matching tilts with affines (6f3b31c5) · Commits · Elphel / imagej-elphel

src/main/java/com/elphel/imagej/orthomosaic/ERSTiltLMA.java

+74 −7

Original line number	Original line	Diff line number	Diff line
	@@ -54,10 +54,13 @@ public class ERSTiltLMA {
	private double [] last_ymfx = null;		private double [] last_ymfx = null;
	private double [][] last_jt = null;		private double [][] last_jt = null;

	public double [][][] aff_pairs_nosr = null;		public double [][][] aff_pairs_inosr = null; // inverted pairs affines w/o scale and rotation
	public double [][][][] aff_tilts = null;		public double [][][][] aff_tilts = null;
	public boolean invert_q2a = false;		public boolean invert_q2a = false;
	// debug		// debug
			public double [][][] aff_pairs = null; // pairwise image-based affines
			public double [][] diff_tilts = null; // pairwise differential tilts

	public boolean last3only = false; // true; // debug feature		public boolean last3only = false; // true; // debug feature
	public double scale_pairs = 1e3; // 1e4; // increase fX and derivatives for pairs		public double scale_pairs = 1e3; // 1e4; // increase fX and derivatives for pairs
	public double delta= 1e-7;		public double delta= 1e-7;
	@@ -99,7 +102,16 @@ public class ERSTiltLMA {
	return svd;		return svd;
	}		}

	public void printResults(boolean degrees) {		/**
			* Get differential tilts between the second and the first scenes in each pair
			* @return [pair]{tiltX,tiltY}
			*/
			public double [][] getDiffTilts(){
			return diff_tilts;
			}


			public void printSceneResults(boolean degrees, boolean percents) {
	double [][] pseudo_xy = getPseudoXY();		double [][] pseudo_xy = getPseudoXY();
	double [][][] ers_affines = getERSAffines();		double [][][] ers_affines = getERSAffines();
	SingularValueDecomposition [] svd = getSVD();		SingularValueDecomposition [] svd = getSVD();
	@@ -116,8 +128,59 @@ public class ERSTiltLMA {
	}		}
	return;		return;
	}		}
			public void printPairsResults(boolean degrees, boolean percents) {
			double sd = degrees? 180/Math.PI : 1.0;
			double sp = percents? 100 : 1;
			String svd_title = SingularValueDecomposition.titleString(degrees);
			double [] fx = getFxDerivs(
			parameters_vector, // double [] vector,
			null, // final double [][] jt, // should be null or initialized with [vector.length][]
			0); // final int debug_level)

			String tab_title_rad = String.format(
			"%4s\t%4s\t%4s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%s",
			"#","scn0","scn1","tiltX","tiltY","tilt","tilt-dir","elevation","pair_\u0394w","residual",svd_title);
			String tab_title_deg = String.format(
			"%4s\t%4s\t%4s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%s",
			"#","scn0","scn1","tiltX","tiltY","tilt","tilt-dir\u00B0","elevation\u00B0","pair_\u0394w","residual",svd_title);
			String tab_title_rad_perc = String.format(
			"%4s\t%4s\t%4s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%s",
			"#","scn0","scn1","tiltX%","tiltY%","tilt%","tilt-dir","elevation","pair_\u0394w%","residual%",svd_title);
			String tab_title_deg_perc = String.format(
			"%4s\t%4s\t%4s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%11s\t%s",
			"#","scn0","scn1","tiltX%","tiltY%","tilt%","tilt-dir\u00B0","elevation\u00B0","pair_\u0394w%","residual%",svd_title);
			String title =degrees ? (percents?tab_title_deg_perc:tab_title_deg) : (percents?tab_title_rad_perc:tab_title_rad);

			String fmt_rad= "%4d\t%4d\t%4d\t%11.8f\t%11.8f\t%11.8f\t%11.8f\t%11.8f\t%11.8f\t%11.8f\t%s";
			String fmt_deg= "%4d\t%4d\t%4d\t%11.8f\t%11.8f\t%11.8f\t%11.6f\t%11.6f\t%11.8f\t%11.8f\t%s";
			String fmt_rad_perc="%4d\t%4d\t%4d\t%11.6f%%\t%11.6f%%\t%11.6f%%\t%11.8f\t%11.8f\t%11.6f%%\t%11.6f%%\t%s";
			String fmt_deg_perc="%4d\t%4d\t%4d\t%11.6f%%\t%11.6f%%\t%11.6f%%\t%11.6f\t%11.6f\t%11.6f%%\t%11.6f%%\t%s";
			String fmt =degrees ? (percents?fmt_deg_perc:fmt_deg) : (percents?fmt_rad_perc:fmt_rad);

