void TableOfReal_drawVerticalLines (TableOfReal me, Graphics graphics, long rowmin, long rowmax) {
	long colmin = 1, colmax = my numberOfColumns;
	fixRows (me, & rowmin, & rowmax);
	Graphics_setInner (graphics);
	Graphics_setWindow (graphics, colmin - 0.5, colmax + 0.5, 0, 1);
	double lineSpacing = getLineSpacing (graphics);   // not earlier!
	double maxTextWidth = getMaxRowLabelWidth (me, graphics, rowmin, rowmax);
	double maxTextHeight = getMaxColumnLabelHeight (me, graphics, 1, my numberOfColumns);

	if (maxTextWidth > 0.0) colmin -= 1;
	for (long col = colmin + 1; col <= colmax; col ++)
		Graphics_line (graphics, col - 0.5, 1 + maxTextHeight, col - 0.5, 1 - lineSpacing * (rowmax - rowmin + 1));
	Graphics_unsetInner (graphics);
}

void Spectrogram_paintInside (Spectrogram me, Graphics g, double tmin, double tmax, double fmin, double fmax,
	double maximum, int autoscaling, double dynamic, double preemphasis, double dynamicCompression)
{
	if (tmax <= tmin) { tmin = my xmin; tmax = my xmax; }
	if (fmax <= fmin) { fmin = my ymin; fmax = my ymax; }
	long itmin, itmax, ifmin, ifmax;
	if (! Matrix_getWindowSamplesX (me, tmin - 0.49999 * my dx, tmax + 0.49999 * my dx, & itmin, & itmax) ||
		 ! Matrix_getWindowSamplesY (me, fmin - 0.49999 * my dy, fmax + 0.49999 * my dy, & ifmin, & ifmax))
		return;
	Graphics_setWindow (g, tmin, tmax, fmin, fmax);
	autoNUMvector <double> preemphasisFactor (ifmin, ifmax);
	autoNUMvector <double> dynamicFactor (itmin, itmax);
	/* Pre-emphasis in place; also compute maximum after pre-emphasis. */
	for (long ifreq = ifmin; ifreq <= ifmax; ifreq ++) {
		preemphasisFactor [ifreq] = (preemphasis / NUMln2) * log (ifreq * my dy / 1000.0);
		for (long itime = itmin; itime <= itmax; itime ++) {
			double value = my z [ifreq] [itime];   /* Power. */
			value = (10.0/NUMln10) * log ((value + 1e-30) / 4.0e-10) + preemphasisFactor [ifreq];   /* dB */
			if (value > dynamicFactor [itime]) dynamicFactor [itime] = value;   /* Local maximum. */
			my z [ifreq] [itime] = value;
		}
	}
	/* Compute global maximum. */
	if (autoscaling) {
		maximum = 0.0;
		for (long itime = itmin; itime <= itmax; itime ++)
			if (dynamicFactor [itime] > maximum) maximum = dynamicFactor [itime];
	}
	/* Dynamic compression in place. */
	for (long itime = itmin; itime <= itmax; itime ++) {
		dynamicFactor [itime] = dynamicCompression * (maximum - dynamicFactor [itime]);
		for (long ifreq = ifmin; ifreq <= ifmax; ifreq ++)
			my z [ifreq] [itime] += dynamicFactor [itime];
	}
	Graphics_image (g, my z,
		itmin, itmax,
		Matrix_columnToX (me, itmin - 0.5),
		Matrix_columnToX (me, itmax + 0.5),
		ifmin, ifmax,
		Matrix_rowToY (me, ifmin - 0.5),
		Matrix_rowToY (me, ifmax + 0.5),
		maximum - dynamic, maximum);
	for (long ifreq = ifmin; ifreq <= ifmax; ifreq ++)
		for (long itime = itmin; itime <= itmax; itime ++) {
			double value = 4.0e-10 * exp ((my z [ifreq] [itime] - dynamicFactor [itime]
				- preemphasisFactor [ifreq]) * (NUMln10 / 10.0)) - 1e-30;
			my z [ifreq] [itime] = value > 0.0 ? value : 0.0;
		}
}

