convert bezier curve to polygonal chain?
I want to split a bezier curve into a polygonal chain with n straight lines. The number of lines being dependent on a maximum allowed angle between 2 connecting lines. I\'m
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i solve it with qt for any svg path including bezier curve , i found in svg module a static function in qsvghandler.cpp which parsePathDataFast from your svg path to QPainterPath and the cherry on the cake!! QPainterPath have three native functions to convert your path to polygon (the big one toFillPolygon and the others which split in a list of polygon toSubpathPolygons or toFillPolygons) along with nice stuff like bounding box, intersected, translate ... ready to use with Boost::Geometry now, not so bad!
the header parsepathdatafast.h
#ifndef PARSEPATHDATAFAST_H #define PARSEPATHDATAFAST_H #include#include bool parsePathDataFast(const QStringRef &dataStr, QPainterPath &path); #endif // PARSEPATHDATAFAST_H the code parsepathdatafast.cpp
#include#include #include #include #include #include Q_CORE_EXPORT double qstrtod(const char *s00, char const **se, bool *ok); // '0' is 0x30 and '9' is 0x39 static inline bool isDigit(ushort ch) { static quint16 magic = 0x3ff; return ((ch >> 4) == 3) && (magic >> (ch & 15)); } static qreal toDouble(const QChar *&str) { const int maxLen = 255;//technically doubles can go til 308+ but whatever char temp[maxLen+1]; int pos = 0; if (*str == QLatin1Char('-')) { temp[pos++] = '-'; ++str; } else if (*str == QLatin1Char('+')) { ++str; } while (isDigit(str->unicode()) && pos < maxLen) { temp[pos++] = str->toLatin1(); ++str; } if (*str == QLatin1Char('.') && pos < maxLen) { temp[pos++] = '.'; ++str; } while (isDigit(str->unicode()) && pos < maxLen) { temp[pos++] = str->toLatin1(); ++str; } bool exponent = false; if ((*str == QLatin1Char('e') || *str == QLatin1Char('E')) && pos < maxLen) { exponent = true; temp[pos++] = 'e'; ++str; if ((*str == QLatin1Char('-') || *str == QLatin1Char('+')) && pos < maxLen) { temp[pos++] = str->toLatin1(); ++str; } while (isDigit(str->unicode()) && pos < maxLen) { temp[pos++] = str->toLatin1(); ++str; } } temp[pos] = '\0'; qreal val; if (!exponent && pos < 10) { int ival = 0; const char *t = temp; bool neg = false; if(*t == '-') { neg = true; ++t; } while(*t && *t != '.') { ival *= 10; ival += (*t) - '0'; ++t; } if(*t == '.') { ++t; int div = 1; while(*t) { ival *= 10; ival += (*t) - '0'; div *= 10; ++t; } val = ((qreal)ival)/((qreal)div); } else { val = ival; } if (neg) val = -val; } else { bool ok = false; val = qstrtod(temp, 0, &ok); } return val; } static inline void parseNumbersArray(const QChar *&str, QVarLengthArray parsePercentageList(const QChar *&str) { QVector points; if (!str) return points; while (str->isSpace()) ++str; while ((*str >= QLatin1Char('0') && *str <= QLatin1Char('9')) || *str == QLatin1Char('-') || *str == QLatin1Char('+') || *str == QLatin1Char('.')) { points.append(toDouble(str)); while (str->isSpace()) ++str; if (*str == QLatin1Char('%')) ++str; while (str->isSpace()) ++str; if (*str == QLatin1Char(',')) ++str; //eat the rest of space while (str->isSpace()) ++str; } return points; } **/ static void