			System.out.println(title);

			double [] fit_err = new double [num_pairs];
			for (int npair=0; npair < num_pairs; npair++) {
			int [] pscenes = {indices[cpairs[npair][0]], indices[cpairs[npair][1]]};
			double [] dtilt_xy = diff_tilts[npair];
			double dtilt = Math.sqrt(dtilt_xy[0]dtilt_xy[0]+dtilt_xy[1]dtilt_xy[1]);
			double tilt_dir = Math.atan2(dtilt_xy[1],dtilt_xy[0]);
			double tilt_ang = Math.atan(dtilt);
			double [][] aff_pair = aff_pairs[npair]; // image-based affine for a pair
			SingularValueDecomposition svd_aff_pair = SingularValueDecomposition.singularValueDecompose(aff_pair);
			// just to see - which is zeroed - beta or gamma? gamma changes, beta stays
			String ssvd = svd_aff_pair.toString(degrees, 1);
			double pair_dw = svd_aff_pair.getDW();
			fit_err[npair] = fx[npair] / scale_pairs; // dW -> %
			System.out.println(String.format(fmt,
			npair, pscenes[0], pscenes[1], spdtilt_xy[0], spdtilt_xy[1], spdtilt, sdtilt_dir, sd*tilt_ang,
			sppair_dw, spfit_err[npair], ssvd));


			}
			return;

			}

	/*		/*
	* Starting with tilts0 and tilt1 = tilt0+tilt_diff (differential		* Starting with tilts0 and tilt1 = tilt0+tilt_diff (differential
	@@ -155,9 +218,13 @@ public class ERSTiltLMA {
	this.cpairs = cpairs;		this.cpairs = cpairs;
	num_scenes = indices.length;		num_scenes = indices.length;
	num_pairs = cpairs.length;		num_pairs = cpairs.length;
	aff_pairs_nosr = new double [num_pairs][][];		aff_pairs = new double [num_pairs][][]; // preserving for stats, not used in processing
			diff_tilts= new double [num_pairs][];
			aff_pairs_inosr = new double [num_pairs][][];
	aff_tilts = new double [num_pairs][2][][];		aff_tilts = new double [num_pairs][2][][];
	for (int npair = 0; npair < num_pairs; npair++) {		for (int npair = 0; npair < num_pairs; npair++) {
			aff_pairs[npair] = affine_pairs[npair]; // preserving for stats
			diff_tilts[npair] = new double [] {tilts[npair][1][0]-tilts[npair][0][0],tilts[npair][1][1]-tilts[npair][0][1]};
	double [][] affine_pair_nors = SingularValueDecomposition.removeTiltRotScale(		double [][] affine_pair_nors = SingularValueDecomposition.removeTiltRotScale(
	affine_pairs[npair], // double [][] A,		affine_pairs[npair], // double [][] A,
	false, // boolean removeTilt,		false, // boolean removeTilt,
	@@ -165,7 +232,7 @@ public class ERSTiltLMA {
	true, // boolean removeScale,		true, // boolean removeScale,
	false, // boolean removeOffset,		false, // boolean removeOffset,
	false); // boolean max_is_scale);		false); // boolean max_is_scale);
	aff_pairs_nosr[npair] = QuatUtils.matInverse2x2(affine_pair_nors); // maybe reverse order and do not use inversion?		aff_pairs_inosr[npair] = QuatUtils.matInverse2x2(affine_pair_nors); // maybe reverse order and do not use inversion?
	for (int i = 0; i < 2; i++) {		for (int i = 0; i < 2; i++) {
	aff_tilts[npair][i] = QuatUtils.tiltToAffine( // convert tilts to affines as they will not be modified later		aff_tilts[npair][i] = QuatUtils.tiltToAffine( // convert tilts to affines as they will not be modified later
	tilts[npair][i]); // double [] tilt,		tilts[npair][i]); // double [] tilt,
	@@ -223,7 +290,7 @@ public class ERSTiltLMA {
	double [][][] aff_err = QuatUtils.pseudoAffineDiffAndDerivatives( //affineDiffAndDerivatives(		double [][][] aff_err = QuatUtils.pseudoAffineDiffAndDerivatives( //affineDiffAndDerivatives(
	pseudo_xy, // double [][] txy, // [scene][direction]		pseudo_xy, // double [][] txy, // [scene][direction]
	aff_tilts[npair], // double [][][] a_tilts,		aff_tilts[npair], // double [][][] a_tilts,
	aff_pairs_nosr[npair], // double [][] iaff_pair, // affine pair inversed		aff_pairs_inosr[npair], // double [][] iaff_pair, // affine pair inversed
	invert_q2a); // boolean invert_q2a) // invert result affines (to match "usual")		invert_q2a); // boolean invert_q2a) // invert result affines (to match "usual")
	if (jt == null) {		if (jt == null) {
	aff_err = new double [][][] {aff_err[0]}; //		aff_err = new double [][][] {aff_err[0]}; //
	@@ -248,7 +315,7 @@ public class ERSTiltLMA {
	for (int ithread = 0; ithread < threads.length; ithread++) {		for (int ithread = 0; ithread < threads.length; ithread++) {
	threads[ithread] = new Thread() {		threads[ithread] = new Thread() {
	public void run() {		public void run() {
	for (int nscene = ai.getAndIncrement(); nscene < num_pairs; nscene = ai.getAndIncrement()) {		for (int nscene = ai.getAndIncrement(); nscene < num_scenes; nscene = ai.getAndIncrement()) {
	int pindx = num_pairs + 2*nscene;		int pindx = num_pairs + 2*nscene;
	for (int j = 0; j < 2; j++) {		for (int j = 0; j < 2; j++) {
	fX[pindx+j] = vector[2*nscene + j];		fX[pindx+j] = vector[2*nscene + j];

