Solves a geometry problem using linear algebra and Heron's formula

redflag.jl

#=
Solves a geometry problem using linear algebra and Heron's formula
See: Red Flag Day Geometry

using Revise
Load with: includet("redflag.jl")

=#

using LinearAlgebra


"""
p_int = line_intersect(p,q,r,s)

Point of intersection of two lines

Paramterrs:
  
  p: Point on line 1, 2x1 Vector
  
  q: Vector direction of line 1, 2x1 Vector
  
  r: Point on line 2, 2x1 Vector
  
  s: Vector direction of line 2, 2x1 Vector
  
Returns:
  
  p_int: Point of intersection of the two lines

"""
function line_intersect(p::Vector{},q::Vector{},r::Vector{},s::Vector{})
	# Check that all inputs are length 3
	if length(p) == 2
		push!(p,0)
	end
	if length(q) == 2
		push!(q,0)
	end
	if length(r) == 2
		push!(r,0)
	end
	if length(s) == 2
		push!(s,0)
	end

	# Bezier parameter for point of intersection
	u = norm(cross(r-p,s))/norm(cross(q,s))
	
	# Point of intersection
	p_int = p + u * q
	
	# Remove zero from third dimension
	pop!(p)
	pop!(q)
	pop!(r)
	pop!(s)
	pop!(p_int)
	
	# Return the vector
	return p_int
	
end
	
"""
A = herons(v1,v2,v3)
	
Returns the area of a triangle using Heron's formula

Paramterrs:

	v1,v2,v3: Vertices of the triangle, 2x1
	
Returns:
	A: Area of the triangle

"""
function herons(v1::Vector{}, v2::Vector{}, v3::Vector{})
	# Lengths of each side
	a = norm(v2 - v1)
	b = norm(v3 - v2)
	c = norm(v1 - v3)
	
	# Semiperimter 
	s = (a + b + c)/2
	
	# Triangle area
	A = sqrt(s*(s-a)*(s-b)*(s-c))
	
	return A
end