void structPointEditor :: v_draw () {
	PointProcess point = static_cast <PointProcess> (our data);
	Sound sound = d_sound.data;
	Graphics_setColour (our graphics.get(), Graphics_WHITE);
	Graphics_setWindow (our graphics.get(), 0.0, 1.0, 0.0, 1.0);
	Graphics_fillRectangle (our graphics.get(), 0.0, 1.0, 0.0, 1.0);
	double minimum = -1.0, maximum = +1.0;
	if (sound && (p_sound_scalingStrategy == kTimeSoundEditor_scalingStrategy_BY_WINDOW || p_sound_scalingStrategy == kTimeSoundEditor_scalingStrategy_BY_WINDOW_AND_CHANNEL)) {
		long first, last;
		if (Sampled_getWindowSamples (sound, our startWindow, our endWindow, & first, & last) >= 1) {
			Matrix_getWindowExtrema (sound, first, last, 1, 1, & minimum, & maximum);
			if (minimum == maximum) minimum -= 1.0, maximum += 1.0;
		}
	}
	Graphics_setWindow (our graphics.get(), our startWindow, our endWindow, minimum, maximum);
	Graphics_setColour (our graphics.get(), Graphics_BLACK);
	if (sound) {
		long first, last;
		if (Sampled_getWindowSamples (sound, our startWindow, our endWindow, & first, & last) > 1) {
			Graphics_setLineType (our graphics.get(), Graphics_DOTTED);
			Graphics_line (our graphics.get(), our startWindow, 0.0, our endWindow, 0.0);
			Graphics_setLineType (our graphics.get(), Graphics_DRAWN);
			Graphics_function (our graphics.get(), sound -> z [1], first, last,
				Sampled_indexToX (sound, first), Sampled_indexToX (sound, last));
		}
	}
	Graphics_setColour (our graphics.get(), Graphics_BLUE);
	Graphics_setWindow (our graphics.get(), our startWindow, our endWindow, -1.0, +1.0);
	for (long i = 1; i <= point -> nt; i ++) {
		double t = point -> t [i];
		if (t >= our startWindow && t <= our endWindow)
			Graphics_line (our graphics.get(), t, -0.9, t, +0.9);
	}
	Graphics_setColour (our graphics.get(), Graphics_BLACK);
	v_updateMenuItems_file ();
}

void Matrix_drawRows (Matrix me, Graphics g, double xmin, double xmax, double ymin, double ymax,
	double minimum, double maximum)
{
	if (xmax <= xmin) { xmin = my xmin; xmax = my xmax; }
	if (ymax <= ymin) { ymin = my ymin; ymax = my ymax; }
	long ixmin, ixmax, iymin, iymax;
	(void) Matrix_getWindowSamplesX (me, xmin, xmax, & ixmin, & ixmax);
	(void) Matrix_getWindowSamplesY (me, ymin, ymax, & iymin, & iymax);
	if (maximum <= minimum)
		(void) Matrix_getWindowExtrema (me, ixmin, ixmax, iymin, iymax, & minimum, & maximum);
	if (maximum <= minimum) { minimum -= 1.0; maximum += 1.0; }
	if (xmin >= xmax) return;
	Graphics_setInner (g);
	for (long iy = iymin; iy <= iymax; iy ++) {
		Graphics_setWindow (g, xmin, xmax,
			minimum - (iy - iymin) * (maximum - minimum),
			maximum + (iymax - iy) * (maximum - minimum));
		Graphics_function (g, my z [iy], ixmin, ixmax,
			Matrix_columnToX (me, ixmin), Matrix_columnToX (me, ixmax));
	}
	Graphics_unsetInner (g);
	if (iymin < iymax)
		Graphics_setWindow (g, xmin, xmax, my y1 + (iymin - 1.5) * my dy, my y1 + (iymax - 0.5) * my dy);
}

void Matrix_scatterPlot (Matrix me, Graphics g, long icx, long icy, double xmin, double xmax, double ymin, double ymax, double size_mm, const char32 *mark, int garnish) {
	long ix = labs (icx), iy = labs (icy);

	if (ix < 1 || ix > my nx || iy < 1 || iy > my nx) {
		return;
	}
	if (xmax <= xmin) {
		(void) Matrix_getWindowExtrema (me, ix, ix, 1, my ny, & xmin, & xmax);
		if (xmax <= xmin) {
			xmin -= 0.5; xmax += 0.5;
		}
	}
	if (ymax <= ymin) {
		(void) Matrix_getWindowExtrema (me, iy, iy, 1, my ny, & ymin, & ymax);
		if (ymax <= ymin) {
			ymin -= 0.5; ymax += 0.5;
		}
	}
	Graphics_setInner (g);
	if (icx < 0) {
		double t = xmin;
		xmin = xmax;
		xmax = t;
	}
	if (icy < 0) {
		double t = ymin;
		ymin = ymax;
		ymax = t;
	}
	Graphics_setWindow (g, xmin, xmax, ymin, ymax);
	for (long i = 1; i <= my ny; i++) {
		if (my z[i][ix] >= xmin && my z[i][ix] <= xmax && my z[i][iy] >= ymin && my z[i][iy] <= ymax) {
			Graphics_mark (g, my z[i][ix], my z[i][iy], size_mm, mark);
		}
	}
	Graphics_unsetInner (g);
	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_marksLeft (g, 2, true, true, false);
		if (ymin * ymax < 0.0) {
			Graphics_markLeft (g, 0.0, true, true, true, nullptr);
		}
		Graphics_marksBottom (g, 2, true, true, false);
		if (xmin * xmax < 0.0) {
			Graphics_markBottom (g, 0.0, true, true, true, nullptr);
		}
	}
}

