Python script that renders a triangle by testing to see if a point is inside the triangle.

triangles.py

import sys,os,math

def distance(p1,p2):
    return abs(math.sqrt( (p2[0]-p1[0])**2 + (p2[1]-p1[1])**2  ))

def getAngle(s1,s2,s3):
    try:
        return math.acos( round((s1**2 + s2**2 - s3**2)/(2*s1*s2),3) ) * (180 / math.pi)
    except:
        return 2

def isInside(triangle,p):

    AB = distance(triangle[0],triangle[1])
    BC = distance(triangle[1],triangle[2])
    CA = distance(triangle[2],triangle[0])

    c = getAngle(AB,BC,CA)
    b = getAngle(CA,AB,BC)
    a = getAngle(BC,CA,AB)

    AP = distance(triangle[0],p)
    BP = distance(triangle[1],p)
    CP = distance(triangle[2],p)

    pa = getAngle(AP,AB,BP)
    pb = getAngle(BC,BP,CP)
    pc = getAngle(CP,CA,AP)

    #print("%f %f %f" % (pa,pb,pc))

    if pa > 90 or pa < 0:
        return False
    if pb > 90 or pb < 0:
        return False
    if pc > 90 or pc < 0:
        return False
    return True

def main():

    WIDTH = 200
    HEIGHT = 200

    a = (0,0)
    b = (10,10)
    c = (15,0)

    inside_point = (5,2)
    outside_point = (-10,0)

    triangle = (a,b,c);


    f=open("out.pgm","w")

    f.write("P2\n")
    f.write("# out.pgm\n")
    f.write(str(WIDTH*2)+ " " + str(HEIGHT*2) + "\n")
    f.write("15\n")
    for h in range(-HEIGHT,HEIGHT):
        for w in range(-WIDTH,WIDTH):
            color = None
            if isInside(triangle,(h,w)):
                color = 9
            else:
                color = 1
            f.write(str(color))

            if w!=WIDTH-1:
                f.write(" ")
            
            
        f.write("\n")
    print("Done")
            

if __name__ == "__main__":
    main()