/* This file is part of the source code for 3D-XplorMath-J, Version 1.0 (January 2008). * Copyright (c) 2008 The 3D-XplorMath Consortium (http://3d-xplormath.org). * This source code is released under a BSD License, which allows redistribution * in source and binary form, with or without modification, provided copyright * and license information are included, and with no warranty or guarantee of * any kind. For details, see http://3d-xplormath.org/j/source/BSDLicense.txt */ package vmm.surface.implicit; import java.awt.Color; import java.awt.Graphics2D; import java.awt.RenderingHints; import java.awt.event.ActionEvent; import java.awt.geom.Line2D; import java.awt.geom.Point2D; import java.util.ArrayList; import vmm.actions.ActionList; import vmm.actions.ToggleAction; import vmm.core.Decoration; import vmm.core.I18n; import vmm.core.Transform; import vmm.core.VMMSave; import vmm.core.View; import vmm.core3D.Transform3D; import vmm.core3D.Vector3D; import vmm.core3D.View3D; public class ClebschCubic extends SurfaceImplicit { double sqr(double x){return x*x;} static double sqrt(double x) { return Math.sqrt(x); } static double cube(double x){return x*x*x;} public double heightFunction(double x, double y, double z) { double height; double xsqr =sqr(x); double ysqr = sqr(y); double zsqr = sqr(z); double xcube = x*xsqr; double ycube = y*ysqr; double zcube = z*zsqr; height = -(81*(xcube + ycube + zcube) - 189*(xsqr*y + xsqr*z + ysqr*x + ysqr*z + zsqr*x + zsqr*y) + 54 * x * y * z + 126*(x * y + x * z + y * z) - 9 * (xsqr + ysqr + zsqr) - 9*(x + y + z) + 1); return height; } public ClebschCubic(){ setDefaultWindow(-3.5, 3.5, -3.5, 3.5); setDefaultViewpoint(new Vector3D(26.5,-7.25,-7.25)); setDefaultViewUp(new Vector3D(0.3608,0.6595,0.6595)); searchRadius.reset(3); randomLineCount.reset(60000); pointCloudCount.reset(12000); level.reset(0); setFramesForMorphing(11); InitializeTwentySevenLineArray(); heightFunctionType = equationType.CUBIC; } public View getDefaultView() { return new ClebschView(); } // The remainder of the class is concerned with drawing the 27 lines on the Clebsch Cubic. private class LinesOnCubic extends Decoration { Vector3D[][] lines = new Vector3D[27][2]; ArrayList lineSegmentsToDraw = new ArrayList(); // also for lines for left stereo image ArrayList lineSegmentsToDrawForRightStereo = new ArrayList(); double computedForSearchRadius; boolean computedForRayTrace; boolean computedForMonocularRayTrace; public void computeDrawData(View view, boolean exhibitNeedsRedraw, Transform previousTransform, Transform newTransform) { synchronized(view) { // synchrnization needed when view style changes during ray-traced rendering. ClebschView cv = (ClebschView)view; // This decoration can only occur in a ClebschView ! boolean needCompute = lineSegmentsToDraw.size() == 0; if (computedForSearchRadius != searchRadius.getValue()) { computedForSearchRadius = searchRadius.getValue(); needCompute = true; for (int i = 0; i < 27; i++) lines[i] = findVisibleSegmentOfClebschLine(i+1, (View3D)view); } boolean rayTraced = cv.getUseRaytraceRendering(); if (computedForRayTrace != rayTraced) { computedForRayTrace = rayTraced; needCompute = true; } boolean monocular = rayTraced && (cv.getViewStyle() == View3D.MONOCULAR_VIEW); if (monocular != computedForMonocularRayTrace) { computedForMonocularRayTrace = monocular; needCompute = true; } if (rayTraced && ! newTransform.equals(previousTransform) ) needCompute = true; if (!needCompute) return; //System.out.println("Compute"); lineSegmentsToDraw.clear(); lineSegmentsToDrawForRightStereo.clear(); if (rayTraced) { if (computedForMonocularRayTrace) { for (Vector3D[] line : lines) if (line != null) findUnHiddenLineSegments(line[0],line[1],cv,(Transform3D)newTransform, lineSegmentsToDraw); } else { Transform3D[] stereoTransform3D = cv.getStereoViewingTransforms(); for (Vector3D[] line : lines) if (line != null) { findUnHiddenLineSegments(line[0],line[1],cv,stereoTransform3D[0], lineSegmentsToDraw); findUnHiddenLineSegments(line[0],line[1],cv,stereoTransform3D[1], lineSegmentsToDrawForRightStereo); } } } else { for (Vector3D[] line : lines) if (line != null) lineSegmentsToDraw.add(line); } } } public void doDraw(Graphics2D g, View view, Transform transform) { ClebschView cv = (ClebschView)view; synchronized(cv) { //System.out.println("Draw " + Math.random()); boolean rayTraced = cv.getUseRaytraceRendering(); if (rayTraced) cv.setColor(Color.BLACK); else if (cv.getViewStyle() == View3D.RED_GREEN_STEREO_VIEW) cv.setColor(null); else // non-anaglyph dot-cloud cv.setColor(Color.RED); if (rayTraced && !computedForMonocularRayTrace) { cv.drawLinesOnCubic(lineSegmentsToDraw, lineSegmentsToDrawForRightStereo); } else { g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); for (Vector3D[] line : lineSegmentsToDraw) cv.drawLine(line[0],line[1]); } } } } public class ClebschView extends ImplicitSurfaceView { // need this to provide access to stereo viewing transforms @VMMSave private boolean drawLines = true; private LinesOnCubic linesDecoration; ToggleAction drawLinesToggle = new ToggleAction(I18n.tr("vmm.surface.implicit.ClebschCubic.DrawLines"),true) { public void actionPerformed(ActionEvent evt) { setDrawLines(getState()); } }; public ClebschView() { linesDecoration = new LinesOnCubic(); addDecoration(linesDecoration); } public boolean getDrawLines() { return drawLines; } public void setDrawLines(boolean drawLines) { if (this.drawLines == drawLines) return; this.drawLines = drawLines; drawLinesToggle.setState(drawLines); if (drawLines) { linesDecoration = new LinesOnCubic(); addDecoration(linesDecoration); } else { removeDecoration(linesDecoration); linesDecoration = null; } } public ActionList getActions() { ActionList actions = super.getActions(); actions.add(null); actions.add(drawLinesToggle); return actions; } Transform3D[] getStereoViewingTransforms() { Transform3D leftTransform, rightTransform; setUpForLeftEye(); leftTransform = (Transform3D)getTransform3D().clone(); setUpForRightEye(); rightTransform = (Transform3D)getTransform3D().clone(); finishStereoView(); return new Transform3D[] { leftTransform, rightTransform }; } void drawLinesOnCubic(ArrayList leftLines, ArrayList rightLines) { Point2D p1 = new Point2D.Double(); Point2D p2 = new Point2D.Double(); setUpForLeftEye(); for (Vector3D[] line : leftLines) { currentGraphics.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); transform3D.objectToDrawingCoords(line[0],p1); transform3D.objectToDrawingCoords(line[1],p2); currentGraphics.draw(new Line2D.Float(p1,p2)); } setUpForRightEye(); for (Vector3D[] line : rightLines) { currentGraphics.