void ERP_drawChannel_number (ERP me, Graphics graphics, long channelNumber, double tmin, double tmax, double vmin, double vmax, bool garnish) {
	if (channelNumber < 1 || channelNumber > my ny) return;
	/*
	 * Automatic domain.
	 */
	if (tmin == tmax) {
		tmin = my xmin;
		tmax = my xmax;
	}
	/*
	 * Domain expressed in sample numbers.
	 */
	long ixmin, ixmax;
	Matrix_getWindowSamplesX (me, tmin, tmax, & ixmin, & ixmax);
	/*
	 * Automatic vertical range.
	 */
	if (vmin == vmax) {
		Matrix_getWindowExtrema (me, ixmin, ixmax, channelNumber, channelNumber, & vmin, & vmax);
		if (vmin == vmax) {
			vmin -= 1.0;
			vmax += 1.0;
		}
	}
	/*
	 * Set coordinates for drawing.
	 */
	Graphics_setInner (graphics);
	Graphics_setWindow (graphics, tmin, tmax, vmin, vmax);
	Graphics_function (graphics, my z [channelNumber], ixmin, ixmax, Matrix_columnToX (me, ixmin), Matrix_columnToX (me, ixmax));
	Graphics_unsetInner (graphics);
	if (garnish) {
		Graphics_drawInnerBox (graphics);
		Graphics_textTop (graphics, true, Melder_wcscat (L"Channel ", my channelNames [channelNumber]));
		Graphics_textBottom (graphics, true, L"Time (s)");
		Graphics_marksBottom (graphics, 2, true, true, false);
		if (0.0 > tmin && 0.0 < tmax)
			Graphics_markBottom (graphics, 0.0, true, true, true, NULL);
		Graphics_markLeft (graphics, vmin, true, true, false, NULL);
		Graphics_markLeft (graphics, vmax, true, true, false, NULL);
			Graphics_markBottom (graphics, 0.0, true, true, true, NULL);
		if (vmin != 0.0 && vmax != 0.0 && (vmin > 0.0) != (vmax > 0.0)) {
			Graphics_markLeft (graphics, 0.0, true, true, true, NULL);
		}
	}

}

void Cepstrum_draw (Cepstrum me, Graphics g, double qmin, double qmax,
                    double minimum, double maximum, int garnish) {
	int autoscaling = minimum >= maximum;

	Graphics_setInner (g);

	if (qmax <= qmin) {
		qmin = my xmin; qmax = my xmax;
	}

	long imin, imax;
	if (! Matrix_getWindowSamplesX (me, qmin, qmax, & imin, & imax)) {
		return;
	}
	autoNUMvector<double> y (imin, imax);

	double *z = my z[1];

	for (long i = imin; i <= imax; i++) {
		y[i] = z[i];
	}

	if (autoscaling) {
		NUMvector_extrema (y.peek(), imin, imax, & minimum, & maximum);
	}

	for (long i = imin; i <= imax; i ++) {
		if (y[i] > maximum) {
			y[i] = maximum;
		} else if (y[i] < minimum) {
			y[i] = minimum;
		}
	}

	Graphics_setWindow (g, qmin, qmax, minimum, maximum);
	Graphics_function (g, y.peek(), imin, imax, Matrix_columnToX (me, imin), Matrix_columnToX (me, imax));

	Graphics_unsetInner (g);

	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_textBottom (g, 1, L"Quefrency");
		Graphics_marksBottom (g, 2, TRUE, TRUE, FALSE);
		Graphics_textLeft (g, 1, L"Amplitude");
	}
}

void LineSpectralFrequencies_drawFrequencies (LineSpectralFrequencies me, Graphics g, double tmin, double tmax, double fmin, double fmax, bool garnish) {
	if (tmax <= tmin) {
		tmin = my xmin;
		tmax = my xmax;
	}
	long itmin, itmax;
	if (! Sampled_getWindowSamples (me, tmin, tmax, & itmin, & itmax)) {
		return;
	}
	if (fmax <= fmin) {
		double f1max, f2min; 
		autoNUMvector<double> f1 (itmin, itmax), f2 (itmin, itmax);
		for (long iframe = itmin; iframe <= itmax; iframe++) {
			f1[iframe] = my d_frames[iframe].frequencies[1];
			f2[iframe] = my d_frames[iframe].frequencies[my d_frames[iframe].numberOfFrequencies];
		}
		NUMvector_extrema (f1.peek(), itmin, itmax, & fmin, & f1max);
		NUMvector_extrema (f2.peek(), itmin, itmax, & f2min, & fmax);
	}
	if (fmax == fmin) {
		fmin = 0;
		fmax += 0.5;
	}

