/* 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.parametric; import java.awt.Color; import vmm.core.Complex; import vmm.core.I18n; import vmm.core.IntegerParam; import vmm.core.Parameter; import vmm.core.RealParamAnimateable; import vmm.core.View; import vmm.core3D.ComplexVector3D; import vmm.core3D.GridTransformMatrix; import vmm.core3D.Vector3D; import vmm.core3D.View3DLit; import vmm.surface.SurfaceView; public class SchoenGyroid extends WeierstrassMinimalSurface { //private RealParamAnimateable aa = new RealParamAnimateable("vmm.surface.parametric.SchwarzPDsurface.aa",0.2,0.48,0.02); public SchoenGyroid() { super(); setDefaultOrientation(View3DLit.NORMAL_ORIENTATION); setDefaultViewUp(new Vector3D(-0.01, 0.69, 0.72)); setDefaultViewpoint(new Vector3D(-25, -32, 29)); setDefaultWindow(-3,3,-2.8,2.2); uPatchCount.setValueAndDefault(12); vPatchCount.setValueAndDefault(12); umin.reset(0.005); umax.reset(0.997); vmin.reset(0.0); vmax.reset(1.0); removeParameter(vmin); removeParameter(vmax); removeParameter(umin); removeParameter(umax); afp.setValue(0.5777/2.0*Math.PI); iFirstInHelper = false; // change the next two booleans for testing (or later for education) wantsToSeeDomain = false; wantsToSeeGaussImage = false; if (wantsToSeeGaussImage) wantsToSeeDomain = true; if (wantsToSeeDomain) {setDefaultViewUp(new Vector3D(0,0,1)); setDefaultViewpoint(new Vector3D(0,0,40));} multipleCopyOptions = new int[] {2}; // canShowConjugateSurface = true; } public View getDefaultView() { //SurfaceView view = (SurfaceView)super.getDefaultView(); // its actually a WMSView WMSView view = new WMSView(); view.setGridSpacing(12); float c0 = (float)0.25; //view.getLightSettings().setLight0(new Color(c0,c0,c0)); view.getLightSettings().setAmbientLight(new Color(c0,c0,c0)); //view.getLightSettings().getDirectionalLight2().setItsColor(new Color((float)0.5,(float)1.0,(float)0.0)); //view.getLightSettings().getDirectionalLight2().setItsDirection (new Vector3D(0.66,-0.34,-0.66)); view.getLightSettings ().setSpecularExponent(95); view.getLightSettings().setSpecularRatio( (float)0.8 ); return view; } private double Phi1,Phi2,rp1,RP2,r1_,R2_,scale; private Vector3D trans, transX, transY, transZ; private Vector3D N_6, N_2, N5_6, surf_6, surf_2, surf5_6, trans_6, trans_2, trans5_6; private GridTransformMatrix m_6, m_2, m5_6; protected void createData() { super.createData(); // helperArray created, flag0 & flag05 are set computePeriodData(); data.discardGridTransforms(); GridTransformMatrix[] trList = new GridTransformMatrix[80]; trList[0] = new GridTransformMatrix(); GridTransformMatrix a = new GridTransformMatrix(); trList[1] = new GridTransformMatrix().scale(-1,-1,-1).reverse(); if (!wantsToSeeDomain) { data.addGridTransform(trList[1]); a = new GridTransformMatrix().scale(-1,-1,1); trans = new Vector3D(transZ.x, transZ.y, 0); trList[2] = new GridTransformMatrix(trList[0]).leftMultiplyBy(a).translate(trans); trList[3] = new GridTransformMatrix(trList[1]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[2]); data.addGridTransform(trList[3]); trans = new Vector3D(-transZ.x, -transZ.y, 0); trList[4] = new GridTransformMatrix(trList[0]).leftMultiplyBy(a).translate(trans); trList[5] = new GridTransformMatrix(trList[1]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[4]); data.addGridTransform(trList[5]); a = new GridTransformMatrix().scale(-1,1,-1); trans = new Vector3D(transY.x, 0, transY.z); trList[6] = new GridTransformMatrix(trList[0]).leftMultiplyBy(a).translate(trans); trList[7] = new GridTransformMatrix(trList[1]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[6]); data.addGridTransform(trList[7]); trans = new Vector3D(-transY.x, 0, -transY.z); trList[8] = new GridTransformMatrix(trList[0]).leftMultiplyBy(a).translate(trans); trList[9] = new GridTransformMatrix(trList[1]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[8]); data.addGridTransform(trList[9]); a = new GridTransformMatrix().scale(1,-1,-1); trans = new Vector3D(0, transX.y, transX.z); trList[10] = new GridTransformMatrix(trList[0]).leftMultiplyBy(a).translate(trans); trList[11] = new