pathArcSegment(QPainterPath &path, qreal xc, qreal yc, qreal th0, qreal th1, qreal rx, qreal ry, qreal xAxisRotation) { qreal sinTh, cosTh; qreal a00, a01, a10, a11; qreal x1, y1, x2, y2, x3, y3; qreal t; qreal thHalf; sinTh = qSin(xAxisRotation * (M_PI / 180.0)); cosTh = qCos(xAxisRotation * (M_PI / 180.0)); a00 = cosTh * rx; a01 = -sinTh * ry; a10 = sinTh * rx; a11 = cosTh * ry; thHalf = 0.5 * (th1 - th0); t = (8.0 / 3.0) * qSin(thHalf * 0.5) * qSin(thHalf * 0.5) / qSin(thHalf); x1 = xc + qCos(th0) - t * qSin(th0); y1 = yc + qSin(th0) + t * qCos(th0); x3 = xc + qCos(th1); y3 = yc + qSin(th1); x2 = x3 + t * qSin(th1); y2 = y3 - t * qCos(th1); path.cubicTo(a00 * x1 + a01 * y1, a10 * x1 + a11 * y1, a00 * x2 + a01 * y2, a10 * x2 + a11 * y2, a00 * x3 + a01 * y3, a10 * x3 + a11 * y3); } // the arc handling code underneath is from XSVG (BSD license) /* * Copyright 2002 USC/Information Sciences Institute * * Permission to use, copy, modify, distribute, and sell this software * and its documentation for any purpose is hereby granted without * fee, provided that the above copyright notice appear in all copies * and that both that copyright notice and this permission notice * appear in supporting documentation, and that the name of * Information Sciences Institute not be used in advertising or * publicity pertaining to distribution of the software without * specific, written prior permission. Information Sciences Institute * makes no representations about the suitability of this software for * any purpose. It is provided "as is" without express or implied * warranty. * * INFORMATION SCIENCES INSTITUTE DISCLAIMS ALL WARRANTIES WITH REGARD * TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL INFORMATION SCIENCES * INSTITUTE BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL * DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA * OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER * TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR * PERFORMANCE OF THIS SOFTWARE. * */ static void pathArc(QPainterPath &path, qreal rx, qreal ry, qreal x_axis_rotation, int large_arc_flag, int sweep_flag, qreal x, qreal y, qreal curx, qreal cury) { qreal sin_th, cos_th; qreal a00, a01, a10, a11; qreal x0, y0, x1, y1, xc, yc; qreal d, sfactor, sfactor_sq; qreal th0, th1, th_arc; int i, n_segs; qreal dx, dy, dx1, dy1, Pr1, Pr2, Px, Py, check; rx = qAbs(rx); ry = qAbs(ry); sin_th = qSin(x_axis_rotation * (M_PI / 180.0)); cos_th = qCos(x_axis_rotation * (M_PI / 180.0)); dx = (curx - x) / 2.0; dy = (cury - y) / 2.0; dx1 = cos_th * dx + sin_th * dy; dy1 = -sin_th * dx + cos_th * dy; Pr1 = rx * rx; Pr2 = ry * ry; Px = dx1 * dx1; Py = dy1 * dy1; /* Spec : check if radii are large enough */ check = Px / Pr1 + Py / Pr2; if (check > 1) { rx = rx * qSqrt(check); ry = ry * qSqrt(check); } a00 = cos_th / rx; a01 = sin_th / rx; a10 = -sin_th / ry; a11 = cos_th / ry; x0 = a00 * curx + a01 * cury; y0 = a10 * curx + a11 * cury; x1 = a00 * x + a01 * y; y1 = a10 * x + a11 * y; /* (x0, y0) is current point in transformed coordinate space. (x1, y1) is new point in transformed coordinate space. The arc fits a unit-radius circle in this space. */ d = (x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0); sfactor_sq = 1.0 / d - 0.25; if (sfactor_sq < 0) sfactor_sq = 0; sfactor = qSqrt(sfactor_sq); if (sweep_flag == large_arc_flag) sfactor = -sfactor; xc = 0.5 * (x0 + x1) - sfactor * (y1 - y0); yc = 0.5 * (y0 + y1) + sfactor * (x1 - x0); /* (xc, yc) is center of the circle. */ th0 = qAtan2(y0 - yc, x0 - xc); th1 = qAtan2(y1 - yc, x1 - xc); th_arc = th1 - th0; if (th_arc < 0 && sweep_flag) th_arc += 2 * M_PI; else if (th_arc > 0 && !sweep_flag) th_arc -= 2 * M_PI; n_segs = qCeil(qAbs(th_arc / (M_PI * 0.5 + 0.001))); for (i = 0; i < n_segs; i++) { pathArcSegment(path, xc, yc, th0 + i * th_arc / n_segs, th0 + (i + 1) * th_arc / n_segs, rx, ry, x_axis_rotation); } } bool parsePathDataFast(const QStringRef &dataStr, QPainterPath &path) { qreal x0 = 0, y0 = 0; // starting point qreal x = 0, y = 0; // current point char lastMode = 0; QPointF ctrlPt; const QChar *str = dataStr.constData(); const QChar *end = str + dataStr.size(); while (str != end) { while (str->isSpace()) ++str; QChar pathElem = *str; ++str; QChar endc = *end; *const_cast (end) = 0; // parseNumbersArray requires 0-termination that QStringRef cannot guarantee QVarLengthArray (end) = endc; if (pathElem == QLatin1Char('z') || pathElem == QLatin1Char('Z')) arg.append(0);//dummy const qreal *num = arg.constData(); int count = arg.count(); while (count > 0) { qreal offsetX = x; // correction offsets qreal offsetY = y; // for relative commands switch (pathElem.unicode()) { case 'm': { if (count < 2) { num++; count--; break; } x = x0 = num[0] + offsetX; y = y0 = num[1] + offsetY; num += 2; count -= 2; path.moveTo(x0, y0); // As per 1.2 spec 8.3.2 The "moveto" commands // If a 'moveto' is followed by multiple pairs of coordinates without explicit commands, // the subsequent pairs shall be treated as implicit 'lineto' commands. pathElem = QLatin1Char('l'); } break; case 'M': { if (count < 2) { num++; count--; break; } x = x0 = num[0]; y = y0 = num[1]; num += 2; count -= 2; path.moveTo(x0, y0); // As per 1.2 spec 8.3.2 The "moveto" commands // If a 'moveto' is followed by multiple pairs of coordinates without explicit commands, // the subsequent pairs shall be treated as implicit 'lineto' commands. pathElem = QLatin1Char('L'); } break; case 'z': case 'Z': { x = x0; y = y0; count--; // skip dummy num++; path.closeSubpath(); } break; case 'l': { if (count < 2) { num++; count--; break; } x = num[0] + offsetX; y = num[1] + offsetY; num += 2; count -= 2; path.lineTo(x, y); } break; case 'L': { if (count < 2) { num++; count--; break; } x = num[0]; y = num[1]; num += 2; count -= 2; path.lineTo(x, y); } break; case 'h': { x = num[0] + offsetX; num++; count--; path.lineTo(x, y); } break; case 'H': { x = num[0]; num++; count--; path.lineTo(x, y); } break; case 'v': { y = num[0] + offsetY; num++; count--; path.lineTo(x, y); } break; case 'V': { y = num[0]; num++; count--; path.lineTo(x, y); } break; case 'c': { if (count < 6) { num += count; count = 0; break; } QPointF c1(num[0] + offsetX, num[1] + offsetY); QPointF c2(num[2] + offsetX, num[3] + offsetY); QPointF e(num[4] + offsetX, num[5] + offsetY); num += 6; count -= 6; path.cubicTo(c1, c2, e); ctrlPt = c2; x = e.x(); y = e.y(); break; } case 