	Graphics_setInner (g);
	Graphics_setWindow (g, tmin, tmax, fmin, fmax);
	for (long iframe = itmin; iframe <= itmax; iframe++) {
		LineSpectralFrequencies_Frame lsf = & my d_frames[iframe];
		double x = Sampled_indexToX (me, iframe);
		for (long ifreq = 1; ifreq <= lsf -> numberOfFrequencies; ifreq++) {
			double y = lsf -> frequencies [ifreq];
			if (y >= fmin && y <= fmax) { 
				Graphics_speckle (g, x, y);
			}
		}
	}
	Graphics_unsetInner (g);
	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_textBottom (g, true, U"Time (seconds)");
		Graphics_textLeft (g, true, U"Frequency (Hz)");
		Graphics_marksBottom (g, 2, true, true, false);
		Graphics_marksLeft (g, 2, true, true, false);
	}
}

void Art_Speaker_fillInnerContour (Art art, Speaker speaker, Graphics g) {
	double f = speaker -> relativeSize * 1e-3;
	double intX [1 + 16], intY [1 + 16], extX [1 + 11], extY [1 + 11];
	double x [1 + 16], y [1 + 16];
	double bodyX, bodyY;
	int i;
	Graphics_Viewport previous;

	Art_Speaker_toVocalTract (art, speaker, intX, intY, extX, extY, & bodyX, & bodyY);
	previous = Graphics_insetViewport (g, 0.1, 0.9, 0.1, 0.9);
	Graphics_setWindow (g, -0.05, 0.05, -0.05, 0.05);
	for (i = 1; i <= 16; i ++) { x [i] = intX [i]; y [i] = intY [i]; }
	Graphics_setGrey (g, 0.8);
	Graphics_fillArea (g, 16, & x [1], & y [1]);
	Graphics_fillCircle (g, bodyX, bodyY, 20 * f);
	Graphics_setGrey (g, 0.0);
	Graphics_resetViewport (g, previous);
}

void TableOfReal_drawTopAndBottomLines (TableOfReal me, Graphics graphics, long rowmin, long rowmax) {
	long colmin = 1, colmax = my numberOfColumns;
	fixRows (me, & rowmin, & rowmax);
	Graphics_setInner (graphics);
	Graphics_setWindow (graphics, colmin - 0.5, colmax + 0.5, 0, 1);
	double lineSpacing = getLineSpacing (graphics);
	double maxTextWidth = getMaxRowLabelWidth (me, graphics, rowmin, rowmax);
	double maxTextHeight = getMaxColumnLabelHeight (me, graphics, 1, my numberOfColumns);

	double left = 0.5;
	if (maxTextWidth > 0.0) left -= maxTextWidth + 2 * lineSpacing;
	double right = colmax + 0.5;
	double top = 1 + maxTextHeight;
	double bottom = 1 - lineSpacing * (rowmax - rowmin + 1);
	Graphics_line (graphics, left, top, right, top);
	Graphics_line (graphics, left, bottom, right, bottom);
	Graphics_unsetInner (graphics);
}

// xmin, xmax in hz versus bark/mel or lin
void BandFilterSpectrogram_drawFrequencyScale (BandFilterSpectrogram me, Graphics g, double xmin, double xmax, double ymin, double ymax, int garnish) {
	if (xmin < 0 || xmax < 0 || ymin < 0 || ymax < 0) {
		Melder_warning (U"Frequencies must be >= 0.");
		return;
	}

	// scale is in hertz
	if (xmin >= xmax) { // autoscaling
		xmin = 0;
		xmax = my v_frequencyToHertz (my ymax);
	}

	if (ymin >= ymax) { // autoscaling
		ymin = my ymin;
		ymax = my ymax;
	}

	long n = 2000;

	Graphics_setInner (g);
	Graphics_setWindow (g, xmin, xmax, ymin, ymax);

	double dx = (xmax - xmin) / (n - 1);
	double x1 = xmin, y1 = my v_hertzToFrequency (x1);
	for (long i = 2; i <= n;  i++) {
		double x2 = x1 + dx, y2 = my v_hertzToFrequency (x2);
		if (NUMdefined (y1) && NUMdefined (y2)) {
			double xo1, yo1, xo2, yo2;
			if (NUMclipLineWithinRectangle (x1, y1, x2, y2, xmin, ymin, xmax, ymax, &xo1, &yo1, &xo2, &yo2)) {
				Graphics_line (g, xo1, yo1, xo2, yo2);
			}
		}
		x1 = x2; y1 = y2;
	}
	Graphics_unsetInner (g);