src/main/java/com/elphel/imagej/orthomosaic/OrthoAltitudeMatch.java

+7 −2

Original line number	Original line	Diff line number	Diff line
	@@ -61,6 +61,8 @@ public class OrthoAltitudeMatch {
	boolean test_quat0 = false;		boolean test_quat0 = false;
	boolean test_quat2= false; // true;		boolean test_quat2= false; // true;
	boolean use_degrees = true;		boolean use_degrees = true;
			boolean use_percents = true;

	boolean debug_tilts = true;		boolean debug_tilts = true;

	boolean invert_order= false; // print them		boolean invert_order= false; // print them
	@@ -160,6 +162,7 @@ public class OrthoAltitudeMatch {
	int [] ipair = {indices[cpair[0]], indices[cpair[1]]};		int [] ipair = {indices[cpair[0]], indices[cpair[1]]};
	if (updateStatus) {		if (updateStatus) {
	IJ.showStatus("Processing pair "+npair+" of "+condensed_pairs.length+" "+ipair[0]+"->"+ipair[1]);		IJ.showStatus("Processing pair "+npair+" of "+condensed_pairs.length+" "+ipair[0]+"->"+ipair[1]);
			IJ.showProgress(1.0*npair/condensed_pairs.length-1);
	}		}
	PairwiseOrthoMatch pairwiseOrthoMatch = ortho_maps[ipair[0]].getMatch(ortho_maps[ipair[1]].getName(), true); // ?		PairwiseOrthoMatch pairwiseOrthoMatch = ortho_maps[ipair[0]].getMatch(ortho_maps[ipair[1]].getName(), true); // ?
	if (pairwiseOrthoMatch == null) {		if (pairwiseOrthoMatch == null) {
	@@ -914,7 +917,9 @@ public class OrthoAltitudeMatch {
	System.out.println("LMA -> "+lma_rslt);		System.out.println("LMA -> "+lma_rslt);
	if (lma_rslt >= 0) {		if (lma_rslt >= 0) {
	if (debugLevel > -3) {		if (debugLevel > -3) {
	ersTiltLMA.printResults(use_degrees);		ersTiltLMA.printSceneResults(use_degrees, use_percents);

