Useful math functions

Lines

Line equation

• Python
• C++

• def compute_line(p1:tuple, p2:tuple):
  	"""Compute line equation : ax + by = c"""
  	a = p2[1] - p1[1]
  	b = p1[0] - p2[0]
  	c = p1[0] * (p2[1] - p1[1]) - p1[1] * (p2[0] - p1[0])
  	return a,b,c
  

• // To be done
  

Line evaluation

• Python
• C++

• def evaluate_line(l:tuple, x:float) -> float:
  	"""Evaluate the line in 'x'
  
  	Args:
  		l (tuple): (a, b, c) for ax + by = c
  		x (float): x to be evaluated
  
  	Returns:
  		float: line value in x
  	"""
  	if l[1] != 0:
  		return (l[2] - l[0] * x) / l[1]
  	else:
  		return x
  

• // To be done
  

Itersections

Lines intersections

• Python
• C++

• def compute_line_inter(l1:tuple, l2:tuple) -> tuple|bool:
  	"""Find the intersection point between two lines if it exists (ax + by = c)"""
  	a1, b1, c1 = l1
  	a2, b2, c2 = l2
  	d = a1*b2 - a2*b1
  	if d:
  		x = (c1*b2 - c2*b1)/d
  		y = (a1*c2 - a2*c1)/d
  		return x, y
  	return False
  

• // To be done
  

Segments intersection

• Python
• C++

• python def compute_segment_inter(p11:tuple, p12:tuple, p21:tuple, p22:tuple) -> tuple|bool: """Find the intersection point between two segment if it exists""" l1 = compute_line(p11, p12) l2 = compute_line(p21, p22) p_inter = compute_line_inter(l1, l2) if p_inter: if point_in_box(p_inter, p11, p12): if point_in_box(p_inter, p21, p22): return p_inter return False

• // To be done
  

Circles intersections

• Python
• C++

• def compute_circle_inter(p1:tuple, r1:float, p2:tuple, r2:float) -> tuple|None:
  	"""Find the intersection point between two circle if it exists"""
  	d = distance(p1, p2)
  	if d >= (r1 + r2):
  		print("No circle intersection found (d >= (r1 + r2)) ! Returned None")
  		return None
  	if d <= abs(r1 - r2):
  		print("No circle intersection found (d < abs(r1 - r2)) ! Returned None")
  		return None
  	if d < 1e-6 and abs(r1 - r2) < 1e-6:
  		print("No circle intersection found (abs(r1 - r2) < 1e-6) ! Returned None")
  		return None
  	
  	# https://lucidar.me/fr/mathematics/how-to-calculate-the-intersection-points-of-two-circles/
  	a = (r1**2 - r2**2 + d**2)/(2*d)
  	# print(p1, r1, p2, r2, d, a)
  	h = sqrt(r1**2 - a**2)
  
  	x5 = p1[0] + (a / d) * (p2[0] - p1[0]) 
  	y5 = p1[1] + (a / d) * (p2[1] - p1[1]) 
  
  	xi1 = x5 - h * (p2[1] - p1[1])/d
  	yi1 = y5 + h * (p2[0] - p1[0])/d
  
  	xi2 = x5 + h * (p2[1] - p1[1])/d
  	yi2 = y5 - h * (p2[0] - p1[0])/d
  
  	pi1 = (xi1, yi1)
  	pi2 = (xi2, yi2)
  	return pi1, pi2
  

• // To be done
  

Segment - rectangle intersection

• Python
• C++

• def compute_segment_rect_inter(line:tuple, line_p1:tuple, line_p2:tuple, rect:list) -> tuple|bool:
  	"""Compute the intersection between two segment
  
  	Args:
  		line (tuple): Line
  		line_p1 (tuple): First point of the segment defined by the line
  		line_p2 (tuple): Second point of the segment defined by the line
  		rect (list): List of point of a rect (x1, y1, x2, y2)
  
  	Returns:
  		bool: If the two segment collide
  	"""
  	# rect = (x1, y1, x2, y2) avec p1 top-left et p2 bottom-right 
  	points = [(rect[0], rect[1], rect[0], rect[3]),
  				(rect[0], rect[3], rect[2], rect[3]),
  				(rect[2], rect[3], rect[2], rect[1]),
  				(rect[2], rect[1], rect[0], rect[1])]
  	for p1x, p1y, p2x, p2y in points:
  		p1 =(p1x, p1y)
  		p2 =(p2x, p2y)
  
  		line_rect = compute_line(p1, p2)
  		intersection = compute_line_inter(line, line_rect)
  
  		if intersection is not False:
  			if point_in_box(intersection, p1, p2):
  				if point_in_box(intersection, line_p1, line_p2):
  					return intersection
  	
  	return False
  

• // To be done
  

Point in shapes

Point in box

• Python
• C++

• def point_in_box(p:tuple, p1:tuple, p2:tuple, error_offset:float = 1e-6) -> bool:
  	"""Check if the point 'p' is in the box defined by p1 and p2
  
  	Args:
  		p (tuple): Point to be checked
  		p1 (tuple): First point
  		p2 (tuple): Second point
  		error_offset (float, optional): Error offset to overcome python binary error on float. Defaults to 1e-6.
  
  	Returns:
  		bool: If the point is in the box
  	"""
  	if p[0] > min(p1[0], p2[0]) - error_offset and p[0] < max(p2[0], p1[0]) + error_offset:
  		if p[1] > min(p1[1], p2[1]) - error_offset and p[1] < max(p2[1], p1[1]) + error_offset:
  			return True
  	return False
  

• // To be done
  

Point in circle

• Python
• C++

• def point_in_circle(p:tuple, center:tuple, radius:float) -> bool:
  	"""Check if the point is in the circle"""
  	if distance(p, center) <= radius:
  		return True
  	return False
  

• // To be done
  

Point in polygon

• Python
• C++

• def point_in_polygon(point:tuple, polygon:list[tuple]) -> bool:
  	"""Check if the point is in the polygon
  
  	Args:
  		point (tuple): Point to be checked
  		polygon (list): List of point defining the polygon
  	"""
  	x, y = point
  	n = len(polygon)
  	inside = False
  	p1x, p1y = polygon[0]
  	for i in range(1, n + 1):
  		p2x, p2y = polygon[i % n]
  		if y > min(p1y, p2y):
  			if y <= max(p1y, p2y):
  				if x <= max(p1x, p2x):
  					if p1y != p2y:
  						xinters = (y - p1y) * (p2x - p1x) / (p2y - p1y) + p1x
  					if p1x == p2x or x <= xinters:
  						inside = not inside
  		p1x, p1y = p2x, p2y
  	return inside
  

• // To be done
  

Tab example

Title

• Python
• C++

• # To be done
  

• // To be done