	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_marksLeft (g, 2, 1, 1, 0);
		Graphics_textLeft (g, 1, Melder_cat (U"Frequency (", my v_getFrequencyUnit (), U")"));
		Graphics_marksBottom (g, 2, 1, 1, 0);
		Graphics_textBottom (g, 1, U"Frequency (Hz)");
	}
}

void RealTier_draw (RealTier me, Graphics g, double tmin, double tmax, double fmin, double fmax,
	int garnish, const char32 *method, const char32 *quantity)
{
	bool drawLines = str32str (method, U"lines") || str32str (method, U"Lines");
	bool drawSpeckles = str32str (method, U"speckles") || str32str (method, U"Speckles");
	long n = my points.size, imin, imax, i;
	if (tmax <= tmin) { tmin = my xmin; tmax = my xmax; }
	Graphics_setWindow (g, tmin, tmax, fmin, fmax);
	Graphics_setInner (g);
	imin = AnyTier_timeToHighIndex (me->asAnyTier(), tmin);
	imax = AnyTier_timeToLowIndex (me->asAnyTier(), tmax);
	if (n == 0) {
	} else if (imax < imin) {
		double fleft = RealTier_getValueAtTime (me, tmin);
		double fright = RealTier_getValueAtTime (me, tmax);
		if (drawLines) Graphics_line (g, tmin, fleft, tmax, fright);
	} else for (i = imin; i <= imax; i ++) {
		RealPoint point = my points.at [i];
		double t = point -> number, f = point -> value;
		if (drawSpeckles) Graphics_speckle (g, t, f);
		if (drawLines) {
			if (i == 1)
				Graphics_line (g, tmin, f, t, f);
			else if (i == imin)
				Graphics_line (g, t, f, tmin, RealTier_getValueAtTime (me, tmin));
			if (i == n)
				Graphics_line (g, t, f, tmax, f);
			else if (i == imax)
				Graphics_line (g, t, f, tmax, RealTier_getValueAtTime (me, tmax));
			else {
				RealPoint pointRight = my points.at [i + 1];
				Graphics_line (g, t, f, pointRight -> number, pointRight -> value);
			}
		}
	}
	Graphics_unsetInner (g);
	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_textBottom (g, true, my v_getUnitText (0, 0, 0));
		Graphics_marksBottom (g, 2, true, true, false);
		Graphics_marksLeft (g, 2, true, true, false);
		if (quantity) Graphics_textLeft (g, true, quantity);
	}
}

void PitchTier_Pitch_draw (PitchTier me, Pitch uv, Graphics g,
	double tmin, double tmax, double fmin, double fmax, int nonPeriodicLineType, int garnish, const char32 *method)
{
	long n = my points.size, imin, imax, i;
	if (nonPeriodicLineType == 0) {
		PitchTier_draw (me, g, tmin, tmax, fmin, fmax, garnish, method);
		return;
	}
	if (tmax <= tmin) { tmin = my xmin; tmax = my xmax; }
	Graphics_setWindow (g, tmin, tmax, fmin, fmax);
	Graphics_setInner (g);
	imin = AnyTier_timeToHighIndex (me->asAnyTier(), tmin);
	imax = AnyTier_timeToLowIndex (me->asAnyTier(), tmax);
	if (n == 0) {
	} else if (imax < imin) {
		double fleft = RealTier_getValueAtTime (me, tmin);
		double fright = RealTier_getValueAtTime (me, tmax);
		Pitch_line (uv, g, tmin, fleft, tmax, fright, nonPeriodicLineType);
	} else for (i = imin; i <= imax; i ++) {
		RealPoint point = my points.at [i];
		double t = point -> number, f = point -> value;
		Graphics_speckle (g, t, f);
		if (i == 1)
			Pitch_line (uv, g, tmin, f, t, f, nonPeriodicLineType);
		else if (i == imin)
			Pitch_line (uv, g, t, f, tmin, RealTier_getValueAtTime (me, tmin), nonPeriodicLineType);
		if (i == n)
			Pitch_line (uv, g, t, f, tmax, f, nonPeriodicLineType);
		else if (i == imax)
			Pitch_line (uv, g, t, f, tmax, RealTier_getValueAtTime (me, tmax), nonPeriodicLineType);
		else {
			RealPoint pointRight = my points.at [i + 1];
			Pitch_line (uv, g, t, f, pointRight -> number, pointRight -> value, nonPeriodicLineType);
		}
	}
	Graphics_unsetInner (g);
	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_textBottom (g, true, U"Time (s)");
		Graphics_marksBottom (g, 2, true, true, false);
		Graphics_marksLeft (g, 2, true, true, false);
		Graphics_textLeft (g, true, U"Frequency (Hz)");
	}
}