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); transform3D.objectToDrawingCoords(line[0],p1); transform3D.objectToDrawingCoords(line[1],p2); currentGraphics.draw(new Line2D.Float(p1,p2)); } finishStereoView(); } } private double implicitFunctionOfSearchSphereAlongRay(int linenum, double t) { Vector3D thePoint = new Vector3D(ClebschLine(linenum,t)); return sqr(thePoint.norm()) - sqr(searchRadius.getValue()); } private Vector3D[] findVisibleSegmentOfClebschLine(int linenum, View3D view) { boolean lineIntersectsSearchSphere; double A,B,C,D,leftEnd,rightEnd; B = 0.5*( implicitFunctionOfSearchSphereAlongRay(linenum,1) - implicitFunctionOfSearchSphereAlongRay(linenum,-1) ); C = implicitFunctionOfSearchSphereAlongRay(linenum,0); A = implicitFunctionOfSearchSphereAlongRay(linenum,1) - B - C; D = B*B-4*A*C; lineIntersectsSearchSphere = (D>0); if (lineIntersectsSearchSphere){ leftEnd = (- B - sqrt(D))/(2*A); rightEnd = (- B + sqrt(D))/(2*A); Vector3D initialPoint = new Vector3D(ClebschLine(linenum, leftEnd)); Vector3D finalPoint = new Vector3D(ClebschLine(linenum, rightEnd)); return new Vector3D[] { initialPoint, finalPoint }; } else return null; } private void findUnHiddenLineSegments(Vector3D pt1, Vector3D pt2, ImplicitSurfaceView view, Transform3D transform, ArrayList linesToDraw) { Vector3D viewPoint = transform.getViewPoint(); double[] theRoots = new double[5]; double pixelSize = transform.getPixelWidth(); Point2D xyPt1 = transform.objectToXYWindowCoords(pt1); Point2D xyPt2 = transform.objectToXYWindowCoords(pt2); double distanceOnScreen = sqrt(sqr(xyPt1.getX() - xyPt2.getX()) + sqr(xyPt1.getY() - xyPt2.getY())); int steps = (int)(distanceOnScreen / pixelSize); if (steps > 100) steps = 100; if (steps == 0) { if (! isHidden(pt1,viewPoint,view,transform,theRoots)) linesToDraw.add( new Vector3D[] { pt1, pt1 }); return; } double pixelsPerStep = distanceOnScreen/steps/pixelSize; Vector3D dv = pt2.minus(pt1).times(1.0/steps); Vector3D A,B,unHiddenSegmentStart; boolean hiddenA, hiddenB; A = pt1; hiddenA = isHidden(A,viewPoint,view,transform,theRoots); unHiddenSegmentStart = hiddenA ? null : A; for (int i = 1; i <= steps; i++) { B = pt1.plus(dv.times(i)); hiddenB = isHidden(B,viewPoint,view,transform,theRoots); if (hiddenA != hiddenB) { Vector3D A1 = A; Vector3D B1 = B; boolean hiddenA1 = hiddenA; double size = pixelsPerStep; Vector3D divisionPt = A1.plus(B1).times(0.5); while (size > 1) { // get distance between endpoints down to 1 pixel or less boolean hiddenMiddle = isHidden(divisionPt,viewPoint,view,transform,theRoots); if (hiddenMiddle == hiddenA1) A1 = divisionPt; else // hiddenMiddle == hiddenB1 B1 = divisionPt; size /= 2; divisionPt = A1.plus(B1).times(0.5); } if (hiddenB) {// and therefore !hiddenA linesToDraw.add(new Vector3D[] { unHiddenSegmentStart, divisionPt }); unHiddenSegmentStart = null; } else // !hiddenB && hiddenA unHiddenSegmentStart = divisionPt; } if (i == steps && !hiddenB) linesToDraw.add(new Vector3D[] {unHiddenSegmentStart, B} ); A = B; hiddenA = hiddenB; } } private boolean isHidden(Vector3D point,Vector3D viewPoint, ImplicitSurfaceView view, Transform3D transform, double[] theRoots) { Vector3D directionToPixel = point.minus(viewPoint).normalized(); double