/** Turns a List<CubicCurve2D.Float> into a SVG Element representing a sketch of that spline. */ Element splineToSketch(SVGDocument document, List<CubicCurve2D.Float> spline) { String svgNS = SVGDOMImplementation.SVG_NAMESPACE_URI; // <g> is an SVG group // TODO: add a random(ish) rotation to the group Element group = document.createElementNS(svgNS, "g"); // For each curve in the path, draw along it using a "brush". In // our case the brush is a simple circle, but this could be changed // to something more advanced. for (CubicCurve2D.Float curve : spline) { // TODO: magic number & step in loop guard for (double i = 0.0; i <= 1.0; i += 0.01) { Point2D result = evalParametric(curve, i); // Add random jitter at some random positive or negative // distance along the unit normal to the tangent of the // curve Point2D n = vectorUnitNormal(evalParametricTangent(curve, i)); float dx = (float) ((Math.random() - 0.5) * n.getX()); float dy = (float) ((Math.random() - 0.5) * n.getY()); Element brush = document.createElementNS(svgNS, "circle"); brush.setAttribute("cx", Double.toString(result.getX() + dx)); brush.setAttribute("cy", Double.toString(result.getY() + dy)); // TODO: magic number for circle radius brush.setAttribute("r", Double.toString(1.0)); brush.setAttribute("fill", "green"); brush.setAttributeNS(null, "z-index", Integer.toString(zOrder.CONTOUR.ordinal())); group.appendChild(brush); } } return group; }
private double doubleVectorAbs(Vector<Vector<Double>> doubleVector) { double totalX = 0; for (Vector<Double> vector : doubleVector) { totalX += Math.pow(vectorAbs(vector), 2); } return Math.sqrt(totalX); }
private void loadHint(TTGlyph a_glyph, EContourPoint a_point, int a_index) { double x = a_point.getX(); double y = a_point.getY(); XHint[] hints = a_point.getHint(); for (int i = 0; i < hints.length; i++) { EHint hint = (EHint) hints[i]; double xHint = hint.getX(); double yHint = hint.getY(); if (x == xHint && y == yHint) { continue; } // if double xDelta = xHint - x; double yDelta = yHint - y; int instruction = TTGlyph.DELTAP1; double deltaStep = ((double) Engine.getEm()) / hint.getPpem() / 8; int xShift = (int) Math.round(xDelta / deltaStep); int yShift = (int) Math.round(yDelta / deltaStep); if (xShift == 0 && yShift == 0) { continue; } // if a_glyph.addInstruction(TTGlyph.PUSHB000); a_glyph.addInstruction((int) hint.getPpem()); a_glyph.addInstruction(TTGlyph.SDB); if (xShift != 0) { a_glyph.addInstruction(TTGlyph.SVTCA1); a_glyph.addInstruction(TTGlyph.PUSHB010); a_glyph.addInstruction(TTGlyph.toDeltaArg(0, xShift)); a_glyph.addInstruction(a_index); a_glyph.addInstruction(1); a_glyph.addInstruction(TTGlyph.DELTAP1); } // if if (yShift != 0) { a_glyph.addInstruction(TTGlyph.SVTCA0); a_glyph.addInstruction(TTGlyph.PUSHB010); a_glyph.addInstruction(TTGlyph.toDeltaArg(0, yShift)); a_glyph.addInstruction(a_index); a_glyph.addInstruction(1); a_glyph.addInstruction(TTGlyph.DELTAP1); } // if } // for i }