			ersTiltLMA.printPairsResults(use_degrees, use_percents);
	}		}
	}		}
	System.out.println();		System.out.println();
	@@ -924,7 +929,7 @@ public class OrthoAltitudeMatch {
	QuatUtils.testPseudoAffineDiffAndDerivatives(		QuatUtils.testPseudoAffineDiffAndDerivatives(
	pseudo_xy, // double [][] xy, // [scene][direction]		pseudo_xy, // double [][] xy, // [scene][direction]
	ersTiltLMA.aff_tilts[npair], // double [][][] a_tilts,		ersTiltLMA.aff_tilts[npair], // double [][][] a_tilts,
	ersTiltLMA.aff_pairs_nosr[npair], // double [][] iaff_pair, // affine pair inversed		ersTiltLMA.aff_pairs_inosr[npair], // double [][] iaff_pair, // affine pair inversed
	invert_q2a); // boolean invert_q2a){ // invert result affines (to match "usual")		invert_q2a); // boolean invert_q2a){ // invert result affines (to match "usual")
	System.out.println();		System.out.println();
	}		}

src/main/java/com/elphel/imagej/orthomosaic/OrthoMapsCollection.java

+42 −3

Original line number	Original line	Diff line number	Diff line
	@@ -6567,6 +6567,9 @@ public class OrthoMapsCollection implements Serializable{
	boolean flt_show_rms = true; // clt_parameters.imp.flt_show_rms; // true;		boolean flt_show_rms = true; // clt_parameters.imp.flt_show_rms; // true;
	boolean flt_show_zoom = true; // clt_parameters.imp.flt_show_zoom; // true;		boolean flt_show_zoom = true; // clt_parameters.imp.flt_show_zoom; // true;
	boolean flt_show_alt = true; // clt_parameters.imp.flt_show_alt; // true;		boolean flt_show_alt = true; // clt_parameters.imp.flt_show_alt; // true;
			boolean flt_show_svd = true;
			boolean flt_show_degrees = true;


	boolean alt_overwrite = clt_parameters.imp.alt_overwrite; // false; // overwrite existing altitude match pairs		boolean alt_overwrite = clt_parameters.imp.alt_overwrite; // false; // overwrite existing altitude match pairs
	boolean alt_pairwise = clt_parameters.imp.alt_pairwise; // false; // overwrite existing altitude match pairs		boolean alt_pairwise = clt_parameters.imp.alt_pairwise; // false; // overwrite existing altitude match pairs
	@@ -6671,7 +6674,10 @@ public class OrthoMapsCollection implements Serializable{
	flt_show_zoom, // boolean show_zoom,		flt_show_zoom, // boolean show_zoom,
	flt_show_alt, // boolean show_alt,		flt_show_alt, // boolean show_alt,
	use_tab, // boolean use_tab,		use_tab, // boolean use_tab,
	null); // String extra_line)		null, // String extra_line)
			flt_show_svd, // boolean show_svd,
			flt_show_degrees); // boolean use_degrees);

	{		{
	System.out.println("Selected\t"+available_pairs.length+"\tscene pairs for matching");		System.out.println("Selected\t"+available_pairs.length+"\tscene pairs for matching");
	if (use_tab) {		if (use_tab) {
	@@ -6682,6 +6688,10 @@ public class OrthoMapsCollection implements Serializable{
	if (flt_show_zoom) System.out.print(String.format("\t%4s", "Zoom"));		if (flt_show_zoom) System.out.print(String.format("\t%4s", "Zoom"));
	if (flt_show_alt) System.out.print(String.format("\t%7s\t%7s\t%7s", "tiltX","tiltY","offs"));		if (flt_show_alt) System.out.print(String.format("\t%7s\t%7s\t%7s", "tiltX","tiltY","offs"));
	if (flt_show_sfm) System.out.print(String.format("\t%5s\t%5s", "SfM0","SfM1"));		if (flt_show_sfm) System.out.print(String.format("\t%5s\t%5s", "SfM0","SfM1"));
			if (flt_show_svd) {
			String svd_title=SingularValueDecomposition.titleString(flt_show_degrees);
			System.out.print("\t"+ svd_title);
			}
	System.out.println();		System.out.println();
	}		}
	for (int i = 0; i < available_pairs.length; i++) {		for (int i = 0; i < available_pairs.length; i++) {
	@@ -7535,6 +7545,30 @@ public class OrthoMapsCollection implements Serializable{
	boolean show_alt,		boolean show_alt,
	boolean use_tab,		boolean use_tab,
	String extra_line) {		String extra_line) {
			return textPairs (
			plist, // int [][] plist,
			show_names, // boolean show_names,
			show_overlap, // boolean show_overlap,
			show_rms, // boolean show_rms,
			show_zoom, // boolean show_zoom,
			show_alt, // boolean show_alt,
			use_tab, // boolean use_tab,
			extra_line, // String extra_line,
			false, // boolean show_svd,
			false); // boolean use_degrees);

