Arc AA Dimension#
Normal Angles
Right Angle
First Sector
Second Sector
Third Sector
Fourth Sector
First Sector
Fifth Sector
Sixth Sector
Seventh Sector
Eighth Sector
Fifth Sector
Arc AA Dimension Properties#
Show/Hide arc_dim_aa Attributes
PIL has a separate arc method with the following properties.
- xy
Four points to define the bounding box. Sequence of [(x0, y0), (x1, y1)] or [x0, y0, x1, y1].
- start
Starting angle, in degrees
- end
Ending angle, in degrees.
- fill
Arc colour
The arc dimension requires the following additional attributes.
- im
PIL image handle, link to the calling program
- dr
PIL drawing handle, link to the calling program
- centre
Arc's circle centre
- radius
Arc's circle radius
- begin
Starting angle, in degrees
- end
Ending angle, in degrees.
- fill
Arc colour, RGB tuple
- text
Text to be written next to the dimension
- font
Font of the text
- arrowhead
Three integer tuple describing the shape and size of the arrow
- back
background colour, RGB tuple
Create Arc AA Dimension#
The arcs used for dimensions are based on circles rather than ellipses, so use the arc centre, its radius and the start and end angles, rather than the box surrounding the circle containing the arc.
The arc dimension shows the angle directly, so no extenders are required, add the text straightaway. Use the PIL image reference, centre, radius, begin and end angles, followed by the text and its font and finally the arrow shape.
Once we have extracted the values from the tuples, calculate the coordinates of the start and end positions. Whether the arrows need to be inward or outward pointing depends on the arc size and is made automatically. Lastly position the text according to the text and arc sizes.
Add a conditional statement to draw a right angle square lines for 90° instead of an arc. If the angle becomes a straight line raise an error.
The utility function polar2cart from DimLinesPIL is particularly useful.
Show/Hide Code test_angle_aa_dim.py
import sys
sys.path.append('../dims')
from PIL import Image, ImageDraw, ImageFont
from collections import defaultdict
from math import radians, sqrt, sin, cos, tan
from DimLinesPIL import polar2cart, angled_text, int_up
from DimLinesAA import WideLineAA, findSect, LineAA, dimension_aa
def plot_sector_points(dr, xm, ym, x, y, sects, fill, all8=1):
# plots all 8 sectors or only 4 sectors in the while loop
if sects[0] < 0:
ltemp = list(sects)
ltemp[0] = -ltemp[0]
sects = tuple(ltemp)
if all8 == 1:
if sects[0] == 1 or sects[1] == 1:
dr.point((xm-x, ym+y), fill) # I Octant
elif sects[0] == 3 or sects[1] == 3:
dr.point((xm-y, ym-x), fill) # III. Octant
elif sects[0] == 5 or sects[1] == 5:
dr.point((xm+x, ym-y), fill) # V Octant
elif sects[0] == 7 or sects[1] == 7:
dr.point((xm+y, ym+x), fill) # VII. Octant
if sects[0] == 4 or sects[1] == 4:
dr.point((xm+x, ym+y), fill) # IV . Octant +x +y
elif sects[0] == 2 or sects[1] == 2:
dr.point((xm+y, ym-x), fill) # II Octant
elif sects[0] == 8 or sects[1] == 8:
dr.point((xm-x, ym-y), fill) # VIII. Octant -x +y
elif sects[0] == 6 or sects[1] == 6:
dr.point((xm-y, ym+x), fill) # VI Octant
def PartCircleAA(dr, xm, ym, r, start, finish, width, sects, fill=(0,0,0),
back=(255,255,221)):
# xm, ym = centre
# draw an antialiased circle on light background
x = -r
y = 0 # IV. Octant from left to bottom left
err = 2 - 2 * r # initial difference
sslope = abs((ym-start[1])/(xm-start[0]))
fslope = abs((ym-finish[1])/(xm-finish[0]))
# check sects
ssect = 0
fsect = 0
plot = 0
ssect, fsect = sects
if sects[0] == sects[1]:
# start, finish in one sector
plot = 0
elif (sects[0] == 0 and sects[1] in (1,3,5,7)) or \
(sects[0] in (2,4,6,8) and sects[1] == 0):
plot = 1
