Rounded Pentagram: Pseudo Fourier Series Animation Using Gnuplot-Hiro's Soliloquy

Contents[hide]

1.YouTube
2.Equations of the curve
3.Simulation [gnuplot]
- 3.1.Source code (PLT file)
- 3.2.Output (PNG file → GIF file)
4.Extra: Pseud-Fourier series animation
- 4.1.Source code (PLT file)
- 4.2.Output (PNG file → GIF file)
5.Referece

YouTube

Equations of the curve

$\begin{cases} x(t)=2\sin 2t - \cos 3t\\ y(t)=\sin 3t - 2 \cos 2t \end{cases}$

Simulation [gnuplot]

Source code (PLT file)

	reset
	set angle degrees

	#=================== Parameter ====================
	# Parameters in drawing
	psPoint = 2 # ps = point size
	lwTrajectory = 2 # lw = line width
	lcPoint = 6 # lc = line color
	numPNG = 0
	LOOP = 3

	DEG_DIV = 1.0 # Resolution of degree, increase by 1/DEG_DIV
	roundNum = 2

	# Select terminal type
	qtMode = 1 # ==1: qt (simulator) / !=1: png (output images for making video)
	print sprintf("[MODE] %s", (qtMode==1 ? 'Simulate in Qt window' :'Output PNG images'))

	#=================== Function ====================
	# Parametric equations of a curve
	x(t) = 2sin(2t)-cos(3*t)
	y(t) = sin(3t)-2cos(2*t)

	# Show the value of the parameter t
	showT(t) = sprintf("{/:Italic t} = %3.1f deg", t)

	#=================== Setting ====================
	if(qtMode==1){
	set term qt size 720, 720 font 'Times'
	} else {
	set term pngcairo size 720, 720 font 'Times'
	folderName = 'png'
	system sprintf('mkdir %s', folderName)
	}

	unset key
	set grid
	set size ratio -1
	set xlabel '{/:Italic x}' font ', 20'
	set ylabel '{/:Italic y}' font ', 20'
	set tics font ', 18'

	# Round off to the i decimal place.
	round(x, i) = 1 / (10.*(i+1)) floor(x * (10.**(i+1)) + 0.5)

	#=================== Calculation ====================
	# Output: "draw_trajectory.txt" is need for plotting the curve.
	dataTrajectory = 'draw_trajectory.txt'
	print sprintf('Start outputting %s ...', dataTrajectory)
	set print dataTrajectory

	# Write items and parameters in outputfile
	print sprintf("# %s", dataTrajectory)
	print sprintf('# DEG_DIV=%d', DEG_DIV)
	print '# t / x / y'

	# Calculate and output the trajectory of the curve
	do for[i=0:360*DEG_DIV:1]{
	t = i/DEG_DIV
	print round(t, roundNum), round(x(t), roundNum), round(y(t), roundNum)
	}

	unset print
	print sprintf('Finish!')

	#=================== Plot ====================
	if(qtMode == 1) {
	print "Start simulation"
	} else {
	print sprintf('Start outputting %d images ...', LOOP(1+360DEG_DIV))
	}

	plotRange = 4
	end(loop, i) = (loop>0) ? 360*DEG_DIV : i

	do for [n=0:LOOP-1:1]{
	do for [i=0:360*DEG_DIV:1]{
	if(qtMode != 1) {
	set output sprintf("%s/img_%04d.png", folderName, numPNG)
	numPNG = numPNG + 1
	}

	# Get the value of time from dataTrajectory
	set yrange [:] # This command enables to remove restrictions on the range of the stats command.
	stats dataTrajectory using 1 every ::i::i nooutput
	theta = STATS_max
	set title showT(theta) left offset screen -0.07, -0.01 font ', 20'

	plot[-plotRange:plotRange][-plotRange:plotRange] \
	dataTrajectory using 2:3 every ::i::i with p ps psPoint pt 7 lc lcPoint, \
	dataTrajectory using 2:3 every ::0::end(n, i) with line lw lwTrajectory lc lcPoint

	if(qtMode == 1) {
	if((n==0 && i==0) \|\| n==LOOP-1 && i==360*DEG_DIV) {
	pause 2 # Wait a few seconds
	}
	pause 0.001 # Adjust the drawing speed
	} else {
	set out # terminal pngcairo
	}
	}
	}