'C': { if (count < 6) { num += count; count = 0; break; } QPointF c1(num[0], num[1]); QPointF c2(num[2], num[3]); QPointF e(num[4], num[5]); num += 6; count -= 6; path.cubicTo(c1, c2, e); ctrlPt = c2; x = e.x(); y = e.y(); break; } case 's': { if (count < 4) { num += count; count = 0; break; } QPointF c1; if (lastMode == 'c' || lastMode == 'C' || lastMode == 's' || lastMode == 'S') c1 = QPointF(2*x-ctrlPt.x(), 2*y-ctrlPt.y()); else c1 = QPointF(x, y); QPointF c2(num[0] + offsetX, num[1] + offsetY); QPointF e(num[2] + offsetX, num[3] + offsetY); num += 4; count -= 4; path.cubicTo(c1, c2, e); ctrlPt = c2; x = e.x(); y = e.y(); break; } case 'S': { if (count < 4) { num += count; count = 0; break; } QPointF c1; if (lastMode == 'c' || lastMode == 'C' || lastMode == 's' || lastMode == 'S') c1 = QPointF(2*x-ctrlPt.x(), 2*y-ctrlPt.y()); else c1 = QPointF(x, y); QPointF c2(num[0], num[1]); QPointF e(num[2], num[3]); num += 4; count -= 4; path.cubicTo(c1, c2, e); ctrlPt = c2; x = e.x(); y = e.y(); break; } case 'q': { if (count < 4) { num += count; count = 0; break; } QPointF c(num[0] + offsetX, num[1] + offsetY); QPointF e(num[2] + offsetX, num[3] + offsetY); num += 4; count -= 4; path.quadTo(c, e); ctrlPt = c; x = e.x(); y = e.y(); break; } case 'Q': { if (count < 4) { num += count; count = 0; break; } QPointF c(num[0], num[1]); QPointF e(num[2], num[3]); num += 4; count -= 4; path.quadTo(c, e); ctrlPt = c; x = e.x(); y = e.y(); break; } case 't': { if (count < 2) { num += count; count = 0; break; } QPointF e(num[0] + offsetX, num[1] + offsetY); num += 2; count -= 2; QPointF c; if (lastMode == 'q' || lastMode == 'Q' || lastMode == 't' || lastMode == 'T') c = QPointF(2*x-ctrlPt.x(), 2*y-ctrlPt.y()); else c = QPointF(x, y); path.quadTo(c, e); ctrlPt = c; x = e.x(); y = e.y(); break; } case 'T': { if (count < 2) { num += count; count = 0; break; } QPointF e(num[0], num[1]); num += 2; count -= 2; QPointF c; if (lastMode == 'q' || lastMode == 'Q' || lastMode == 't' || lastMode == 'T') c = QPointF(2*x-ctrlPt.x(), 2*y-ctrlPt.y()); else c = QPointF(x, y); path.quadTo(c, e); ctrlPt = c; x = e.x(); y = e.y(); break; } case 'a': { if (count < 7) { num += count; count = 0; break; } qreal rx = (*num++); qreal ry = (*num++); qreal xAxisRotation = (*num++); qreal largeArcFlag = (*num++); qreal sweepFlag = (*num++); qreal ex = (*num++) + offsetX; qreal ey = (*num++) + offsetY; count -= 7; qreal curx = x; qreal cury = y; pathArc(path, rx, ry, xAxisRotation, int(largeArcFlag), int(sweepFlag), ex, ey, curx, cury); x = ex; y = ey; } break; case 'A': { if (count < 7) { num += count; count = 0; break; } qreal rx = (*num++); qreal ry = (*num++); qreal xAxisRotation = (*num++); qreal largeArcFlag = (*num++); qreal sweepFlag = (*num++); qreal ex = (*num++); qreal ey = (*num++); count -= 7; qreal curx = x; qreal cury = y; pathArc(path, rx, ry, xAxisRotation, int(largeArcFlag), int(sweepFlag), ex, ey, curx, cury); x = ex; y = ey; } break; default: return false; } lastMode = pathElem.toLatin1(); } } return true; } One question, i doesn't find Q_PI constant in the standard qt headers and i replace it with M_PI hope is OK!!
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