAD) // this is possible if Pstart or Pend is not onto the circumference
return;
TPointD Rstart_rot_ang(cos_ang * Rstart.x - sin_ang * Rstart.y,
sin_ang * Rstart.x + cos_ang * Rstart.y);
TPointD Rstart_rot_90(-Rstart.y, Rstart.x);
quad = new TQuadratic(aliasPstart,
aliasPstart + tan_semiang * Rstart_rot_90,
Center + Rstart_rot_ang);
quadArray.push_back(quad);
// quad->computeMinStepAtNormalSize ();
// And moves anticlockwise the starting point on the circumference by 'ang' degrees
Rstart = Rstart_rot_ang;
aliasPstart = quad->getP2();
cross_prod = cross(Rstart, Rend); // it's Rstart x Rend
dot_prod = Rstart * Rend;
// after the rotation of 'ang' degrees, the remaining part of the arc could be a 0 degree
// arc, so it must stop and exit from the function
if ((cross_prod <= 0) && (dot_prod > 0.95 * sqr_radius))
return;
}
if ((cross_prod > 0) && (dot_prod > 0)) // the last quadratic curve approximates an arc shorter than a 'ang' degrees arc
{
TPointD Rstart_rot_90(-Rstart.y, Rstart.x);
double deg_index = (sqr_radius - dot_prod) / (sqr_radius + dot_prod);
quad = new TQuadratic(aliasPstart,
(deg_index < 0) ? 0.5 * (aliasPstart + Pend) : aliasPstart + sqrt(deg_index) * Rstart_rot_90,
Pend);
quadArray.push_back(quad);
} else // the last curve, already computed, is as TLong as a 'ang' degrees arc
quadArray.back()->setP2(Pend);
}
//---------------------------------------------------------------------------
// copia arrayUp e arrayDown nel vettore dell'outline
// se le dimensioni sono diverse il vettore con il numero
// minore di quadratiche viene riempito con quadratiche degeneri
// con i punti di controllo coincidenti nell'ultimo estremo valido
void copy(/*std::ofstream& cout,*/
const std::vector<TQuadratic *> &arrayUp,
const std::vector<TQuadratic *> &arrayDown,
outlineBoundary &ob)
{
int minSize = std::min(arrayUp.size(), arrayDown.size());
assert(minSize > 0);
int i;
for (i = 0; i < minSize; ++i) {
//cout<<"left: "<< *(arrayUp[i])<< "right: "<<*(arrayDown[i])<<std::endl;
//cout<"left: "<< arrayUp[i].getP0()<<", "arrayUp[i].getP1()<<", "arrayUp[i].getP2()<< "right: "<< << arrayDown[i].getP0()<<", "arrayDown[i].getP1()<<", "arrayDown[i].getP2()<<endl;
ob.push_back(outlineEdge(arrayUp[i], arrayDown[i]));
}
if (arrayUp.size() != arrayDown.size()) {
const std::vector<TQuadratic *> &vMaxSize = arrayUp.size() > arrayDown.size() ? arrayUp : arrayDown;
const std::vector<TQuadratic *> &vMinSize = arrayUp.size() < arrayDown.size() ? arrayUp : arrayDown;
int delta = vMaxSize.size() - vMinSize.size();
if (arrayUp.size() > arrayDown.size())
while (i < minSize + delta) {
//cout<<"left: "<< arrayUp[i]<< "right: "<< 0<<std::endl;
ob.push_back(outlineEdge(arrayUp[i], (TQuadratic *)0));
i++;
}
else
while (i < minSize + delta) {
//cout<<"left: "<< 0 << "right: "<< arrayDown[i]<<std::endl;
ob.push_back(outlineEdge((TQuadratic *)0, arrayDown[i]));
i++;
}
}
}
//---------------------------------------------------------------------------
inline void changeQuadraticDirection(TQuadratic *q)
{
TPointD p = q->getP2();
q->setP2(q->getP0());