void TextGrid_Pitch_drawSeparately (TextGrid grid, Pitch pitch, Graphics g, double tmin, double tmax,
	double fmin, double fmax, int showBoundaries, int useTextStyles, int garnish, int speckle, int unit)
{
	int ntier = grid -> tiers -> size;
	if (tmax <= tmin) tmin = grid -> xmin, tmax = grid -> xmax;
	if (Function_isUnitLogarithmic (pitch, Pitch_LEVEL_FREQUENCY, unit)) {
		fmin = Function_convertStandardToSpecialUnit (pitch, fmin, Pitch_LEVEL_FREQUENCY, unit);
		fmax = Function_convertStandardToSpecialUnit (pitch, fmax, Pitch_LEVEL_FREQUENCY, unit);
	}
	if (unit == kPitch_unit_HERTZ_LOGARITHMIC)
		Pitch_draw (pitch, g, tmin, tmax, pow (10, fmin - 0.25 * (fmax - fmin) * ntier), pow (10, fmax), FALSE, speckle, unit);
	else
		Pitch_draw (pitch, g, tmin, tmax, fmin - 0.25 * (fmax - fmin) * ntier, fmax, FALSE, speckle, unit);
	TextGrid_Sound_draw (grid, NULL, g, tmin, tmax, showBoundaries, useTextStyles, FALSE);
	/*
	 * Restore window for the sake of margin drawing.
	 */
	Graphics_setWindow (g, tmin, tmax, fmin - 0.25 * (fmax - fmin) * ntier, fmax);
	if (unit == kPitch_unit_HERTZ_LOGARITHMIC)
		fmin = pow (10, fmin), fmax = pow (10, fmax);
	if (garnish) {
		Graphics_drawInnerBox (g);
		if (unit == kPitch_unit_HERTZ_LOGARITHMIC) {
			Graphics_markLeftLogarithmic (g, fmin, TRUE, TRUE, FALSE, NULL);
			Graphics_markLeftLogarithmic (g, fmax, TRUE, TRUE, FALSE, NULL);
			autoMarks_logarithmic (g, fmin, fmax, FALSE);
		} else if (unit == kPitch_unit_SEMITONES_100) {
			Graphics_markLeft (g, fmin, TRUE, TRUE, FALSE, NULL);
			Graphics_markLeft (g, fmax, TRUE, TRUE, FALSE, NULL);
			autoMarks_semitones (g, fmin, fmax, FALSE);
		} else {
			Graphics_markLeft (g, fmin, TRUE, TRUE, FALSE, NULL);
			Graphics_markLeft (g, fmax, TRUE, TRUE, FALSE, NULL);
			autoMarks (g, fmin, fmax, FALSE);
		}
		static MelderString buffer = { 0 };
		MelderString_empty (& buffer);
		MelderString_append (& buffer, L"Pitch (", Function_getUnitText (pitch, Pitch_LEVEL_FREQUENCY, unit, Function_UNIT_TEXT_GRAPHICAL), L")");
		Graphics_textLeft (g, true, buffer.string);
		Graphics_textBottom (g, true, L"Time (s)");
		Graphics_marksBottom (g, 2, true, true, true);
	}
}

void SPINET_drawSpectrum (SPINET me, Graphics g, double time, double fromErb, double toErb,
                          double minimum, double maximum, int enhanced, int garnish) {
	long ifmin, ifmax, icol = Sampled2_xToLowColumn (me, time);   // ppgb: don't use Sampled2_xToColumn for integer rounding
	double **z = enhanced ? my s : my y;
	if (icol < 1 || icol > my nx) {
		return;
	}
	if (toErb <= fromErb) {
		fromErb = my ymin;
		toErb = my ymax;
	}
	Sampled2_getWindowSamplesY (me, fromErb, toErb, &ifmin, &ifmax);
	autoNUMvector<double> spec (1, my ny);