GridTransformMatrix(trList[1]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[10]); data.addGridTransform(trList[11]); trans = new Vector3D(0, -transX.y, -transX.z); trList[12] = new GridTransformMatrix(trList[0]).leftMultiplyBy(a).translate(trans); trList[13] = new GridTransformMatrix(trList[1]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[12]); data.addGridTransform(trList[13]); trList[14] = new GridTransformMatrix(trList[0]).leftMultiplyBy(m_6).translate(trans_6); trList[15] = new GridTransformMatrix(trList[1]).leftMultiplyBy(m_6).translate(trans_6); data.addGridTransform(trList[14]); data.addGridTransform(trList[15]); trans = new Vector3D(trans_6.negated()); trList[16] = new GridTransformMatrix(trList[0]).leftMultiplyBy(m_6).translate(trans); trList[17] = new GridTransformMatrix(trList[1]).leftMultiplyBy(m_6).translate(trans); data.addGridTransform(trList[16]); data.addGridTransform(trList[17]); trList[18] = new GridTransformMatrix(trList[0]).leftMultiplyBy(m_2).translate(trans_2); trList[19] = new GridTransformMatrix(trList[1]).leftMultiplyBy(m_2).translate(trans_2); data.addGridTransform(trList[18]); data.addGridTransform(trList[19]); trans = new Vector3D(trans_2.negated()); trList[20] = new GridTransformMatrix(trList[0]).leftMultiplyBy(m_2).translate(trans); trList[21] = new GridTransformMatrix(trList[1]).leftMultiplyBy(m_2).translate(trans); data.addGridTransform(trList[20]); data.addGridTransform(trList[21]); trList[22] = new GridTransformMatrix(trList[0]).leftMultiplyBy(m5_6).translate(trans5_6); trList[23] = new GridTransformMatrix(trList[1]).leftMultiplyBy(m5_6).translate(trans5_6); data.addGridTransform(trList[22]); data.addGridTransform(trList[23]); trans = new Vector3D(trans5_6.negated()); trList[24] = new GridTransformMatrix(trList[0]).leftMultiplyBy(m5_6).translate(trans); trList[25] = new GridTransformMatrix(trList[1]).leftMultiplyBy(m5_6).translate(trans); data.addGridTransform(trList[24]); data.addGridTransform(trList[25]); if (getNumberOfPieces()==2) { trans = new Vector3D(trans_2.negated()); trList[26] = new GridTransformMatrix(trList[12]).leftMultiplyBy(m_2).translate(trans); trList[27] = new GridTransformMatrix(trList[13]).leftMultiplyBy(m_2).translate(trans); data.addGridTransform(trList[26]); data.addGridTransform(trList[27]); trList[28] = new GridTransformMatrix(trList[2]).leftMultiplyBy(m_6).translate(trans_6); trList[29] = new GridTransformMatrix(trList[3]).leftMultiplyBy(m_6).translate(trans_6); // trans = new Vector3D(trans_2.negated()); data.addGridTransform(trList[28]);// data.addGridTransform(trList[29]); trList[30] = new GridTransformMatrix(trList[6]).leftMultiplyBy(m5_6).translate(trans5_6); trList[31] = new GridTransformMatrix(trList[7]).leftMultiplyBy(m5_6).translate(trans5_6); data.addGridTransform(trList[30]);// data.addGridTransform(trList[31]); trList[32] = new GridTransformMatrix(trList[6]).leftMultiplyBy(m_6).translate(trans_6); trList[33] = new GridTransformMatrix(trList[7]).leftMultiplyBy(m_6).translate(trans_6); data.addGridTransform(trList[32]);// data.addGridTransform(trList[33]); trList[34] = new GridTransformMatrix(trList[4]).leftMultiplyBy(m_2).translate(trans_2); trList[35] = new GridTransformMatrix(trList[5]).leftMultiplyBy(m_2).translate(trans_2); data.addGridTransform(trList[34]); data.addGridTransform(trList[35]); // The following pieces stick out as flags: // //trList[26] = new GridTransformMatrix(trList[4]).leftMultiplyBy(m_6).translate(trans); // //trList[27] = new GridTransformMatrix(trList[5]).leftMultiplyBy(m_6).translate(trans_6); // //trList[26] = new GridTransformMatrix(trList[2]).leftMultiplyBy(m5_6).translate(trans); // //trList[27] = new GridTransformMatrix(trList[3]).leftMultiplyBy(m5_6).translate(trans5_6); //trList[26] = new GridTransformMatrix(trList[2]).leftMultiplyBy(m_2).translate(trans); //trList[27] = new GridTransformMatrix(trList[3]).leftMultiplyBy(m_2).translate(trans_2); //trList[26] = new GridTransformMatrix(trList[6]).leftMultiplyBy(m_2).translate(trans); //trList[27] = new