q->setP0(p);
}
//---------------------------------------------------------------------------
// cambia il verso del vettore di quadratiche (vedi changeDirection di tstroke.cpp)
void changeDirection(std::vector<TQuadratic *> &array, bool onlyQuads = false)
{
UINT chunkCount = array.size();
UINT to = tfloor(chunkCount * 0.5);
UINT i;
if (chunkCount & 1)
changeQuadraticDirection(array[to]);
--chunkCount;
for (i = 0; i < to; ++i) {
changeQuadraticDirection(array[i]);
changeQuadraticDirection(array[chunkCount - i]);
if (!onlyQuads)
std::swap(array[i], array[chunkCount - i]);
}
}
//---------------------------------------------------------------------------
// estrae i punti necessari a costruire la semicirconferenza
// iniziale e finale di una curva cicciona
TQuadratic getCircleQuarter(const TThickQuadratic *tq, int versus)
{
TQuadratic out;
TPointD v = versus ? -tq->getSpeed(0.0) : tq->getSpeed(1.0);
if (norm2(v))
v = normalize(v);
TPointD center = versus ? tq->getP0() : tq->getP2();
double radius = versus ? tq->getThickP0().thick : tq->getThickP2().thick;
out.setP0(center + (versus ? rotate270(v) : rotate90(v)) * radius);
out.setP1(center + v * radius);
out.setP2(center + (versus ? rotate90(v) : rotate270(v)) * radius);
return out;
}
//---------------------------------------------------------------------------
void drawQuadratic(const TQuadratic &quad, double pixelSize)
{
double m_min_step_at_normal_size = localComputeStep(quad, pixelSize);
// It draws the curve as a linear piecewise approximation
double invSqrtScale = 1.0;
// First of all, it computes the control circles of the curve in screen coordinates
TPointD scP0 = quad.getP0();
TPointD scP1 = quad.getP1();
TPointD scP2 = quad.getP2();
TPointD A = scP0 - 2 * scP1 + scP2;
TPointD B = scP0 - scP1;
double h;
h = invSqrtScale * m_min_step_at_normal_size;
double h2 = h * h;
TPointD P = scP0, D2 = 2 * h2 * A, D1 = A * h2 - 2 * B * h;
if (h < 0 || isAlmostZero(h))
return;
assert(h > 0);
// It draws the whole curve, using forward differencing
glBegin(GL_LINE_STRIP); // The curve starts from scP0
glVertex2d(scP0.x, scP0.y);
for (double t = h; t < 1; t = t + h) {
P = P + D1;
D1 = D1 + D2;
glVertex2d(P.x, P.y);
}
glVertex2d(scP2.x, scP2.y); // The curve ends in scP2
glEnd();
}
//---------------------------------------------------------------------------
} // end of unnamed namespace
//-----------------------------------------------------------------------------
void makeOutline(const TStroke *stroke, int startQuad, int endQuad,
outlineBoundary &ob, double error2)
{
//std::ofstream cout("c:\\temp\\outline.txt");
assert(stroke);
assert(startQuad >= 0);
assert(endQuad < stroke->getChunkCount());
assert(startQuad <= endQuad);
TThickQuadratic *tq;
std::vector<TQuadratic *> arrayUp, arrayDown;
TQuadratic arc;
if (!stroke->getChunkCount())
return;
//if (startQuad==0)
{
const TThickQuadratic *tq = stroke->getChunk(startQuad);
// trova i punti sul cerchio che corrispondono
// a due fette di 90 gradi.
// Ritorna una quadratica invece di tre singoli punti solo per compattezza.