	for (long i = 1; i <= my ny; i++) {
		spec[i] = z[i][icol];
	}
	if (maximum <= minimum) {
		NUMvector_extrema (spec.peek(), ifmin, ifmax, &minimum, &maximum);
	}
	if (maximum <= minimum) {
		minimum -= 1;
		maximum += 1;
	}
	for (long i = ifmin; i <= ifmax; i++) {
		if (spec[i] > maximum) {
			spec[i] = maximum;
		} else if (spec[i] < minimum) {
			spec[i] = minimum;
		}
	}
	Graphics_setInner (g);
	Graphics_setWindow (g, fromErb, toErb, minimum, maximum);
	Graphics_function (g, spec.peek(), ifmin, ifmax, Sampled2_rowToY (me, ifmin), Sampled2_rowToY (me, ifmax));
	Graphics_unsetInner (g);
	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_textBottom (g, 1, U"Frequency (ERB)");
		Graphics_marksBottom (g, 2, 1, 1, 0);
		Graphics_textLeft (g, 1, U"strength");
		Graphics_marksLeft (g, 2, 1, 1, 0);
	}
}

static void _Cepstrum_draw (Cepstrum me, Graphics g, double qmin, double qmax, double minimum, double maximum, int power, int garnish) {
	int autoscaling = minimum >= maximum;

	Graphics_setInner (g);

	if (qmax <= qmin) {
		qmin = my xmin; qmax = my xmax;
	}

	long imin, imax;
	if (! Matrix_getWindowSamplesX (me, qmin, qmax, & imin, & imax)) {
		return;
	}
	autoNUMvector<double> y (imin, imax);

	for (long i = imin; i <= imax; i++) {
		y[i] = my v_getValueAtSample (i, (power ? 1 : 0), 0);
	}

	if (autoscaling) {
		NUMvector_extrema (y.peek(), imin, imax, & minimum, & maximum);
	} else {
		for (long i = imin; i <= imax; i ++) {
			if (y[i] > maximum) {
				y[i] = maximum;
			} else if (y[i] < minimum) {
				y[i] = minimum;
			}
		}
	}
	Graphics_setWindow (g, qmin, qmax, minimum, maximum);
	Graphics_function (g, y.peek(), imin, imax, Matrix_columnToX (me, imin), Matrix_columnToX (me, imax));

	Graphics_unsetInner (g);

	if (garnish) {
		Graphics_drawInnerBox (g);
		Graphics_textBottom (g, true, U"Quefrency (s)");
		Graphics_marksBottom (g, 2, true, true, false);
		Graphics_textLeft (g, true, power ? U"Amplitude (dB)" : U"Amplitude");
		Graphics_marksLeft (g, 2, true, true, false);
	}
}

void Matrix_paintSurface (Matrix me, Graphics g, double xmin, double xmax, double ymin, double ymax,
	double minimum, double maximum, double elevation, double azimuth)
{
	if (xmax <= xmin) { xmin = my xmin; xmax = my xmax; }
	if (ymax <= ymin) { ymin = my ymin; ymax = my ymax; }
	long ixmin, ixmax, iymin, iymax;
	(void) Matrix_getWindowSamplesX (me, xmin, xmax, & ixmin, & ixmax);
	(void) Matrix_getWindowSamplesY (me, ymin, ymax, & iymin, & iymax);
	if (maximum <= minimum)
		(void) Matrix_getWindowExtrema (me, ixmin, ixmax, iymin, iymax, & minimum, & maximum);
	if (maximum <= minimum) { minimum -= 1.0; maximum += 1.0; }
	Graphics_setInner (g);
	Graphics_setWindow (g, -1.0, 1.0, minimum, maximum);
	Graphics_surface (g, my z,
		ixmin, ixmax, Matrix_columnToX (me, ixmin), Matrix_columnToX (me, ixmax),
		iymin, iymax, Matrix_rowToY (me, iymin), Matrix_rowToY (me, iymax),
		minimum, maximum, elevation, azimuth);
	Graphics_unsetInner (g);
}

void GaussianMixture_drawMarginalPdf (GaussianMixture me, Graphics g, long d, double xmin, double xmax, double ymin, double ymax, long npoints, long nbins, int garnish)
{
	if (d < 1 || d > my dimension)
	{ Melder_warning1 (L"Dimension doesn't agree."); return;}
	if (npoints <= 1) npoints = 1000;
	double *p = NUMdvector (1, npoints);
	if (p == 0) return;
	double nsigmas = 2, *v = NUMdvector (1, my dimension);
	if (v == NULL) goto end;

	if (xmax <= xmin &&
		! GaussianMixture_getIntervalAlongDirection (me, d, nsigmas, &xmin, &xmax)) goto end;