	# Output the curve
	set term pngcairo size 720, 720 font 'Times'
	set output "trajectory_plot.png"
	plot[-plotRange:plotRange][-plotRange:plotRange] \
	dataTrajectory using 2:3 every ::0::360*DEG_DIV with line lw lwTrajectory lc lcPoint
	set out
	print sprintf('Finish this program')

view raw rounded_pentagram.plt hosted with ❤ by GitHub

Output (PNG file → GIF file)

Extra: Pseud-Fourier series animation

Source code (PLT file)

	reset
	set angle degrees

	#=================== Parameter ====================
	# Parameters in drawing
	psPoint = 2 # ps = point size
	lwCircle = 2 # lw = line width
	lwCursor = 2
	lwTrajectory = 2
	lcCursor = -1 # lc = line color
	lcPoint = 6
	lcCircle1 = 2
	lcCircle2 = 4
	numPNG = 0
	LOOP = 3

	DEG_DIV = 1.0 # Resolution of degree, increase by 1/DEG_DIV
	roundNum = 2
	plotRange = 10 # Set the range of x/y axis [-plotRange:plotRange]
	offsetXtCircle = -6.5 # Offset of the center of circles plotting a curve
	offsetYtCircle = -6.5

	# Select terminal type
	qtMode = 0 # ==1: qt (simulator) / !=1: png (output images for making video)
	print sprintf("[MODE] %s", (qtMode==1 ? 'Simulate in Qt window' :'Output PNG images'))

	#=================== Function ====================
	# Parametric equations of a curve
	x(t) = 2sin(2t)-cos(3*t)
	y(t) = sin(3t)-2cos(2*t)

	# Show the value of the parameter t
	showT(t) = sprintf("{/:Italic t} = %3.1f deg", t)

	#=================== Setting ====================
	if(qtMode==1){
	set term qt size 720, 720 font 'Times'
	} else {
	set term pngcairo size 720, 720 font 'Times'
	folderName = 'png_with_circles'
	system sprintf('mkdir %s', folderName)
	}

	unset key
	set grid
	set size ratio -1
	set xlabel '{/:Italic x}' font ', 20'
	set ylabel '{/:Italic y}' font ', 20'
	set tics font ', 18'

	# Round off to the i decimal place.
	round(x, i) = 1 / (10.*(i+1)) floor(x * (10.**(i+1)) + 0.5)

	#=================== Calculation ====================
	# Output: "draw_trajectory.txt" is need for plotting the curve.
	dataTrajectory = 'draw_trajectory.txt'
	print sprintf('Start outputting %s ...', dataTrajectory)
	set print dataTrajectory

	# Write items and parameters in outputfile
	print sprintf("# %s", dataTrajectory)
	print sprintf('# DEG_DIV=%d', DEG_DIV)
	print '# t / x / y'

	# Calculate and output the trajectory of the curve
	do for[i=0:360*DEG_DIV:1]{
	t = i/DEG_DIV
	print round(t, roundNum), round(x(t), roundNum), round(y(t), roundNum)
	}

	unset print
	print sprintf('Finish!')