projOfViewPtOnDirection = viewPoint.dot(directionToPixel); Vector3D intercpt = viewPoint.minus(directionToPixel.times(projOfViewPtOnDirection)); Line3D lineFromViewptToPixel = new Line3D(intercpt,directionToPixel); Vector3D firstIntersection = view.GetFirstIntersectionsOfLineWithCubicSurface(lineFromViewptToPixel, theRoots); if (firstIntersection.x == -12345.0) return false; // Theoretically, this shouldn't happen since the point being tested in on the surface. Vector3D directionFromIntersectionToPoint = point.minus(firstIntersection); if (directionFromIntersectionToPoint.norm() < 0.05) { // The first intersection point is actually the point that we are testing, so it is not hidden. return false; } // In theory, the answer should now be true, since the point being tested is // supposed to be a point on the surface. However, to allow for numerical errors, // check whehter the first intersection is actually *behind* the point. return ! (directionFromIntersectionToPoint.dot(directionToPixel) < 0); } /* According to Matthias Weber (who calculated them using Mathematica) the parametric equations for the 27 lines on the Clebsch Cubic are: {1 (-1/3, -t, t) } {2 (-1/3 + 3*t, 0, t) } {3 (-t, -1/3, t) } {4 (0, -1/3 + 3*t, t) } {5 (0, (1 + 3*t)/9, t) } {6 (0, 1/3 - t, t) } {7 ((1 + 3*t)/9, 0, t) } {8 ( 1/3 - t, 0, t) } {9 (1/3, 2/3 - t, t) } {10 (2/3 - t, 1/3, t) } {11 ((5 - 3*sqrt(5) + 6*sqrt(5)*t)/30, 1/6 - 1/(6*sqrt(5)) + t - (3*t)/sqrt(5), t) } {12 ((7 - 3*sqrt(5))/6 + (-3 + sqrt(5))*t,1/2 - sqrt(5)/6 + sqrt(5)*t, t) } {13 ((1 - sqrt(5) + 3*(-5 + 3*sqrt(5))*t)/12, (3 + sqrt(5) + 3*(-3 + sqrt(5))*t)/12, t) } {14 ((3 - sqrt(5) - 3*(3 + sqrt(5))*t)/12, (1 + sqrt(5) - 3*(5 + 3*sqrt(5))*t)/12, t) } {15 (1/2 - sqrt(5)/6 + sqrt(5)*t, (7 - 3*sqrt(5))/6 + (-3 + sqrt(5))*t, t) } {16 (1/6 - 1/(6*sqrt(5)) + t - (3*t)/sqrt(5), (5 - 3*sqrt(5) + 6*sqrt(5)*t)/30, t) } {17 ((1 + sqrt(5) - 3*(5 + 3*sqrt(5))*t)/12, (3 - sqrt(5) - 3*(3 + sqrt(5))*t)/12, t) } {18 ((3 + sqrt(5) + 3*(-3 + sqrt(5))*t)/12, (1 - sqrt(5) + 3*(-5 + 3*sqrt(5))*t)/12, t) } {19 ((3 + sqrt(5) - 6*sqrt(5)*t)/6, (7 + 3*sqrt(5) - 6*(3 + sqrt(5))*t)/6, t) } {20 ((5 + sqrt(5))/30 + t + (3*t)/sqrt(5), (5 + 3*sqrt(5) - 6*sqrt(5)*t)/30, t) } {21 ((5 + 3*sqrt(5) - 6*sqrt(5)*t)/30, (5 + sqrt(5))/30 + t + (3*t)/sqrt(5), t) } {22 ((7 + 3*sqrt(5) - 6*(3 + sqrt(5))*t)/6, (3 + sqrt(5) - 6*sqrt(5)*t)/6, t) } {23 (-1/3 + 3*t, t, 0) } {24 (-t, t, -1/3) } {25 (1/9 + t/3, t, 0) } {26 (1/3 - t, t, 0) } {27 (2/3 - t, t, 1/3) } */ /* The i_th Clebsch Line will be given parametrically by: (TwentySevenLineArray[i][1][1] + TwentySevenLineArray[i[]1][2]t , TwentySevenLineArray[i][2][1] + TwentySevenLineArray[i][2][2]t, TwentySevenLineArray[i][3][1] + TwentySevenLineArray[i]3][2]t) so */ double[][][] TwentySevenLineArray = new double[28][4][3]; protected Vector3D ClebschLine(int linenum, double t) { Vector3D thePoint = new Vector3D(); thePoint.x = TwentySevenLineArray[linenum][1][1] + TwentySevenLineArray[linenum][1][2] * t; thePoint.y = TwentySevenLineArray[linenum][2][1] + TwentySevenLineArray[linenum][2][2] * t; thePoint.z = TwentySevenLineArray[linenum][3][1] + TwentySevenLineArray[linenum][3][2] * t; return thePoint; } protected void InitializeTwentySevenLineArray() { TwentySevenLineArray[1][1][1] = -1.0/3.0; TwentySevenLineArray[1][1][2] = 