private static Point2D evalParametric(CubicCurve2D curve, double t) { if (null == curve) { return null; } // B(t) = (1-t)^3 P_0 + 3(1-t)^2t C_1 + 3(1 - t)t^2 C_2 + t^3 P_1 // do nothing fancy, just calculate it. double rx = ((Math.pow((1 - t), 3) * curve.getX1())) + (3 * Math.pow((1 - t), 2) * t * curve.getCtrlX1()) + (3 * (1 - t) * t * t * curve.getCtrlX2()) + (t * t * t * curve.getX2()); double ry = ((Math.pow((1 - t), 3) * curve.getY1())) + (3 * Math.pow((1 - t), 2) * t * curve.getCtrlY1()) + (3 * (1 - t) * t * t * curve.getCtrlY2()) + (t * t * t * curve.getY2()); return new Point2D.Float((float) rx, (float) ry); }
/** * Calculates the unit normal of a particular vector, where the vector is represented by the * direction and magnitude of the line segment from (0,0) to (p.x, p.y). * * @param p * @return */ private static Point2D vectorUnitNormal(Point2D p) { // if null object passed or if the passed vector has zero length if (null == p || ((0 == p.getX()) && (0 == p.getY()))) { return null; } // normalise the input "vector" // 1. get length of vector (Pythagoras) // 2. divide both x and y by this length // note: c cannot be 0 as we've already considered zero length input // vectors above. double c = Math.sqrt((p.getX() * p.getX()) + (p.getY() * p.getY())); double nvx = p.getX() / c; double nvy = p.getY() / c; // Now rotate (nvx, nvy) by 90 degrees to get the normal for the // input vector. // rx = nvx * cos (pi/2) - nvy * sin (pi/2) // ty = nvx * sin (pi/2) + nvy * cos (pi/2) // but cos (pi/2) = 0 and sin (pi/2) = 1, so this simplifies return new Point2D.Float((float) (-1 * nvy), (float) nvx); }
public void build_bricks() { ImagePlus imp; ImagePlus orgimp; ImageStack stack; FileInfo finfo; if (lvImgTitle.isEmpty()) return; orgimp = WindowManager.getImage(lvImgTitle.get(0)); imp = orgimp; finfo = imp.getFileInfo(); if (finfo == null) return; int[] dims = imp.getDimensions(); int imageW = dims[0]; int imageH = dims[1]; int nCh = dims[2]; int imageD = dims[3]; int nFrame = dims[4]; int bdepth = imp.getBitDepth(); double xspc = finfo.pixelWidth; double yspc = finfo.pixelHeight; double zspc = finfo.pixelDepth; double z_aspect = Math.max(xspc, yspc) / zspc; int orgW = imageW; int orgH = imageH; int orgD = imageD; double orgxspc = xspc; double orgyspc = yspc; double orgzspc = zspc; lv = lvImgTitle.size(); if (filetype == "JPEG") { for (int l = 0; l < lv; l++) { if (WindowManager.getImage(lvImgTitle.get(l)).getBitDepth() != 8) { IJ.error("A SOURCE IMAGE MUST BE 8BIT GLAYSCALE"); return; } } } // calculate levels /* int baseXY = 256; int baseZ = 256; if (z_aspect < 0.5) baseZ = 128; if (z_aspect > 2.0) baseXY = 128; if (z_aspect >= 0.5 && z_aspect < 1.0) baseZ = (int)(baseZ*z_aspect); if (z_aspect > 1.0 && z_aspect <= 2.0) baseXY = (int)(baseXY/z_aspect); IJ.log("Z_aspect: " + z_aspect); IJ.log("BaseXY: " + baseXY); IJ.log("BaseZ: " + baseZ); */ int baseXY = 256; int baseZ = 128; int dbXY = Math.max(orgW, orgH) / baseXY; if (Math.max(orgW, orgH) % baseXY > 0) dbXY *= 2; int dbZ = orgD / baseZ; if (orgD % baseZ > 0) dbZ *= 2; lv = Math.max(log2(dbXY), log2(dbZ)) + 1; int ww = orgW; int hh = orgH; int dd = orgD; for (int l = 0; l < lv; l++) { int bwnum = ww / baseXY; if (ww % baseXY > 0) bwnum++; int bhnum = hh / baseXY; if (hh % baseXY > 0) bhnum++; int bdnum = dd / baseZ; if (dd % baseZ > 0) bdnum++; if (bwnum % 2 == 0) bwnum++; if (bhnum % 2 == 0) bhnum++; if (bdnum % 2 == 0) bdnum++; int bw = (bwnum <= 1) ? ww : ww / bwnum + 1 + (ww % bwnum > 0 ? 1 : 0); int bh = (bhnum <= 1) ? hh : hh / bhnum + 1 + (hh % bhnum > 0 ? 