Question

Draw the letters A and B of English alphabet using multiple Bezier curves.

Answer 1

Solution:

Note: I am writing the code in python. Please make sure about proper indentation.

def make_bezier(xys):
    # xys should be a sequence of 2-tuples (Bezier control points)
    n=len(xys)
    combinations=pascal_row(n-1)
    def bezier(ts):
        # This uses basic general formula for bezier curves
        # http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Generalization
        result=[]
        for t in ts:
            tpowers=(t**i for i in range(n))
            upowers=reversed([(1-t)**i for i in range(n)])
            coefs=[c*a*b for c,a,b in zip(combinations,tpowers,upowers)]
            result.append(
                tuple(sum([coef*p for coef,p in zip(coefs,ps)]) for ps in zip(*xys)))
        return result
    return bezier

def pascal_row(n):
    # This returns the nth row of Pascal's Triangle
    result=[1]
    x,numerator=1,n
    for denominator in range(1,n//2+1):
        # print(numerator,denominator,x)
        x*=numerator
        x/=denominator
        result.append(x)
        numerator-=1
    if n&1==0:
        # n is even
        result.extend(reversed(result[:-1]))
    else:
        result.extend(reversed(result)) 
    return result
        
import Image
import ImageDraw
        
if __name__=='__main__':
        im = Image.new('RGBA', (100, 100), (0, 0, 0, 0)) 
        draw = ImageDraw.Draw(im)
        ts=[t/100.0 for t in range(101)]

        xys=[(0,100),(25,50),(50,0)]
        bezier=make_bezier(xys)
        points=bezier(ts)

        xys=[(50,0),(75,50),(100,100)]
        bezier=make_bezier(xys)
        points.extend(bezier(ts))

        xys=[(100,100),(85,75),(75,50)]
        bezier=make_bezier(xys)
        points.extend(bezier(ts))

        xys=[(75,50),(50,50),(25,50)]
        bezier=make_bezier(xys)
        points.extend(bezier(ts))
        
draw.polygon(points,fill=None,outline='red')
im.save('LetterA.png')

#letter B

im = Image.new('RGBA', (100, 100), (0, 0, 0, 0)) 
draw = ImageDraw.Draw(im)
ts=[t/100.0 for t in range(101)]

xys=[(0,0),(0,50),(0,100)]
bezier=make_bezier(xys)
points=bezier(ts)

xys=[(0,100),(100,100),(0,50)]
bezier=make_bezier(xys)
points.extend(bezier(ts))

draw.polygon(points,fill=None,outline='red')
im.save('LetterB.png')