	{
		double pmax = 0, dx = (xmax - xmin) / (npoints - 1);
		double scalef = nbins <= 0 ? 1 : 1; // TODO
		for (long i = 1; i <= npoints; i++)
		{
			double x = xmin + (i - 1) * dx;
			for (long k = 1; k <= my dimension; k++) v[k] = k == d ? 1 : 0;
			p[i] = scalef * GaussianMixture_getMarginalProbabilityAtPosition (me, v, x);
			if (p[i] > pmax) pmax = p[i];
		}
		if (ymin >= ymax) { ymin = 0; ymax = pmax; }

		Graphics_setInner (g);
		Graphics_setWindow (g, xmin, xmax, ymin, ymax);
		Graphics_function (g, p, 1, npoints, xmin, xmax);
		Graphics_unsetInner (g);

		if (garnish)
		{
			Graphics_drawInnerBox (g);
			Graphics_markBottom (g, xmin, 1, 1, 0, NULL);
			Graphics_markBottom (g, xmax, 1, 1, 0, NULL);
			Graphics_markLeft (g, ymin, 1, 1, 0, NULL);
			Graphics_markLeft (g, ymax, 1, 1, 0, NULL);
		}
	}

end:
	NUMdvector_free (p, 1); NUMdvector_free (v, 1);
}

void TableOfReal_drawAsNumbers_if (TableOfReal me, Graphics graphics, long rowmin, long rowmax, int iformat, int precision,
	const wchar_t *conditionFormula, Interpreter interpreter)
{
	try {
		autoMatrix original = TableOfReal_to_Matrix (me);
		autoMatrix conditions = original.clone ();
		fixRows (me, & rowmin, & rowmax);
		Graphics_setInner (graphics);
		Graphics_setWindow (graphics, 0.5, my numberOfColumns + 0.5, 0, 1);
		double leftMargin = getLeftMargin (graphics);   // not earlier!
		double lineSpacing = getLineSpacing (graphics);   // not earlier!
		double maxTextWidth = getMaxRowLabelWidth (me, graphics, rowmin, rowmax);
		double maxTextHeight = getMaxColumnLabelHeight (me, graphics, 1, my numberOfColumns);
		Matrix_formula (original.peek(), conditionFormula, interpreter, conditions.peek());

		Graphics_setTextAlignment (graphics, Graphics_CENTRE, Graphics_BOTTOM);
		for (long icol = 1; icol <= my numberOfColumns; icol ++) {
			if (my columnLabels && my columnLabels [icol] && my columnLabels [icol] [0])
				Graphics_text (graphics, icol, 1, my columnLabels [icol]);
		}
		for (long irow = rowmin; irow <= rowmax; irow ++) {
			double y = 1 - lineSpacing * (irow - rowmin + 0.6);
			Graphics_setTextAlignment (graphics, Graphics_RIGHT, Graphics_HALF);
			if (my rowLabels && my rowLabels [irow] && my rowLabels [irow] [0])
				Graphics_text (graphics, 0.5 - leftMargin, y, my rowLabels [irow]);
			Graphics_setTextAlignment (graphics, Graphics_CENTRE, Graphics_HALF);
			for (long icol = 1; icol <= my numberOfColumns; icol ++) if (conditions -> z [irow] [icol] != 0.0) {
				wchar_t text [40];
				print4 (text, my data [irow] [icol], iformat, 0, precision);
				Graphics_text (graphics, icol, y, text);
			}
		}
		if (maxTextHeight) {
			double left = 0.5;
			if (maxTextWidth > 0.0) left -= maxTextWidth + 2 * leftMargin;
			Graphics_line (graphics, left, 1, my numberOfColumns + 0.5, 1);
		}
		Graphics_unsetInner (graphics);
	} catch (MelderError) {
		Melder_throw (me, ": numbers not drawn.");
	}
}

void TableOfReal_drawHorizontalLines (TableOfReal me, Graphics graphics, long rowmin, long rowmax) {
	long colmin = 1, colmax = my numberOfColumns;
	fixRows (me, & rowmin, & rowmax);
	Graphics_setInner (graphics);
	Graphics_setWindow (graphics, colmin - 0.5, colmax + 0.5, 0, 1);
	double lineSpacing = getLineSpacing (graphics);
	double maxTextWidth = getMaxRowLabelWidth (me, graphics, rowmin, rowmax);
	double maxTextHeight = getMaxColumnLabelHeight (me, graphics, 1, my numberOfColumns);

	double left = 0.5;
	double top = rowmin;
	if (maxTextWidth > 0.0) left -= maxTextWidth + 2 * lineSpacing;
	if (maxTextHeight > 0.0) rowmin -= 1;
	double right = colmax + 0.5;
	for (long irow = rowmin; irow < rowmax; irow ++) {
		double y = 1 - lineSpacing * (irow - top + 1);
		Graphics_line (graphics, left, y, right, y);
	}
	Graphics_unsetInner (graphics);
}