/* 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 vmm3d.surface.parametric;
import java.awt.Color;
import vmm3d.core.Complex;
import vmm3d.core.I18n;
import vmm3d.core.IntegerParam;
import vmm3d.core.Parameter;
import vmm3d.core.RealParamAnimateable;
import vmm3d.core.View;
import vmm3d.core3D.ComplexVector3D;
import vmm3d.core3D.GridTransformMatrix;
import vmm3d.core3D.Vector3D;
import vmm3d.core3D.View3DLit;
import vmm3d.surface.SurfaceView;
public class SchoenGyroid extends WeierstrassMinimalSurface {
//private RealParamAnimateable aa = new RealParamAnimateable("vmm3d.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);
}
}
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