/* 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 SchwarzPDsurface extends WeierstrassMinimalSurface { private RealParamAnimateable aa = new RealParamAnimateable("vmm.surface.parametric.SchwarzPDsurface.aa",0.2,0.48,0.02); private RealParamAnimateable bb = new RealParamAnimateable("vmm.surface.parametric.SchwarzPDsurface.bb",0.6,0.52,0.98); //ComplexVector3D[][] integrationGrid; //boolean needsIntegrationGrid = true; public SchwarzPDsurface() { super(); addParameter(bb); bb.setMaximumValueForInput(0.99); // if one wants to morph that far, increase resolution bb.setMinimumValueForInput(0.05); addParameter(aa); aa.setMaximumValueForInput(0.95); // if one wants to morph that far, increase resolution aa.setMinimumValueForInput(0.02); setDefaultOrientation(View3DLit.REVERSE_ORIENTATION); setDefaultViewUp(new Vector3D(-0.045, 0.4, 0.915)); setDefaultViewpoint(new Vector3D(12, -44, 20)); setDefaultWindow(-3,3,-2.8,2.2); uPatchCount.setValueAndDefault(12); vPatchCount.setValueAndDefault(12); umin.reset(0.005); umax.reset(0.995); vmin.reset(0.0); vmax.reset(1.0); removeParameter(vmin); removeParameter(vmax); removeParameter(umin); removeParameter(umax); //afp.setValue(Math.PI/2); 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)0.2; //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(100); view.getLightSettings().setSpecularRatio( (float)0.8 ); return view; } private int um,vm; private double Phi1,Phi2,rp1,RP2,r1_,R2_,scale; private Complex xWidth, yWidth, zWidth; private Vector3D centerRE, centerRE_, centerIM, trans; protected void createData() { super.createData(); // helperArray created, flag0 & flag05 are set computePeriodData(); data.discardGridTransforms(); GridTransformMatrix[] trList = new GridTransformMatrix[64]; trList[0] = new GridTransformMatrix(); GridTransformMatrix a = new GridTransformMatrix(); trList[1] = new GridTransformMatrix().scale(-1,-1,-1).reverse(); if (!wantsToSeeDomain) { data.addGridTransform(trList[1]); if (!inAssociateMorph) { if (flag0){ a = new GridTransformMatrix().scale(-1,-1,1); trans = new Vector3D(centerRE.x, centerRE.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]); a = new GridTransformMatrix().scale(1,-1,-1); trans = new Vector3D(0, centerRE.y, centerRE.z); for (int e=0; e < 4; e++){ trList[4+e] = new GridTransformMatrix(trList[e]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[4+e]); } a = new GridTransformMatrix().scale(-1,-1,-1); //.reverse(); for (int e=0; e < 8; e++){ trList[8+e] = new GridTransformMatrix(trList[e]).leftMultiplyBy(a).translate(centerRE); data.addGridTransform(trList[8+e]); } trans = new Vector3D(centerRE.x, centerRE.y, -centerRE.z); for (int e=0; e < 4; e++){ trList[16+e] = new GridTransformMatrix(trList[e]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[16+e]); trList[20+e] = new GridTransformMatrix(trList[12+e]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[20+e]); } if (getNumberOfPieces()==2) { trans = new Vector3D(4*xWidth.re,0,0); for (int e=0; e < 24; e++){ trList[24+e] = new GridTransformMatrix(trList[e]).translate(trans); data.addGridTransform(trList[24+e]); } } // if (getNumberOfPieces()==2) } // if (flag0) if (flag05){ a = new GridTransformMatrix().scale(-1,-1,1).reverse(); trans = new Vector3D(centerIM.x, centerIM.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]); a = new GridTransformMatrix().scale(1,-1,-1).reverse(); trans = new Vector3D(0, centerIM.y, centerIM.z); 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(centerIM.x, 0, centerIM.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]); a = new GridTransformMatrix().scale(1,-1,-1).reverse(); trans = new Vector3D(0, -centerIM.y, -centerIM.