TQuadratic
arc = getCircleQuarter(tq, QUARTER_BEGIN);
// estrae le quadratiche che corrispondono ad i due archi...
splitCircularArcIntoQuadraticCurves(tq->getP0(), arc.getP0(), arc.getP1(), arrayUp);
// e le ordina in modo che l'outline sia composta sempre da
// una curva superiore ed una inferiore corrispondente
changeDirection(arrayUp);
splitCircularArcIntoQuadraticCurves(tq->getP0(), arc.getP1(), arc.getP2(), arrayDown);
changeDirection(arrayDown, true);
// copia le curve nell'outline; se gli array non hanno la stessa dimensione
// quello con meno curve viene riempito con curve improprie
// che hanno i punti di controllo coincidente con l'ultimo estremo valido
//cout<<"quads del semicerchio left:"<<std::endl;
copy(/*cout, */ arrayUp, arrayDown, ob);
}
for (int i = startQuad; i <= endQuad; ++i) {
tq = (TThickQuadratic *)stroke->getChunk(i);
TThickPoint p0 = tq->getThickP0();
TThickPoint p1 = tq->getThickP1();
TThickPoint p2 = tq->getThickP2();
if (p0.x == p1.x) {
if (p1.x == p2.x && ((p1.y > p0.y && p1.y > p2.y) || (p1.y < p0.y && p1.y < p2.y)))
tq = new TThickQuadratic(p0, 0.5 * (p0 + p1), p1);
} else if (p0.y == p1.y) {
if (p0.y == p2.y && ((p1.x > p0.x && p1.x > p2.x) || (p1.x < p0.x && p1.x < p2.x)))
tq = new TThickQuadratic(p0, 0.5 * (p0 + p1), p1);
} else {
double fac1 = 1.0 / (p0.x - p1.x);
double fac2 = 1.0 / (p0.y - p1.y);
double aux1 = fac1 * (p2.x - p1.x);
double aux2 = fac2 * (p2.y - p1.y);
double aux3 = fac1 * (p0.x - p2.x);
double aux4 = fac2 * (p0.y - p2.y);
if ((areAlmostEqual(aux1, aux2) && aux1 >= 0) ||
(areAlmostEqual(aux3, aux4) && aux3 >= 0 && aux3 <= 1))
tq = new TThickQuadratic(p0, 0.5 * (p0 + p1), p1);
}
//cout<<"quad# "<<i<<":" <<*tq<<std::endl;
makeOutline(/*cout, */ ob, *tq, error2);
if (tq != stroke->getChunk(i))
delete tq;
}
arrayUp.clear();
arrayDown.clear();
// come sopra ultimo pezzo di arco
// if (endQuad==stroke->getChunkCount()-1)
{
arc = getCircleQuarter(tq, QUARTER_END);
splitCircularArcIntoQuadraticCurves(tq->getP2(), arc.getP1(), arc.getP0(), arrayUp);
changeDirection(arrayUp);
splitCircularArcIntoQuadraticCurves(tq->getP2(), arc.getP2(), arc.getP1(), arrayDown);
changeDirection(arrayDown, true);
//cout<<"quads del semicerchio right:"<<std::endl;
copy(/*cout,*/ arrayUp, arrayDown, ob);
}
}
//-----------------------------------------------------------------------------
void drawOutline(const outlineBoundary &ob, double pixelSize)
{
for (UINT i = 0; i < ob.size(); ++i) {
drawQuadratic(*ob[i].first, pixelSize);
drawQuadratic(*ob[i].second, pixelSize);
}
}
void computeOutlines(const TStroke *stroke, int startQuad, int endQuad,
std::vector<TQuadratic *> &quadArray, double error2)
{
outlineBoundary ob;
makeOutline(stroke, startQuad, endQuad, ob, error2);
assert(quadArray.empty());
quadArray.resize(ob.size() * 2);
int i, count = 0;
for (i = 0; i < (int)ob.size(); i++)
if (ob[i].first)
quadArray[count++] = ob[i].first;
for (i = (int)ob.size() - 1; i >= 0; i--)
if (ob[i].second)
quadArray[count++] = ob[i].second;
quadArray.resize(count);
for (i = 0; i < (int)quadArray.size(); i++)
quadArray[i]->reverse();
std::reverse(quadArray.begin(), quadArray.end());
}
//-----------------------------------------------------------------------------
// End Of File
//-----------------------------------------------------------------------------