I had previously done a series of posts on polygon offset intended as a practical guide for accomplishing the task quickly. Some kind folks pointed out that I was making things considerably harder than necessary by using trigonometric functions when vector math would be easier and less error prone.

A coworker lent me his Java code that does polygon offset. I translated it into python (2.5) using the pyeuclid module:

import euclid as eu

import copy

OFFSET = 0.15

# coordinates

# PT 1

MONASTERY = [(1.1, 0.75),

# PT 2

(1.2, 1.95),

. . .

# PT 21

(1.1, 0.75)]

def scaleadd(origin, offset, vectorx):

"""

From a vector representing the origin,

a scalar offset, and a vector, returns

a Vector3 object representing a point

offset from the origin.

(Multiply vectorx by offset and add to origin.)

"""

multx = vectorx * offset

return multx + origin

def getinsetpoint(pt1, pt2, pt3):

"""

Given three points that form a corner (pt1, pt2, pt3),

returns a point offset distance OFFSET to the right

of the path formed by pt1-pt2-pt3.

pt1, pt2, and pt3 are two tuples.

Returns a Vector3 object.

"""

origin = eu.Vector3(pt2[0], pt2[1], 0.0)

v1 = eu.Vector3(pt1[0] - pt2[0],

pt1[1] - pt2[1], 0.0)

v1.normalize()

v2 = eu.Vector3(pt3[0] - pt2[0],

pt3[1] - pt2[1], 0.0)

v2.normalize()

v3 = copy.copy(v1)

v1 = v1.cross(v2)

v3 += v2

if v1.z < 0.0:

retval = scaleadd(origin, -OFFSET, v3)

else:

retval = scaleadd(origin, OFFSET, v3)

return retval

polyinset = []

lenpolygon = len(MONASTERY)

i = 0

poly = MONASTERY

while i < lenpolygon - 2:

polyinset.append(getinsetpoint(poly[i],

poly[i + 1], poly[i + 2]))

i += 1

polyinset.append(getinsetpoint(poly[-2],

poly[0], poly[1]))

polyinset.append(getinsetpoint(poly[0],

poly[1], poly[2]))

The result:

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Hey thanks heaps for writing this up. You should have seen the crazy quadrant atan2 path I was going down!

ReplyDeleteCould you link in your post the Java code your coworker passed you on?

ReplyDeleteMiguel,

ReplyDeleteI'm sorry. I no longer have access to the Java code.

Carl T.

It's a pity. Thanks anyway.

ReplyDeleteDear Carl,

ReplyDeleteMany thanks for this nice code.

I think there is a small bug:

In "getinsetpoint", the vector v3 should be normalized before passing to "scaleadd".

Furthermore, the final offset is not as the prescribed OFFSET and the angle between vectors should be taken into account.

A possible solution could be:

def getinsetpoint(pt1, pt2, pt3,offset):

"""

Given three points that form a corner (pt1, pt2, pt3),

returns a point offset distance OFFSET to the right

of the path formed by pt1-pt2-pt3.

pt1, pt2, and pt3 are two tuples.

Returns a Vector3 object.

"""

origin = eu.Vector3(pt2[0], pt2[1], 0.0)

v1 = eu.Vector3(pt1[0] - pt2[0],

pt1[1] - pt2[1], 0.0)

v1.normalize()

v2 = eu.Vector3(pt3[0] - pt2[0],

pt3[1] - pt2[1], 0.0)

v2.normalize()

v3 = copy.copy(v1)

v1 = v1.cross(v2)

v3 += v2

v3.normalize()

cs=v3.dot(v2)

a1=cs*v2

a2=v3-a1

if cs>0:

alpha=sqrt(a2.magnitude_squared())

else:

alpha=-sqrt(a2.magnitude_squared())

if v1.z < 0.0:

retval = scaleadd(origin, -offset/alpha, v3)

else:

retval = scaleadd(origin, offset/alpha, v3)

return retval

@Ahmad Thank you for stopping by and for reviewing the code. I don't have gnuplot handy at the moment to see what would happen if I instituted the changes you suggest. I think what I did originally is just inspect the plot and felt that it looked OK. What I need to do is measure the actual offset in the code and report it. I probably won't get to this immediately, but I intend to take a second look at this.

ReplyDeleteAgain, thank you for the rigor with which you reviewed this code. Carl T.