Programming a figure in Python, even offline

"""
Animation inspired from Vincent Pantaloni in this article (in french) : https://afdm.apmep.fr/rubriques/ouvertures/mathematiques-du-jonglage/
"""

ph = addCalc('ph', '0') # Adds to the MathGraph32 figure a calculation, calculation whose value will be changed in function draw, creating the animation.
n_balls = addCalc('nballs', '5') # Adds to the figure a real calculation xith name nballs. Modifiable but ust be odd and >= 3
nballs = getValue(n_balls) #Returns the current value of MathGraph32 calculation nballs
valph = 0
def draw(): # Function used for the animation, changing the formula of MathGraph32 calculation ph and recalculating and updating all the objects depending on ph
	global valph
	valph += 0.0075
	giveFormulaTo('ph', str(valph))
	updateDependantDisplay(ph) # We recalculate and redraw only the objects depending on calculation ph
	
dimf = getFigDim() # Returns a list containing the dimension of the working wiindow (SVG) in pixels
width = dimf[0]
height = dimf[1]
zoomFig(width/2, height/2, 2) # We apply a zoom of factor 2 on the figure
addTimerButton(draw, 1/60) # Adds a Start - Stop button that will call function draw every 1/60 second
O = getPointByName('O') # We memorize point O , frame origin as a point object (faster to use the object rather than its name in the following code)
setAngleUnity('radian') # We set radian unity on our figure
# Strating creating fixed objects of the figure (objects not depending on ph)
head_0 = addPointXY(0, 2)
setHidden(head_0)
head_radius = 0.7
head = addCircleOr(head_0, head_radius, 'black', '-', 2)
head_0_position = getPointPosition(head_0)
head_base = addPointXY(head_0_position.x, head_0_position.y - head_radius)
setHidden(head_base)

spine_base = addPointXY(0, head_0_position.y - 4)
setHidden(spine_base)
torso = addSegment(head_base, spine_base, 'black', '-', 2)

shoulder_y = head_0_position.y - 1.5
l_shoulder = addPointXY(1.25, shoulder_y, '', 'black', 'O')
r_shoulder = addPointXY(-1.25, shoulder_y, '', "black", 'O')

shoulders = addSegment(l_shoulder, r_shoulder, 'black', '-', 2)
up_arm_0 = addPointXY(0.0, -1.0)
setHidden(up_arm_0)
    
l_arm_ph = addCalc('larmph', 'mod(nballs * ph,1)')
l_arm_th = addCalc('larmth', '2.0 * pi * larmph')

l_up_th = addCalc('lupth', '-0.25 * larmph * sin(larmth)')
v_l_up_arm = addImPointRotation(up_arm_0, O, l_up_th)
setHidden(v_l_up_arm)
l_elbow = addImPointTranslation(v_l_up_arm, O, l_shoulder)

l_forearm_x = addCalc('lforearmx', '-0.75 * cos(larmth)')
l_forearm_y = addCalc('lforearmy', '0.5 * (sin(larmth) - 0.8)')

v_l_forearm = addPointXY(l_forearm_x, l_forearm_y)
setHidden(v_l_forearm)
l_hand = addImPointTranslation(v_l_forearm, O, l_elbow)
mesabsleft = addXMeasure(l_hand, 'masabsleft')
mesordleft = addYMeasure(l_hand, 'masordleft')
l_hand_comp = addCalcComp('lhand', 'masabsleft + i*masordleft')

l_up_arm = addSegment(l_shoulder, l_elbow, 'green', '-', 2)
l_forearm = addSegment(l_elbow, l_hand, 'green', '-', 2)

r_arm_ph = addCalc('rarmph', 'mod(larmph + 0.5, 1)')
r_arm_th = addCalc('rarmth', '2.0 * pi * rarmph')

r_up_th = addCalc('rupth', '0.25 * rarmph * sin(rarmth)')

v_r_up_arm = addImPointRotation(up_arm_0, O, r_up_th)
setHidden(v_r_up_arm)
r_elbow = addImPointTranslation(v_r_up_arm, O, r_shoulder)

r_forearm_x = addCalc('rforearmx', '0.75 * cos(rarmth)')
r_forearm_y = addCalc('rforearmy', '0.5 * (sin(rarmth) - 0.8)')
v_r_forearm = addPointXY(r_forearm_x, r_forearm_y)
setHidden(v_r_forearm)
r_hand = addImPointTranslation(v_r_forearm, O, r_elbow)
mesabsright = addXMeasure(r_hand, 'mesabsright')
mesordright = addYMeasure(r_hand, 'mesordright')
r_hand_comp = addCalcComp('rhand', 'mesabsright+i*mesordright')
r_up_arm = addSegment(r_shoulder, r_elbow, 'red', '-', 2)
r_forearm = addSegment(r_elbow, r_hand, 'red', '-', 2)
# Fin de la création des objest fixes de la figure (qui ne dépendent pas de h)

ball_colors = ["blue", "green", "red", "#ffbf00", "cyan"]

# In this function, MathGraph3n calculation objects must be assigned names depending  on i, because otherwise we will have errors of same name assigned to several calculations
def make_ball(i):
	stri = str(i)
	j = 'j' + stri # Name of the calculation that represents the current i value in the following MathGraph32 calculations
	addCalc(j, stri)
	ballph = 'ballph' + stri # Nom de calcul dans mtg32
	ball_ph = addCalc(ballph, f"mod(2.0 * (ph * nballs + {j}),nballs * 2)") 
	airph = 'airph' + stri # Calculation name in mtg32
	# f followed by " is used to insert in  string between "" the content of variables with name inside of brackets. So {j} insert the content of j string variable in the string
	air_ph = addCalc(airph, f"mod({ballph}, nballs) / (nballs - 1)")
	airltorx = 'airltorx' + stri  # Nom de calcul dans mtg32
	air_l_to_r_x = addCalc(airltorx, f"0.5 - {airph} * 2.5")
	airrtolx = 'airrtolx' + stri # Nom de calcul dans mtg32
	air_r_to_l_x = addCalc(airrtolx, f"-0.5 + {airph} * 2.5")
	airy = 'airy' + stri # Nom de calcul dans mtg32
	air_y = addCalc(airy, f"2 + 1.0 - 15.0 * ({airph} - 0.5)^2")
	airltor = 'airltor' + stri # Nom de calcul complexe dans mtg32
	air_l_to_r = addCalcComp(airltor, f"{airltorx}+i*{airy}")
	airrtol = 'airrtol' + stri # Nom de calcul complexe dans mtg32
	air_r_to_l = addCalcComp(airrtol, f"{airrtolx}+i*{airy}")
	# Here under we define a complex formula vald for MathGraph32 (if we  want our figure to be dynamic we must not use Python if condition)
	forcalc = f"if({ballph} <= nballs - 1, {airltor}, if({ballph} <= nballs ,rhand, if({ballph} <= 2*nballs - 1,{airrtol}, lhand)))"

	color = ball_colors[i % 5]
	point = addPointZ(f"{forcalc}", '') # The point is defined by its complex affix given bu formula forcalc
	setHidden(point)
	circle = addCircleOr(point, 0.15, 'black', '-', 2)
	return addSurface(circle, color, 'fill')

for i in range(nballs):
    make_ball(i)