if sects[0] < 0:
plot = 1
maxdi = [0]
for n in range(0, width+1):
maxdi.append(maxdi[n] + 2 * (r-n) -1)
maxdi.remove(0)
maxd = maxdi[0]
# ensure inner aa working with conditions for single aa
# find maxd of smallest main circle
maxdsm = 2 * (r-width+1) - 1
# thick factor used outer main lines
thfact = (width-1)/2
def errs(comp, size,j):
return 255 if comp == 255 else int((255-comp) * j / size) + comp
diffs = defaultdict(list)
diffs = defaultdict(lambda:back, diffs)
for i in range(maxd):
if fill == (0,0,0):
diffs[i] = tuple(int(255*i/maxd) for k in range(3))
else:
diffs[i] = tuple(errs(fill[k],maxd,i) for k in range(3))
diffsm = defaultdict(list)
diffsm = defaultdict(lambda:back, diffsm)
for i in range(maxdsm):
if fill == (0,0,0):
diffsm[i] = tuple(int(255*i/maxdsm) for k in range(3))
else:
diffsm[i] = tuple(errs(fill[k],maxdsm,i) for k in range(3))
while -x > y - 1:
# actual and inverse slope
aslope = abs((-y)/(-x))
cslope = abs(-x/(y+0.2))
if ssect in (1,5) and plot == 0:
if aslope >= sslope:
plot = 1
elif fsect in (1,5) and plot == 1:
if aslope >= fslope:
plot = 0
elif fsect in (2,6) and plot == 0: # and ssect > 0:
if cslope <= fslope:
plot = 1
elif ssect in (2,6) and plot == 1:
if cslope <= sslope:
plot = 0
elif ssect in (3,7) and plot == 0:
if cslope <= sslope:
plot = 1
elif fsect in (3,7) and plot == 1:
if cslope <= fslope:
plot = 0
elif fsect in (4,8) and plot == 0:
if aslope >= fslope:
plot = 1
elif ssect in (4,8) and plot == 1:
if aslope >= sslope:
plot = 0
err0 = err
e2 = err-(2*y+1)-(2*x+1) # abs(err+2*(x+y)-2)
ea = abs(e2)
out = max(0,int(ea-thfact))
if plot == 1:
plot_sector_points(dr, xm, ym, x, y, sects, (diffs[out] if out > 0 else fill),
all8 = (1 if (xm+x, ym+y) != (xm-y, ym-x) \
or (x==-r and y == 0) else 0))
# fill out diagonals
x0 = -x
eout = abs(e2 + 2*x0 + 2*y + 2)
if eout < maxd: # and (width-1)//2 == 0
if plot == 1:
plot_sector_points(dr, xm, ym, x-1, y+1, sects, (diffs[eout] if eout > 0 else fill),
all8 = (1 if (xm+x, ym+y) != (xm-y, ym-x) else 0))
ein = e2
x0 = -x
for n in range(0, width):
ein = ein-(2*(x0-n)-1)
e0 = -ein
if n < width-2:
fact = fill
elif n == width-1:
fact = diffs[abs(int(e0-maxd*thfact/10))] if n==0 else \
diffsm[e0-maxdi[n-1]]
else:
fact = diffsm[max(0,int(abs(e0-maxdi[n])-maxdsm*thfact/10))] # e2-maxdsm
if plot == 1:
plot_sector_points(dr, xm, ym, x+n+1, y, sects, fact,
all8 = (1 if (xm+x, ym+y) != (xm-y, ym-x) else 0))
if (err0 <= y):
y += 1
err += y * 2 + 1 # e_xy+e_y < 0
if (err0 > x or err > y): # e_xy+e_x > 0 or no 2nd y-step
x += 1
# aa missed by diagonals
eout = abs(e2 + 2*y - 1)
if eout < maxd:
if plot == 1:
plot_sector_points(dr, xm, ym, x-1, y, sects, (diffs[eout] if eout > 0 else fill),
all8 = (1 if (xm+x, ym+y) != (xm-y, ym-x) else 0))
err += x * 2 + 1 # -> x-step now
def make_arc_aa(dr, centre, radius, start, finish, width=1, fill=(0,0,0), back = (255,255,221)):
xm,ym = centre
sq = findSect((xm, ym), (start[0], start[1]))
fq = findSect((xm, ym), (finish[0], finish[1]))
sects = ()
diff_sect = fq[0] - sq[0]
if diff_sect == 0:
sects = sq[0],fq[0]
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
elif (diff_sect == 1) or (sq[0] == 8 and fq[0] == 1):
sects = sq[0],0
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
sects = 0,fq[0]
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
elif (diff_sect == 2) or (sq[0] == 8 and fq[0] == 2) or (sq[0] == 7 and fq[0] == 1):
sects = sq[0],0
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
if sq[0] < 8:
sects = -sq[0]-1,-sq[0]-1
else:
sects = -1,-1
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
sects = 0,fq[0]
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
elif (diff_sect == 3) or (sq[0] == 8 and fq[0] == 3) or (sq[0] == 7 and fq[0] == 2):