			}
			public String [] textPairs (
			int [][] plist,
			boolean show_names,
			boolean show_overlap,
			boolean show_rms,
			boolean show_zoom,
			boolean show_alt,
			boolean use_tab,
			String extra_line,
			boolean show_svd,
			boolean use_degrees) {
	boolean show_sfm = show_alt;		boolean show_sfm = show_alt;

	// TODO: show SfM of each scene		// TODO: show SfM of each scene
	@@ -7563,6 +7597,11 @@ public class OrthoMapsCollection implements Serializable{
	}		}
	}		}
	if (show_sfm) text_pairs[i] += String.format(use_tab?"\t%5.1f\t%5.1f":" S %5.1f %5.1f", sfm_gain[0],sfm_gain[1]);		if (show_sfm) text_pairs[i] += String.format(use_tab?"\t%5.1f\t%5.1f":" S %5.1f %5.1f", sfm_gain[0],sfm_gain[1]);
			if (show_svd && use_tab && (pairwiseOrthoMatch.getAffine()!=null)) { // now only for tab
			SingularValueDecomposition svd = SingularValueDecomposition.singularValueDecompose(pairwiseOrthoMatch.getAffine());
			String ssvd = svd.toString(use_degrees, 1);
			text_pairs[i] += "\t"+ssvd;
			}
	}		}
	}		}
	if (extra_line !=null) {		if (extra_line !=null) {

src/main/java/com/elphel/imagej/orthomosaic/QuatUtils.java

+36 −13

Original line number	Original line	Diff line number	Diff line
	@@ -1466,13 +1466,36 @@ q11 - q22 = c3
	double [][][] a_tilts,		double [][][] a_tilts,
	double [][] iaff_pair, // affine pair inversed		double [][] iaff_pair, // affine pair inversed
	boolean invert_q2a){ // invert result affines (to match "usual")		boolean invert_q2a){ // invert result affines (to match "usual")
	double delta= 1e-6;		double delta= 1e-8;
			/*
	xy = new double [][] {		xy = new double [][] {
			{xy[0][0]-0.1,xy[0][1]+0.1},
			{xy[1][0]+0.1,xy[1][1]+0.1}
			};

			a_tilts = new double[][][] {
			{
			{a_tilts[0][0][0], a_tilts[0][0][1]-0.01},
			{a_tilts[0][1][0]-0.01,a_tilts[0][1][1]}
			},
			{
			{a_tilts[1][0][0], a_tilts[1][0][1]-0.1},
			{a_tilts[1][1][0]-0.1, a_tilts[1][1][1]}
			}
			};

			iaff_pair = new double [][] {
			{iaff_pair[0][0], iaff_pair[0][1]+0.1},
			{iaff_pair[1][0]+0.1,iaff_pair[1][1]}
			};

			*/
			double [][] xy_m = new double [][] {
	{xy[0][0],xy[0][1]},		{xy[0][0],xy[0][1]},
	{xy[1][0],xy[1][1]}		{xy[1][0],xy[1][1]}
	};		};

	a_tilts = new double[][][] {		double [][][] a_tilts_m= new double[][][] {
	{		{
	{a_tilts[0][0][0],a_tilts[0][0][1]},		{a_tilts[0][0][0],a_tilts[0][0][1]},
	{a_tilts[0][1][0],a_tilts[0][1][1]}		{a_tilts[0][1][0],a_tilts[0][1][1]}
	@@ -1483,14 +1506,14 @@ q11 - q22 = c3
	}		}
	};		};

