By the way, a solution doesn't even need to use any trigonometry, because a squared-off miter joint is by-definition orthogonal to the line. Here's some proof-of-concept code:
def rndint(x): return int(round(x))
def cappedline(surface, color, p0,p1, width=1, rounded=True):
radius = width * 0.5
delta = ( p1[0]-p0[0], p1[1]-p0[1] )
orthog = [ delta[1], -delta[0] ]
scale = radius / (orthog[0]*orthog[0] + orthog[1]*orthog[1])**0.5
orthog[0]*=scale; orthog[1]*=scale
points = [
( p0[0]-orthog[0], p0[1]-orthog[1] ),
( p0[0]+orthog[0], p0[1]+orthog[1] ),
( p1[0]+orthog[0], p1[1]+orthog[1] ),
( p1[0]-orthog[0], p1[1]-orthog[1] )
]
pygame.draw.polygon(surface, color, points)
if rounded:
#Could have added these to the polygon points instead, but then we'd have had to choose a subdivision accuracy.
pygame.draw.circle(surface, color, (rndint(p0[0]),rndint(p0[1])), rndint(radius))
pygame.draw.circle(surface, color, (rndint(p1[0]),rndint(p1[1])), rndint(radius))
pygame.draw.cappedline = cappedline
Note that this also supports rounded corners by drawing circles on the ends, although this is rather limited by the (poor) accuracy of the circle drawing routine, and doesn't look fabulous at small widths.