0; TwentySevenLineArray[1][2][1] = 0; TwentySevenLineArray[1][2][2] = -1; TwentySevenLineArray[1][3][1] = 0; TwentySevenLineArray[1][3][2] = 1; TwentySevenLineArray[2][1][1] = -1.0/3.0; TwentySevenLineArray[2][1][2] = 3; TwentySevenLineArray[2][2][1] = 0; TwentySevenLineArray[2][2][2] = 0; TwentySevenLineArray[2][3][1] = 0; TwentySevenLineArray[2][3][2] = 1; TwentySevenLineArray[3][1][1] = 0; TwentySevenLineArray[3][1][2] = -1; TwentySevenLineArray[3][2][1] = -1.0/3.0; TwentySevenLineArray[3][2][2] = 0; TwentySevenLineArray[3][3][1] = 0; TwentySevenLineArray[3][3][2] = 1; TwentySevenLineArray[4][1][1] = 0; TwentySevenLineArray[4][1][2] = 0; TwentySevenLineArray[4][2][1] = -1.0/3.0; TwentySevenLineArray[4][2][2] = 3; TwentySevenLineArray[4][3][1] = 0; TwentySevenLineArray[4][3][2] = 1; TwentySevenLineArray[5][1][1] = 0; TwentySevenLineArray[5][1][2] = 0; TwentySevenLineArray[5][2][1] = 1.0/9.0; TwentySevenLineArray[5][2][2] = 1.0/3.0; TwentySevenLineArray[5][3][1] = 0; TwentySevenLineArray[5][3][2] = 1; TwentySevenLineArray[6][1][1] = 0; TwentySevenLineArray[6][1][2] = 0; TwentySevenLineArray[6][2][1] = 1.0/3.0; TwentySevenLineArray[6][2][2] = -1; TwentySevenLineArray[6][3][1] = 0; TwentySevenLineArray[6][3][2] = 1; TwentySevenLineArray[7][1][1] = 1.0/9.0; TwentySevenLineArray[7][1][2] = 1.0/3.0; TwentySevenLineArray[7][2][1] = 0; TwentySevenLineArray[7][2][2] = 0; TwentySevenLineArray[7][3][1] = 0; TwentySevenLineArray[7][3][2] = 1; TwentySevenLineArray[8][1][1] = 1.0/3.0; TwentySevenLineArray[8][1][2] = -1; TwentySevenLineArray[8][2][1] = 0; TwentySevenLineArray[8][2][2] = 0; TwentySevenLineArray[8][3][1] = 0; TwentySevenLineArray[8][3][2] = 1; TwentySevenLineArray[9][1][1] = 1.0/3.0; TwentySevenLineArray[9][1][2] = 0; TwentySevenLineArray[9][2][1] = 2.0/3.0; TwentySevenLineArray[9][2][2] = -1; TwentySevenLineArray[9][3][1] = 0; TwentySevenLineArray[9][3][2] = 1; TwentySevenLineArray[10][1][1] = 2.0/3.0; TwentySevenLineArray[10][1][2] = -1; TwentySevenLineArray[10][2][1] = 1.0/3.0; TwentySevenLineArray[10][2][2] = 0; TwentySevenLineArray[10][3][1] = 0; TwentySevenLineArray[10][3][2] = 1; TwentySevenLineArray[11][1][1] = 1.0/6.0 - sqrt(5)/10.0 ; TwentySevenLineArray[11][1][2] = sqrt(5)/5.0; TwentySevenLineArray[11][2][1] = 1.0/6.0 - 1/(6*sqrt(5)); TwentySevenLineArray[11][2][2] = 1 - 3.0/sqrt(5); TwentySevenLineArray[11][3][1] = 0; TwentySevenLineArray[11][3][2] = 1; TwentySevenLineArray[12][1][1] = (7 - 3*sqrt(5))/6.0; TwentySevenLineArray[12][1][2] = (-3 + sqrt(5)); TwentySevenLineArray[12][2][1] = 1.0/2.0 - sqrt(5)/6.0 ; TwentySevenLineArray[12][2][2] = sqrt(5); TwentySevenLineArray[12][3][1] = 0; TwentySevenLineArray[12][3][2] = 1; TwentySevenLineArray[13][1][1] = (1 - sqrt(5))/12.0; TwentySevenLineArray[13][1][2] = (-5 + 3*sqrt(5) )/4.0; TwentySevenLineArray[13][2][1] = (3 + sqrt(5))/12.0; TwentySevenLineArray[13][2][2] = (-3 + sqrt(5))/4.0; TwentySevenLineArray[13][3][1] = 0; TwentySevenLineArray[13][3][2] = 1; TwentySevenLineArray[14][1][1] = (3 - sqrt(5))/12.0 ; TwentySevenLineArray[14][1][2] = -(3 + sqrt(5))/4.0; TwentySevenLineArray[14][2][1] = (1 + sqrt(5))/12.0; TwentySevenLineArray[14][2][2] = -(5 + 3*sqrt(5))/4.0; TwentySevenLineArray[14][3][1] = 0; TwentySevenLineArray[14][3][2] = 1; TwentySevenLineArray[15][1][1] = 