	iaff_pair = new double [][] {		double [][] iaff_pair_m = new double [][] {
	{iaff_pair[0][0],iaff_pair[0][1]},		{iaff_pair[0][0],iaff_pair[0][1]},
	{iaff_pair[1][0],iaff_pair[1][1]}		{iaff_pair[1][0],iaff_pair[1][1]}
	};		};
	testPseudoAffineDiffAndDerivatives(		testPseudoAffineDiffAndDerivatives(
	xy, // double [][] xy, // [scene][direction]		xy_m, // double [][] xy, // [scene][direction]
	a_tilts, // double [][][] a_tilts,		a_tilts_m, // double [][][] a_tilts,
	iaff_pair, // double [][] iaff_pair, // affine pair inversed		iaff_pair_m, // double [][] iaff_pair, // affine pair inversed
	invert_q2a, // boolean invert_q2a, // invert result affines (to match "usual")		invert_q2a, // boolean invert_q2a, // invert result affines (to match "usual")
	delta); // double delta);		delta); // double delta);
	}		}
	@@ -1544,11 +1567,11 @@ q11 - q22 = c3
	System.out.println(String.format("%5s\t%20s\t%20s\t%20s\t%20s",		System.out.println(String.format("%5s\t%20s\t%20s\t%20s\t%20s",
	"mode#", "dx0", "dy0", "dx1", "dy1"));		"mode#", "dx0", "dy0", "dx1", "dy1"));
	System.out.println(String.format("%5s\t%20.12f\t%20.12f\t%20.12f\t%20.12f",		System.out.println(String.format("%5s\t%20.12f\t%20.12f\t%20.12f\t%20.12f",
	"deriv", sdWdW[0], sdWdW[1], sdWdW[2], sdWdW[3]));		"deriv", sdWdW[1], sdWdW[2], sdWdW[3], sdWdW[4]));
	System.out.println(String.format("%5s\t%20.12f\t%20.12f\t%20.12f\t%20.12f",		System.out.println(String.format("%5s\t%20.12f\t%20.12f\t%20.12f\t%20.12f",
	"delta", sdWdW_delta[0], sdWdW_delta[1],sdWdW_delta[2],sdWdW_delta[3]));		"delta", sdWdW_delta[1], sdWdW_delta[2],sdWdW_delta[3],sdWdW_delta[4]));
	System.out.println(String.format("%5s\t%20.12f\t%20.12f\t%20.12f\t%20.12f",		System.out.println(String.format("%5s\t%20.12f\t%20.12f\t%20.12f\t%20.12f",
	"diff", s(dWdW_delta[0]-dWdW[0]), s(dWdW_delta[1]-dWdW[1]), s(dWdW_delta[2]-dWdW[2]), s(dWdW_delta[3]-dWdW[3])));		"diff", s(dWdW_delta[1]-dWdW[1]), s(dWdW_delta[2]-dWdW[2]), s(dWdW_delta[3]-dWdW[3]), s(dWdW_delta[4]-dWdW[4])));
	System.out.println ("Change xy[0][0] >= 1.0 to exit");		System.out.println ("Change xy[0][0] >= 1.0 to exit");
	System.out.println ();		System.out.println ();
	}		}

src/main/java/com/elphel/imagej/orthomosaic/SingularValueDecomposition.java

+11 −5

Original line number	Original line	Diff line number	Diff line
	@@ -49,6 +49,11 @@ public class SingularValueDecomposition {
	public double getMinScale() {return Math.min(w1,w2);}		public double getMinScale() {return Math.min(w1,w2);}
	public double getMaxScale() {return Math.max(w1,w2);}		public double getMaxScale() {return Math.max(w1,w2);}

			// Measure of tilt - difference between singular values (they both are assumed to be ~= 1.0)
			public double getDW() {
			return Math.abs(w1-w2);
			}