	#=================== Plot ====================
	if(qtMode == 1) {
	print "Start simulation"
	} else {
	print sprintf('Start outputting %d images ...', LOOP(1+360DEG_DIV))
	}

	end(loop, i) = (loop>0) ? 360*DEG_DIV : i

	do for [n=0:LOOP-1:1]{
	do for [i=0:360*DEG_DIV:1]{
	if(qtMode != 1) {
	set output sprintf("%s/img_%04d.png", folderName, numPNG)
	numPNG = numPNG + 1
	}

	# Get the value of time from either of txt files
	set yrange [:] # This command enables to remove restrictions on the range of the stats command.
	stats dataTrajectory using 1 every ::i::i nooutput
	theta = STATS_max
	set title showT(theta) left offset screen -0.07, -0.01 font ', 20'

	# Circles drawing x(t) and locating on the y-axis
	# x(t) = 2sin(2t)-cos(3*t)
	cx1_x = 0 + 2sin(2theta)
	cx1_y = offsetXtCircle + 2cos(2theta)
	cx2_x = cx1_x - cos(3*theta)
	cx2_y = cx1_y - sin(3*theta)
	set object 1 circle at 0, offsetXtCircle size 2 fs empty border lt lcCircle1 lw lwCircle
	set object 2 circle at cx1_x, cx1_y size 1 fs empty border lt lcCircle2 lw lwCircle
	set arrow 1 nohead from 0, offsetXtCircle to cx1_x, cx1_y lt lcCircle1 lw lwCircle
	set arrow 2 nohead from cx1_x, cx1_y to cx2_x, cx2_y lt lcCircle2 lw lwCircle
	set object 3 circle at cx1_x, cx1_y size 0.1 fs solid fc lt lcCircle1 lw lwCircle front
	set object 4 circle at cx2_x, cx2_y size 0.1 fs solid fc lt lcCircle2 lw lwCircle front
	set arrow 3 nohead from cx2_x, cx2_y to cx2_x, plotRange lt lcCursor lw lwCursor
	# set arrow 3 nohead from cx2_x, cx2_y to x(theta), y(theta) lt lcCursor lw lwCursor

	# Circles drawing y(t) and locating on the x-axis
	# y(t) = sin(3t)-2cos(2*t)
	cy1_x = offsetYtCircle + cos(3*theta)
	cy1_y = 0 + sin(3*theta)
	cy2_x = cy1_x - 2sin(2theta)
	cy2_y = cy1_y - 2cos(2theta)
	set object 5 circle at offsetYtCircle, 0 size 1 fs empty border lt lcCircle1 lw lwCircle
	set object 6 circle at cy1_x, cy1_y size 2 fs empty border lt lcCircle2 lw lwCircle
	set arrow 4 nohead from offsetYtCircle, 0 to cy1_x, cy1_y lt lcCircle1 lw lwCircle
	set arrow 5 nohead from cy1_x, cy1_y to cy2_x, cy2_y lt lcCircle2 lw lwCircle
	set object 7 circle at cy1_x, cy1_y size 0.1 fs solid fc lt lcCircle1 lw lwCircle front
	set object 8 circle at cy2_x, cy2_y size 0.1 fs solid fc lt lcCircle2 lw lwCircle front
	set arrow 6 nohead from cy2_x, cy2_y to plotRange, cy2_y lt lcCursor lw lwCursor
	# set arrow 6 nohead from cy2_x, cy2_y to x(theta), y(theta) lt lcCursor lw lwCursor

	plot[-plotRange:plotRange][-plotRange:plotRange] \
	dataTrajectory using 2:3 every ::i::i with p ps psPoint pt 7 lc lcPoint, \
	dataTrajectory using 2:3 every ::0::end(n, i) with line lw lwTrajectory lc lcPoint

	if(qtMode == 1) {
	if((n==0 && i==0) \|\| n==LOOP-1 && i==360*DEG_DIV) {
	pause 2 # Wait a few seconds
	}
	pause 0.001 # Adjust the drawing speed
	} else {
	set out # terminal pngcairo
	}
	}
	}

	# Output the curve
	set term pngcairo size 720, 720 font 'Times'
	set output "trajectory_plot_with_circles.png"
	plot[-plotRange:plotRange][-plotRange:plotRange] \
	dataTrajectory using 2:3 every ::360DEG_DIV::360DEG_DIV with p ps psPoint pt 7 lc lcPoint, \
	dataTrajectory using 2:3 every ::0::360*DEG_DIV with line lw lwTrajectory lc lcPoint
	set out
	print sprintf('Finish this program')