1.0/2.0 - sqrt(5)/6.0 ; TwentySevenLineArray[15][1][2] = sqrt(5); TwentySevenLineArray[15][2][1] = (7 - 3*sqrt(5))/6.0; TwentySevenLineArray[15][2][2] = -3 + sqrt(5); TwentySevenLineArray[15][3][1] = 0; TwentySevenLineArray[15][3][2] = 1; TwentySevenLineArray[16][1][1] = 1.0/6.0 - 1/(6*sqrt(5)); TwentySevenLineArray[16][1][2] = 1 - 3.0/sqrt(5); TwentySevenLineArray[16][2][1] = 1.0/6.0 - sqrt(5)/10; TwentySevenLineArray[16][2][2] = sqrt(5)/5.0; TwentySevenLineArray[16][3][1] = 0; TwentySevenLineArray[16][3][2] = 1; TwentySevenLineArray[17][1][1] = (1 + sqrt(5))/12.0; TwentySevenLineArray[17][1][2] = -(5 + 3*sqrt(5))/4.0; TwentySevenLineArray[17][2][1] = (3-sqrt(5))/12.0; TwentySevenLineArray[17][2][2] = -(3+sqrt(5))/4.0; TwentySevenLineArray[17][3][1] = 0; TwentySevenLineArray[17][3][2] = 1; TwentySevenLineArray[18][1][1] = (3.0 + sqrt(5))/12.0; TwentySevenLineArray[18][1][2] = (-3+sqrt(5))/4.0; TwentySevenLineArray[18][2][1] = (1-sqrt(5))/12.0; TwentySevenLineArray[18][2][2] = (-5+3*sqrt(5))/4.0; TwentySevenLineArray[18][3][1] = 0; TwentySevenLineArray[18][3][2] = 1; TwentySevenLineArray[19][1][1] = (3+sqrt(5))/6.0; TwentySevenLineArray[19][1][2] = -sqrt(5); TwentySevenLineArray[19][2][1] = (7+3*sqrt(5))/6.0; TwentySevenLineArray[19][2][2] = -(3+sqrt(5)); TwentySevenLineArray[19][3][1] = 0; TwentySevenLineArray[19][3][2] = 1; TwentySevenLineArray[20][1][1] = (5+sqrt(5))/30.0; TwentySevenLineArray[20][1][2] = 1+3/sqrt(5); TwentySevenLineArray[20][2][1] = 5+3*sqrt(5) ; TwentySevenLineArray[20][2][2] = -sqrt(5)/5.0; TwentySevenLineArray[20][3][1] = 0; TwentySevenLineArray[20][3][2] = 1; TwentySevenLineArray[21][1][1] = 1.0/6.0+sqrt(5)/10.0; TwentySevenLineArray[21][1][2] = -sqrt(5)/5; TwentySevenLineArray[21][2][1] = (5+sqrt(5))/30.0; TwentySevenLineArray[21][2][2] = 1+3.0/sqrt(5); TwentySevenLineArray[21][3][1] = 0; TwentySevenLineArray[21][3][2] = 1; TwentySevenLineArray[22][1][1] = (7 + 3*sqrt(5))/6.0; TwentySevenLineArray[22][1][2] = -(3 + sqrt(5)); TwentySevenLineArray[22][2][1] = (3 + sqrt(5))/6.0; TwentySevenLineArray[22][2][2] = -sqrt(5); TwentySevenLineArray[22][3][1] = 0; TwentySevenLineArray[22][3][2] = 1; TwentySevenLineArray[23][1][1] = -1.0/3.0; TwentySevenLineArray[23][1][2] = 3; TwentySevenLineArray[23][2][1] = 0; TwentySevenLineArray[23][2][2] = 1; TwentySevenLineArray[23][3][1] = 0; TwentySevenLineArray[23][3][2] = 0; TwentySevenLineArray[24][1][1] = 0; TwentySevenLineArray[24][1][2] = -1; TwentySevenLineArray[24][2][1] = 0; TwentySevenLineArray[24][2][2] = 1; TwentySevenLineArray[24][3][1] = -1.0/3.0; TwentySevenLineArray[24][3][2] = 0; TwentySevenLineArray[25][1][1] = 1.0/9.0; TwentySevenLineArray[25][1][2] = 1.0/3.0; TwentySevenLineArray[25][2][1] = 0; TwentySevenLineArray[25][2][2] = 1; TwentySevenLineArray[25][3][1] = 0; TwentySevenLineArray[25][3][2] = 0; TwentySevenLineArray[26][1][1] = 1.0/3.0; TwentySevenLineArray[26][1][2] = -1; TwentySevenLineArray[26][2][1] = 0; TwentySevenLineArray[26][2][2] = 1; TwentySevenLineArray[26][3][1] = 0; TwentySevenLineArray[26][3][2] = 0; TwentySevenLineArray[27][1][1] = 2.0/3.0; TwentySevenLineArray[27][1][2] = -1; TwentySevenLineArray[27][2][1] = 0; TwentySevenLineArray[27][2][2] = 1; TwentySevenLineArray[27][3][1] = 1.0/3.0; TwentySevenLineArray[27][3][2] = 0; } }