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]); trans = new Vector3D(2*centerIM.x, 0, 2*centerIM.z); trList[10] = new GridTransformMatrix(trList[8]).translate(trans); trList[11] = new GridTransformMatrix(trList[9]).translate(trans); data.addGridTransform(trList[10]); data.addGridTransform(trList[11]); a = new GridTransformMatrix().scale(-1,1,-1).reverse(); trans = new Vector3D(centerIM.x, 0, -1*centerIM.z); trList[12] = new GridTransformMatrix(trList[8]).leftMultiplyBy(a).translate(trans); trList[13] = new GridTransformMatrix(trList[9]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[12]); data.addGridTransform(trList[13]); trans = new Vector3D(0, -2*centerIM.y, 0); trList[14] = new GridTransformMatrix(trList[0]).translate(trans); trList[15] = new GridTransformMatrix(trList[1]).translate(trans); data.addGridTransform(trList[14]); data.addGridTransform(trList[15]); if (getNumberOfPieces()==2) { a = new GridTransformMatrix().scale(-1,-1,1).reverse(); trans = new Vector3D(-centerIM.x, -centerIM.y, 0); for (int e=0; e < 16; e++){ trList[16+e] = new GridTransformMatrix(trList[e]).leftMultiplyBy(a).translate(trans); data.addGridTransform(trList[16+e]); } } // if (getNumberOfPieces()==2) } // if (flag05) } // 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; } // Index of grid point closest to branch value P. jP is the larger of the two branch point indices. /* protected void p_Index(){ jP = (int) Math.floor((PL-vmin.getValue())/(vmax.getValue()-vmin.getValue())*(vcount-1)); } */ /** * 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(); Phi1 = Math.PI*aa.getValue(); Phi2 = Math.PI*bb.getValue(); rp1 = Math.tan(Phi1/2.0); RP2 = Math.tan(Phi2/2.0); r1_ = rp1 - 1.0/rp1; R2_ = RP2 - 1.0/RP2; scale= Math.sqrt(Math.sqrt((0.1+aa.getValue()) * (1.1 - bb.getValue()) ) /(bb.getValue() - aa.getValue()) ); um = 1;//(int) Math.floor((ucount-1)); vm = 1;//(int) Math.floor(vcount/2); } /** * 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(){ if (flag0) { ComplexVector3D aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount*5/6)])); xWidth = aux.x; aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount/2)])); zWidth = aux.z; aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount/6)])); yWidth = aux.y; centerRE = new Vector3D(-2*xWidth.re, -2*yWidth.re, -2*zWidth.re); centerRE_ = new Vector3D(2*xWidth.re, 2*yWidth.re, 2*zWidth.re); } if (flag05) { ComplexVector3D aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount*5/6)])); zWidth = aux.z; aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount/2)])); yWidth = aux.y; aux = new ComplexVector3D(helperToMinimal(helperArray[ucount-1][(int)Math.floor(vcount/6)])); xWidth = aux.x; centerIM = new Vector3D(2*xWidth.im, 2*yWidth.im, 2*zWidth.im); } //System.out.println(centerRE.z); } /** * Override to close the hole around the images of P, -1/P. */ /* public Vector3D surfacePoint(double u, double v) { ComplexVector3D eW,auxW; int i = (int) Math.floor(0.25 + (u-umin.getValue())/du ); int j = (int) Math.floor(0.25 + (v-vmin.getValue())/dv ); //Complex zInitial = domainGrid(umin.getValue() + i*du, vmin.getValue() + j*dv); //Complex z = domainGrid(u,v); if ((!inAssociateMorph)&&(i==ucount-1)&&(j==jP)) eW = new ComplexVector3D(ComplexVector3D.ORIGIN); else if ((!inAssociateMorph)&&(i==ucount-1)&&(j==vcount-1-jP)) { eW = new ComplexVector3D(halfPeriod); } else { auxW = new ComplexVector3D(helperArray[i][j].plus( ComplexVectorOneStepIntegrator(domainGrid(umin.getValue() + i*du, vmin.getValue() + j*dv), domainGrid(u,v)) )); eW = new ComplexVector3D(auxW.y.minus(auxW.x), (auxW.y.plus(auxW.x)).times(I_C), auxW.z ); if ((!inAssociateMorph)&&(flag0)) { if ((i==ucount-1)&&(j <= jP)&&(j >= vcount-1-jP)) eW.z.assign(ZERO_C); if ((i==ucount-1)&&(j > jP)) {eW.assign(ZERO_C, ZERO_C, eW.z); } if ((i==ucount-1)&&(j < vcount-1-jP)) { eW.assign(halfPeriod.x, halfPeriod.y, eW.z); } } } if (wantsToSeeDomain) return new Vector3D(eW.z.re, eW.z.im, 0); else if (AFP==0) return eW.re(); else return (eW.re().times(Math.cos(AFP))).plus((eW.im().times(Math.sin(AFP)))); } */ }