	public static String titleString(boolean degrees) {		public static String titleString(boolean degrees) {
	SingularValueDecomposition svd= new SingularValueDecomposition(0,0,0,0,0);		SingularValueDecomposition svd= new SingularValueDecomposition(0,0,0,0,0);
	return svd.toString(degrees, 2);		return svd.toString(degrees, 2);
	@@ -67,20 +72,21 @@ public class SingularValueDecomposition {
	//System.out.println("svd_affine_pair= ["+svd_affine_pair.scale+ ","+svd_affine_pair.getTiltAngle()+ ","+svd_affine_pair.gamma+ ","+svd_affine_pair.rot+		//System.out.println("svd_affine_pair= ["+svd_affine_pair.scale+ ","+svd_affine_pair.getTiltAngle()+ ","+svd_affine_pair.gamma+ ","+svd_affine_pair.rot+
	// "] tilt="+(svd_affine_pair.getTiltAngle()180/Math.PI)+ "\u00B0, dir="+(svd_affine_pair.gamma180/Math.PI)+"\u00B0");		// "] tilt="+(svd_affine_pair.getTiltAngle()180/Math.PI)+ "\u00B0, dir="+(svd_affine_pair.gamma180/Math.PI)+"\u00B0");
	String tab_title_rad = String.format("%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s",		String tab_title_rad = String.format("%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s",
	"scale","tilt","gamma","beta","rot", "w1", "w2", "ratio");		"scale","tilt","gamma","beta","rot", "w1", "w2", "\u0394w"); // ratio");
	String tab_title_deg = String.format("%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s",		String tab_title_deg = String.format("%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s\t%10s",
	"scale","tilt\u00B0","gamma\u00B0","beta\u00B0","rot\u00B0", "w1", "w2", "ratio");		"scale","tilt\u00B0","gamma\u00B0","beta\u00B0","rot\u00B0", "w1", "w2", "\u0394w"); // ratio");
	String tab_fmt_rad = "%10.8f\t%10.7f\t%10.7f\t%10.7f\t%10.7f\t%10.8f\t%10.8f\t%10.8f";		String tab_fmt_rad = "%10.8f\t%10.7f\t%10.7f\t%10.7f\t%10.7f\t%10.8f\t%10.8f\t%10.8f";
	String tab_fmt_deg = "%10.8f\t%10.5f\t%10.5f\t%10.5f\t%10.5f\t%10.8f\t%10.8f\t%10.8f";		String tab_fmt_deg = "%10.8f\t%10.5f\t%10.5f\t%10.5f\t%10.5f\t%10.8f\t%10.8f\t%10.8f";
	String fmt_rad = " scale=%10.8f,tilt= %10.7f, gamma=%10.7f, beta=%10.7f, rot=%10.7f, w1=%10.8f, w2=%10.8f, ratio=%10.8f";		String fmt_rad = " scale=%10.8f,tilt= %10.7f, gamma=%10.7f, beta=%10.7f, rot=%10.7f, w1=%10.8f, w2=%10.8f, \u0394w=%10.8f"; // ratio=%10.8f";
	String fmt_deg = " scale=%10.8f,tilt= %10.5f\u00B0, gamma=%10.5f\u00B0, beta=%10.5f\u00B0, rot=%10.5f\u00B0, w1=%10.8f, w2=%10.8f, ratio=%10.8f";		String fmt_deg = " scale=%10.8f,tilt= %10.5f\u00B0, gamma=%10.5f\u00B0, beta=%10.5f\u00B0, rot=%10.5f\u00B0, w1=%10.8f, w2=%10.8f, \u0394w=%10.8f"; // ratio=%10.8f\";
	if (tab_mode==2) {		if (tab_mode==2) {
	return degrees?tab_title_deg:tab_title_rad;		return degrees?tab_title_deg:tab_title_rad;
	}		}
	String fmt = (tab_mode==1)?(degrees ? tab_fmt_deg : tab_fmt_rad):(degrees ? fmt_deg : fmt_rad);		String fmt = (tab_mode==1)?(degrees ? tab_fmt_deg : tab_fmt_rad):(degrees ? fmt_deg : fmt_rad);
	double s = degrees ? (180/Math.PI):1;		double s = degrees ? (180/Math.PI):1;
	// String fmt=degrees ? fmt_deg : fmt_rad;		// String fmt=degrees ? fmt_deg : fmt_rad;
	return String.format(fmt, scale, sgetTiltAngle(), sgamma, sbeta, srot, w1, w2, ratio);		// return String.format(fmt, scale, sgetTiltAngle(), sgamma, sbeta, srot, w1, w2, ratio);
			return String.format(fmt, scale, sgetTiltAngle(), sgamma, sbeta, srot, w1, w2, Math.abs(w1-w2));
	}		}

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