GridTransformMatrix(trList[7]).leftMultiplyBy(m_2).translate(trans_2); //trList[36] = new GridTransformMatrix(trList[4]).leftMultiplyBy(m5_6).translate(trans); //trList[37] = new GridTransformMatrix(trList[5]).leftMultiplyBy(m5_6).translate(trans5_6); //data.addGridTransform(trList[36]); //data.addGridTransform(trList[37]); } // if (getNumberOfPieces()==2) /* a = new GridTransformMatrix().scale(-1,-1,-1); trans = new Vector3D(0, 0, 0); for (int e=0; e < 38; e++){ trList[38+e] = new GridTransformMatrix(trList[e]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[38+e]); } */ if (!inAssociateMorph) { } // if (!inAssociateMorph) } // (!wantsToSeeDomain) } public static double paramRescale(double x){ double y; y = Math.sin(Math.PI/2*x); return y*y; } // override the default Cartesian Grid protected Complex domainGrid(double u, double v){ double ph = 0; Complex z; double r = Math.sin(Math.PI/2*u); if (v <= 1.0/3.0) ph = -Math.PI + Phi1*paramRescale(3*v); else if ((v > 1.0/3.0)&&(v <= 2.0/3.0)) ph = -Math.PI + Phi1 + (Phi2-Phi1)*paramRescale(3*v-1); else if (v > 2.0/3.0) ph = -Math.PI + Phi2 + (Math.PI-Phi2)*paramRescale(3*v-2); z = new Complex(r*Math.cos(ph), r*Math.sin(ph)); if (wantsToSeeGaussImage) z = gauss(z); return z; } /** * The following two functions are the Weierstrass data that * define this surface. It is best shown on the above domainGrid. */ protected Complex gauss(Complex z) { Complex z2 = z.times(z); Complex z2_ = new Complex(1-z2.re, -z2.im); z2.re = 1 + z2.re; Complex w = z2_.inverse().times(z2); double x = -2*w.im - r1_; w.im = 2*w.re; w.re = x; Complex aux = w.times(-2/(R2_ - r1_)); aux.re = -aux.re -1; aux.im = -aux.im; Complex aux2 = aux.times(aux); aux2.re = aux2.re - 1; // The next two lines are crucial, they achieve an analytic continuation: Complex g2 = (aux2.squareRootNearer(aux)).minus(aux); return g2.squareRootNearer(I1_C); } protected Complex hPrime(Complex z) { // return g^2 / ((z^2-1)*(g^4-1)) Complex z2 = z.times(z); z2.re = z2.re - 1; Complex w = gauss(z); Complex g2 = w.times(w); Complex g4 = g2.times(g2); g4.re = g4.re - 1; g4.assignTimes(z2); w = (g4.inverse()).times(g2); w.assignTimes(scale); return w; } protected void redoConstants(){ // global variables independent of the points, hence thread safe super.redoConstants(); AFP = afp.getValue(); Phi1 = Math.PI/3.0; Phi2 = Math.PI*2.0/3.0; rp1 = Math.tan(Phi1/2.0); RP2 = Math.tan(Phi2/2.0); r1_ = rp1 - 1.0/rp1; R2_ = RP2 - 1.0/RP2; scale= 1.0; } /** * We want to center the surface (one hexagon) already at the helper Level. */ protected ComplexVector3D getCenter(){ ComplexVector3D gC = new ComplexVector3D(helperArray[0][0]); gC = (gC.plus(helperArray[0][vcount-1])).times(0.5); return gC; } public void computePeriodData(){ ComplexVector3D aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(0)])); transZ = aux.re().times(2*Math.cos(AFP)).plus(aux.im().times(2*Math.sin(AFP))); aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount*1.0/3.0)])); transX = aux.re().times(2*Math.cos(AFP)).plus(aux.im().times(2*Math.sin(AFP))); aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount*2.0/3.0)])); transY = aux.re().times(2*Math.cos(AFP)).plus(aux.im().times(2*Math.sin(AFP))); surf_6 = surfacePoint(umax.getValue(),1.0/6.0); N_6 = surfaceNormal(umax.getValue(),1.0/6.0); double sc = surf_6.dot(N_6); trans_6 = surf_6.linComb(2,-2*sc, N_6); m_6 = GridTransformMatrix.SetGridTransformMatrix(0,0,1,0, 0,1,0,0, 1,0,0,0, true); surf_2 = surfacePoint(umax.getValue(),1.0/2.0); N_2 = surfaceNormal(umax.getValue(),1.0/2.0); sc = surf_2.dot(N_2); trans_2 = surf_2.linComb(2,-2*sc, N_2); m_2 = GridTransformMatrix.SetGridTransformMatrix(0,-1,0,0, -1,0,0,0, 0,0,1,0, true); surf5_6 = surfacePoint(umax.getValue(),5.0/6.0); N5_6 = surfaceNormal(umax.getValue(),5.0/6.0); sc = surf5_6.dot(N5_6); trans5_6 = surf5_6.linComb(2,-2*sc, N5_6); m5_6 = GridTransformMatrix.SetGridTransformMatrix(1,0,0,0, 0,0,1,0, 0,1,0,0, true); //System.out.println(N5_6.x);System.out.println(N5_6.y);System.out.println(N5_6.z); //System.out.println(surf5_6.x);System.out.println(surf5_6.y);System.out.println(surf5_6.z); } }