1 : 0); int bd = (bdnum <= 1) ? dd : dd / bdnum + 1 + (dd % bdnum > 0 ? 1 : 0); bwlist.add(bw); bhlist.add(bh); bdlist.add(bd); IJ.log("LEVEL: " + l); IJ.log(" width: " + ww); IJ.log(" hight: " + hh); IJ.log(" depth: " + dd); IJ.log(" bw: " + bw); IJ.log(" bh: " + bh); IJ.log(" bd: " + bd); int xyl2 = Math.max(ww, hh) / baseXY; if (Math.max(ww, hh) % baseXY > 0) xyl2 *= 2; if (lv - 1 - log2(xyl2) <= l) { ww /= 2; hh /= 2; } IJ.log(" xyl2: " + (lv - 1 - log2(xyl2))); int zl2 = dd / baseZ; if (dd % baseZ > 0) zl2 *= 2; if (lv - 1 - log2(zl2) <= l) dd /= 2; IJ.log(" zl2: " + (lv - 1 - log2(zl2))); if (l < lv - 1) { lvImgTitle.add(lvImgTitle.get(0) + "_level" + (l + 1)); IJ.selectWindow(lvImgTitle.get(0)); IJ.run( "Scale...", "x=- y=- z=- width=" + ww + " height=" + hh + " depth=" + dd + " interpolation=Bicubic average process create title=" + lvImgTitle.get(l + 1)); } } for (int l = 0; l < lv; l++) { IJ.log(lvImgTitle.get(l)); } Document doc = newXMLDocument(); Element root = doc.createElement("BRK"); root.setAttribute("version", "1.0"); root.setAttribute("nLevel", String.valueOf(lv)); root.setAttribute("nChannel", String.valueOf(nCh)); root.setAttribute("nFrame", String.valueOf(nFrame)); doc.appendChild(root); for (int l = 0; l < lv; l++) { IJ.showProgress(0.0); int[] dims2 = imp.getDimensions(); IJ.log( "W: " + String.valueOf(dims2[0]) + " H: " + String.valueOf(dims2[1]) + " C: " + String.valueOf(dims2[2]) + " D: " + String.valueOf(dims2[3]) + " T: " + String.valueOf(dims2[4]) + " b: " + String.valueOf(bdepth)); bw = bwlist.get(l).intValue(); bh = bhlist.get(l).intValue(); bd = bdlist.get(l).intValue(); boolean force_pow2 = false; /* if(IsPowerOf2(bw) && IsPowerOf2(bh) && IsPowerOf2(bd)) force_pow2 = true; if(force_pow2){ //force pow2 if(Pow2(bw) > bw) bw = Pow2(bw)/2; if(Pow2(bh) > bh) bh = Pow2(bh)/2; if(Pow2(bd) > bd) bd = Pow2(bd)/2; } if(bw > imageW) bw = (Pow2(imageW) == imageW) ? imageW : Pow2(imageW)/2; if(bh > imageH) bh = (Pow2(imageH) == imageH) ? imageH : Pow2(imageH)/2; if(bd > imageD) bd = (Pow2(imageD) == imageD) ? imageD : Pow2(imageD)/2; */ if (bw > imageW) bw = imageW; if (bh > imageH) bh = imageH; if (bd > imageD) bd = imageD; if (bw <= 1 || bh <= 1 || bd <= 1) break; if (filetype == "JPEG" && (bw < 8 || bh < 8)) break; Element lvnode = doc.createElement("Level"); lvnode.setAttribute("lv", String.valueOf(l)); lvnode.setAttribute("imageW", String.valueOf(imageW)); lvnode.setAttribute("imageH", String.valueOf(imageH)); lvnode.setAttribute("imageD", String.valueOf(imageD)); lvnode.setAttribute("xspc", String.valueOf(xspc)); lvnode.setAttribute("yspc", String.valueOf(yspc)); lvnode.setAttribute("zspc", String.valueOf(zspc)); lvnode.setAttribute("bitDepth", String.valueOf(bdepth)); root.appendChild(lvnode); Element brksnode = doc.createElement("Bricks"); brksnode.setAttribute("brick_baseW", String.valueOf(bw)); brksnode.setAttribute("brick_baseH", String.valueOf(bh)); brksnode.setAttribute("brick_baseD", String.valueOf(bd)); lvnode.appendChild(brksnode); ArrayList<Brick> bricks = new ArrayList<Brick>(); int mw, mh, md, mw2, mh2, md2; double tx0, ty0, tz0, tx1, ty1, tz1; double bx0, by0, bz0, bx1, by1, bz1; for (int k = 0; k < imageD; k += bd) { if (k > 0) k--; for (int j = 0; j < imageH; j += bh) { if (j > 0) j--; for (int i = 0; i < imageW; i += bw) { if (i > 0) i--; mw = Math.min(bw, imageW - i); mh = Math.min(bh, imageH - j); md = Math.min(bd, imageD - k); if (force_pow2) { mw2 = Pow2(mw); mh2 = Pow2(mh); md2 = Pow2(md); } else { mw2 = mw; mh2 = mh; md2 = md; } if (filetype == "JPEG") { if (mw2 < 8) mw2 = 8; if (mh2 < 8) mh2 = 8; } tx0 = i == 0 ? 