sects = sq[0],0
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
if sq[0] < 7:
sects = -sq[0]-2,-sq[0]-2
else:
sects = -1,-1
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
if sq[0] < 8:
sects = -sq[0]-1,-sq[0]-1
else:
sects = -2,-2
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
sects = 0,fq[0]
PartCircleAA(dr, xm, ym, radius, start, finish, width, sects,
fill=fill, back = back)
def arc_dim_aa(im,dr,centre,radius,begin,end,fill=(0,0,0),text=None,font=None,
arrowhead=(8,10,3),back=(225,225,221),aall=0):
# x,y,radius all relate to centre coords and radius, give 2 angles
rtimes2 = max(60, radius*2)
if isinstance(begin, int):
beginp = polar2cart(centre, begin, rtimes2)
if isinstance(end, int):
endp = polar2cart(centre, end, rtimes2)
if isinstance(begin, tuple):
beginp = begin
begin, rayb = cart2polar(centre, begin)
if isinstance(end, tuple):
endp = end
end, raye = cart2polar(centre, end)
beginr = radians(begin)
endr = radians(end)
bq = findSect(centre, beginp)
eq = findSect(centre, endp)
if bq[1] in (3,4) and eq[1] in (1,2):
alpha = (360 - begin + end)/2
diff = 360 - begin + end
else:
alpha = (begin + end)/2
diff = end - begin
if diff == 180:
raise Exception('arc_dim_aa: angle is 180°, begin {} end {}' \
' difference {} cannot draw dimension'.format(begin, end, diff))
if diff == 90:
ax, ay = polar2cart(centre, begin, radius)
bx, by = polar2cart(centre, end, radius)
dx, dy = polar2cart(centre, alpha, radius*sqrt(2))
LineAA(dr, (ax,ay), (dx,dy), fill=fill, back=back)
LineAA(dr, (bx,by), (dx,dy), fill=fill, back=back)
else:
x, y = centre
d1, d2, d3 = arrowhead
# placement of arrows, 'first' point inwards
order = 'last' if radians(diff) * radius > 4 * arrowhead[1] else 'first'
# find begin and end arc
start = int_up(x + radius * cos(beginr)), int_up(y + radius * sin(beginr))
finish = int_up(x + radius * cos(endr)), int_up(y + radius * sin(endr))
dimension_aa(im,dr, start, angle=(begin - 90), arrow=order,fill=fill,back=back)
dimension_aa(im,dr, finish, angle=(end + 90), arrow=order,fill=fill,back=back)
start_arc = polar2cart(start, (begin + 90), d1)
finish_arc = polar2cart(finish, end - 90, d1)
if order == 'first':
make_arc_aa(dr, centre, radius, beginp, endp, fill=fill, back=back)
else:
make_arc_aa(dr, centre, radius, start_arc, finish_arc, fill=fill, back=back)
# placement of text
if text is None:
text = str(diff) + '°'
if font is None:
font_size=15
font = ImageFont.truetype('consola.ttf', font_size)
# (wide, ht) = font.getsize(text)
unused1, unused2, wide, ht = font.getbbox(text)
# stop upside down text
if bq[1] in (3,4) and eq[1] in (1,2):
alpha = begin + alpha -360
angle = alpha - 90
da = 7
if diff == 90:
X, Y = polar2cart(centre, alpha, radius * sqrt(2) + da)
else:
t = tan(radians(diff/2))
a = wide/ 2 / t
size = max(radius, a)
X, Y = polar2cart(centre, alpha, size + ht/2+da) # alpha
angled_text(im, (X, Y), text, angle, font, aall=aall)
if __name__ == "__main__":
Xm = 101 #w//2
Ym = 101 # h//2
Radius = 30
w, h = 201, 201
Back = (255,255,221)
image = Image.new('RGB', (w,h), Back) #'#FFFFDD'
drawl = ImageDraw.Draw(image)
beg = 260
Diff = 105
e = beg + Diff if beg + Diff < 360 else beg + Diff - 360
#e = 15
left = polar2cart((Xm,Ym), beg, Radius*2)
right = polar2cart((Xm,Ym), e, Radius*2)
#print((beg+e)/2)
#al = polar2cart((Xm,Ym), (beg+e)/2, Radius*2)
#drawl.line([al,(Xm,Ym)], fill ='red')
WideLineAA(drawl, left, [Xm,Ym], fill=(0,0,255), width=2, back=Back)
WideLineAA(drawl, right, [Xm,Ym], fill=(0,0,255), width=2, back=Back)
arc_dim_aa(image, drawl, (Xm, Ym), Radius, beg, e, fill=(0,0,0),
back = Back)
image.show()
#image.save('../../temp/arc_dim_'+ str(beg)+'_'+str(diff)+'.png')