0.0d : ((mw2 - mw + 0.5d) / mw2); ty0 = j == 0 ? 0.0d : ((mh2 - mh + 0.5d) / mh2); tz0 = k == 0 ? 0.0d : ((md2 - md + 0.5d) / md2); tx1 = 1.0d - 0.5d / mw2; if (mw < bw) tx1 = 1.0d; if (imageW - i == bw) tx1 = 1.0d; ty1 = 1.0d - 0.5d / mh2; if (mh < bh) ty1 = 1.0d; if (imageH - j == bh) ty1 = 1.0d; tz1 = 1.0d - 0.5d / md2; if (md < bd) tz1 = 1.0d; if (imageD - k == bd) tz1 = 1.0d; bx0 = i == 0 ? 0.0d : (i + 0.5d) / (double) imageW; by0 = j == 0 ? 0.0d : (j + 0.5d) / (double) imageH; bz0 = k == 0 ? 0.0d : (k + 0.5d) / (double) imageD; bx1 = Math.min((i + bw - 0.5d) / (double) imageW, 1.0d); if (imageW - i == bw) bx1 = 1.0d; by1 = Math.min((j + bh - 0.5d) / (double) imageH, 1.0d); if (imageH - j == bh) by1 = 1.0d; bz1 = Math.min((k + bd - 0.5d) / (double) imageD, 1.0d); if (imageD - k == bd) bz1 = 1.0d; int x, y, z; x = i - (mw2 - mw); y = j - (mh2 - mh); z = k - (md2 - md); bricks.add( new Brick( x, y, z, mw2, mh2, md2, 0, 0, tx0, ty0, tz0, tx1, ty1, tz1, bx0, by0, bz0, bx1, by1, bz1)); } } } Element fsnode = doc.createElement("Files"); lvnode.appendChild(fsnode); stack = imp.getStack(); int totalbricknum = nFrame * nCh * bricks.size(); int curbricknum = 0; for (int f = 0; f < nFrame; f++) { for (int ch = 0; ch < nCh; ch++) { int sizelimit = bdsizelimit * 1024 * 1024; int bytecount = 0; int filecount = 0; int pd_bufsize = Math.max(sizelimit, bw * bh * bd * bdepth / 8); byte[] packed_data = new byte[pd_bufsize]; String base_dataname = basename + "_Lv" + String.valueOf(l) + "_Ch" + String.valueOf(ch) + "_Fr" + String.valueOf(f); String current_dataname = base_dataname + "_data" + filecount; Brick b_first = bricks.get(0); if (b_first.z_ != 0) IJ.log("warning"); int st_z = b_first.z_; int ed_z = b_first.z_ + b_first.d_; LinkedList<ImageProcessor> iplist = new LinkedList<ImageProcessor>(); for (int s = st_z; s < ed_z; s++) iplist.add(stack.getProcessor(imp.getStackIndex(ch + 1, s + 1, f + 1))); // ImagePlus test; // ImageStack tsst; // test = NewImage.createByteImage("test", imageW, imageH, imageD, // NewImage.FILL_BLACK); // tsst = test.getStack(); for (int i = 0; i < bricks.size(); i++) { Brick b = bricks.get(i); if (ed_z > b.z_ || st_z < b.z_ + b.d_) { if (b.z_ > st_z) { for (int s = 0; s < b.z_ - st_z; s++) iplist.pollFirst(); st_z = b.z_; } else if (b.z_ < st_z) { IJ.log("warning"); for (int s = st_z - 1; s > b.z_; s--) iplist.addFirst(stack.getProcessor(imp.getStackIndex(ch + 1, s + 1, f + 1))); st_z = b.z_; } if (b.z_ + b.d_ > ed_z) { for (int s = ed_z; s < b.z_ + b.d_; s++) iplist.add(stack.getProcessor(imp.getStackIndex(ch + 1, s + 1, f + 1))); ed_z = b.z_ + b.d_; } else if (b.z_ + b.d_ < ed_z) { IJ.log("warning"); for (int s = 0; s < ed_z - (b.z_ + b.d_); s++) iplist.pollLast(); ed_z = b.z_ + b.d_; } } else { IJ.log("warning"); iplist.clear(); st_z = b.z_; ed_z = b.z_ + b.d_; for (int s = st_z; s < ed_z; s++) iplist.add(stack.getProcessor(imp.getStackIndex(ch + 1, s + 1, f + 1))); } if (iplist.size() != b.d_) { IJ.log("Stack Error"); return; } // int zz = st_z; int bsize = 0; byte[] bdata = new byte[b.w_ * b.h_ * b.d_ * bdepth / 8]; Iterator<ImageProcessor> ipite = iplist.iterator(); while (ipite.hasNext()) { // ImageProcessor tsip = tsst.getProcessor(zz+1); ImageProcessor ip = ipite.next(); ip.setRoi(b.x_, b.y_, b.w_, b.h_); if (bdepth == 8) { byte[] data = (byte[]) ip.crop().getPixels(); System.arraycopy(data, 0, bdata, bsize, data.length); bsize += data.length; } else if (bdepth == 16) { ByteBuffer buffer = ByteBuffer.allocate(b.w_ * b.h_ * bdepth / 8); buffer.order(ByteOrder.LITTLE_ENDIAN); short[] data = (short[]) ip.crop().getPixels(); for (short e : data) buffer.putShort(e); System.arraycopy(buffer.array(), 0, bdata, bsize, buffer.array().length); bsize += buffer.array().length; } else if (bdepth == 32) { ByteBuffer buffer = ByteBuffer.allocate(b.w_ * b.h_ * bdepth / 8); buffer.order(ByteOrder.LITTLE_ENDIAN); float[] data = (float[]) ip.crop().getPixels(); for (float e : data) buffer.putFloat(e); System.arraycopy(buffer.array(), 0, bdata, bsize, buffer.array().length); bsize += buffer.array().length; } } String filename = basename + "_Lv" + String.valueOf(l) + "_Ch" + String.valueOf(ch) + "_Fr" + String.valueOf(f) + "_ID" + String.valueOf(i); int offset = bytecount; int datasize = bdata.length; if (filetype == "RAW") { int dummy = -1; // do nothing } if (filetype == "JPEG" && bdepth == 8) { try { DataBufferByte db = new DataBufferByte(bdata, datasize); Raster raster = Raster.createPackedRaster(db, b.w_, b.h_ * b.d_, 8, null); BufferedImage img = new BufferedImage(b.w_, b.h_ * b.d_, BufferedImage.TYPE_BYTE_GRAY); img.setData(raster); ByteArrayOutputStream baos = new ByteArrayOutputStream(); ImageOutputStream ios = ImageIO.createImageOutputStream(baos); String format = "jpg"; Iterator<javax.imageio.ImageWriter> iter = ImageIO.getImageWritersByFormatName("jpeg"); javax.imageio.ImageWriter writer = iter.next(); ImageWriteParam iwp = writer.getDefaultWriteParam(); iwp.setCompressionMode(ImageWriteParam.MODE_EXPLICIT); iwp.setCompressionQuality((float) jpeg_quality * 0.01f); writer.setOutput(ios); writer.write(null, new IIOImage(img, null, null), iwp); // ImageIO.write(img, format, baos); bdata = baos.toByteArray(); datasize = bdata.length; } catch (IOException e) { e.printStackTrace(); return; } } if (filetype == "ZLIB") { byte[] tmpdata = new byte[b.w_ * b.h_ * b.d_ * bdepth / 8]; Deflater compresser = new Deflater(); compresser.setInput(bdata); compresser.setLevel(Deflater.DEFAULT_COMPRESSION); compresser.setStrategy(Deflater.DEFAULT_STRATEGY); compresser.finish(); datasize = compresser.deflate(tmpdata); bdata = tmpdata; compresser.end(); } if (bytecount + datasize > sizelimit && bytecount > 0) { BufferedOutputStream fis = null; try { File file = new File(directory + current_dataname); fis = new BufferedOutputStream(new FileOutputStream(file)); fis.write(packed_data, 0, bytecount); } catch (IOException e) { e.printStackTrace(); return; } finally { try { if (fis != null) fis.close(); } catch (IOException e) { e.printStackTrace(); return; } } filecount++; current_dataname = base_dataname + "_data" + filecount; bytecount = 0; offset = 0; System.arraycopy(bdata, 0, packed_data, bytecount, datasize); bytecount += datasize; } else { System.arraycopy(bdata, 0, packed_data, bytecount, datasize); bytecount += datasize; } Element filenode = doc.createElement("File"); filenode.setAttribute("filename", current_dataname); filenode.setAttribute("channel", String.valueOf(ch)); filenode.setAttribute("frame", String.valueOf(f)); filenode.setAttribute("brickID", String.valueOf(i)); filenode.setAttribute("offset", String.valueOf(offset)); filenode.setAttribute("datasize", String.valueOf(datasize)); filenode.setAttribute("filetype", String.valueOf(filetype)); fsnode.appendChild(filenode); curbricknum++; IJ.showProgress((double) (curbricknum) / (double) (totalbricknum)); } if (bytecount > 0) { BufferedOutputStream fis = null; try { File file = new File(directory + current_dataname); fis = new BufferedOutputStream(new FileOutputStream(file)); fis.write(packed_data, 0, bytecount); } catch (IOException e) { e.printStackTrace(); return; } finally { try { if (fis != null) fis.close(); } catch (IOException e) { e.printStackTrace(); return; } } } } } for (int i = 0; i < bricks.size(); i++) { Brick b = bricks.get(i); Element bricknode = doc.createElement("Brick"); bricknode.setAttribute("id", String.valueOf(i)); bricknode.setAttribute("st_x", String.valueOf(b.x_)); bricknode.setAttribute("st_y", String.valueOf(b.y_)); bricknode.setAttribute("st_z", String.valueOf(b.z_)); bricknode.setAttribute("width", String.valueOf(b.w_)); bricknode.setAttribute("height", String.valueOf(b.h_)); bricknode.setAttribute("depth", String.valueOf(b.d_)); brksnode.appendChild(bricknode); Element tboxnode = doc.createElement("tbox"); tboxnode.setAttribute("x0", String.valueOf(b.tx0_)); tboxnode.setAttribute("y0", String.valueOf(b.ty0_)); tboxnode.setAttribute("z0", String.valueOf(b.tz0_)); tboxnode.setAttribute("x1", String.valueOf(b.tx1_)); tboxnode.setAttribute("y1", String.valueOf(b.ty1_)); tboxnode.setAttribute("z1", String.valueOf(b.tz1_)); bricknode.appendChild(tboxnode); Element bboxnode = doc.createElement("bbox"); bboxnode.setAttribute("x0", String.valueOf(b.bx0_)); bboxnode.setAttribute("y0", String.valueOf(b.by0_)); bboxnode.setAttribute("z0", String.valueOf(b.bz0_)); bboxnode.setAttribute("x1", String.valueOf(b.bx1_)); bboxnode.setAttribute("y1", String.valueOf(b.by1_)); bboxnode.setAttribute("z1", String.valueOf(b.bz1_)); bricknode.appendChild(bboxnode); } if (l < lv - 1) { imp = WindowManager.getImage(lvImgTitle.get(l + 1)); int[] newdims = imp.getDimensions(); imageW = newdims[0]; imageH = newdims[1]; imageD = newdims[3]; xspc = orgxspc * ((double) orgW / (double) imageW); yspc = orgyspc * ((double) orgH / (double) imageH); zspc = orgzspc * ((double) orgD / (double) imageD); bdepth = imp.getBitDepth(); } } File newXMLfile = new File(directory + basename + ".vvd"); writeXML(newXMLfile, doc); for (int l = 1; l < lv; l++) { imp = WindowManager.getImage(lvImgTitle.get(l)); imp.changes = false; imp.close(); } }
private double gainFunction(double x) { return 1 / (1 + Math.exp(-x)); }
private double vectorAbs(Vector<Double> vector) { double totalX = 0; for (Double x : vector) totalX += Math.pow(x, 2); return Math.sqrt(totalX); }