Alex Tweedly wrote:
I'll post a couple of suggested solutions shortly (once I've got the
stack running properly)
There are two approaches (at least) that consistently get the same
answers as we all intuitively "know" are correct.
By AREA.
Calculate the (signed) area between each edge and some baseline (i.e.
the area enclosed by the edge itself, its projectino onto the baseline
and the two projection lines). Sum this area for all edges. Looking at
whether this is positive or negative gives an answer.
By Point.
Find the leftmost, lowest point (**). (i.e. the one with the lowest X
value, and of all those having the same X value, the lowest Y value).
(Note that this same point (value) can occur multiple times in a
polygon, due to self-intersection or self-overlapping polygons - this
doesn't matter, just pick any of those points). Looking at the previous
and next points, determine the change of direction implied for these two
edges (you could use the cross-product to do this, or simply normalize
and compare the gradients).
(**) - this description assumes 'normal' cartesian coordinates. Beware
that RunRev uses a coordinate system where the vertical axis is
"upside-down", so increasing Y values are associated with moving downawards.
Some sample code - adopted from elsewhere (and translated into revtalk)
- with only moderate testing, but I'm fairly confident I converted it
fairly accurately.
(It's a bit wordy, but seemed clearer that way).
constant kDebug = false
on mouseUp
put empty into field "F"
repeat with i = 1 to the number of controls
if char 2 to -2 of word 2 of the name of control i = "Polygon" then
repeat for each line L in the points of control i
put L & "; " after field "F"
end Repeat
put CR after field "F"
if calculateflowusingarea (i, kDebug) then
put "counterclockwise" & CR after field "F"
else
put "clockwise" & CR after field "F"
end if
if calculateflowusingpoint (i, false) then
put "counterclockwise" & CR after field "F"
else
put "clockwise" & CR after field "F"
end if
end if
end repeat
end mouseUp
function calculateflowusingarea P, pDebug
put the points of control P into tPoints
put item 1 of line 1 of tPoints into x2
put item 2 of line 1 of tPoints into y2
put 0 into total
repeat for each line L in tPoints
put x2 into x1
put y2 into y1
put item 1 of L into x2
put item 2 of L into y2
put (x2-x1) * (0.5*(y1+y2)) into t
if pDebug then put (x2-x1) && (x2-x1)*0.5*(y2+y1) && x1 && y1 &&
x2 && y2 && t & CR after field F
add t to total
put L into tLast
end repeat
-- close the polygon in the case where Rev has an open polygon
if tLast <> line 1 of tPoints then
put x2 into x1
put y2 into y1
put item 1 of line 1 of tPoints into x2
put item 2 of line 1 of tPoints into y2
put (x2-x1) * (0.5*(y1+y2)) into t
if pDebug then put (x2-x1) && (x2-x1)*0.5*(y2+y1) && x1 && y1 &&
x2 && y2 && t & CR after field F
add t to total
end if
if pDebug then put "Total is " & total & CR after field "F"
return total > 0 -- i.e. true if the polygon is counter-clockwise
end calculateflowusingarea
function calculateflowusingpoint P, pDebug
put the points of control P into tPoints
-- find the leftmost, lowest point
put item 1 of line 1 of tPoints into x
put item 2 of line 1 of tPoints into y
repeat with i = 1 to the number of lines in tPoints
if item 1 of line i of tPoints < x or \
(item 1 of line i of tPoints = x and item 2 of line 1 of
tPoints <= y) then
put item 1 of line i of tPoints into x
put item 2 of line i of tPoints into y
put i into tOne
end if
end repeat
-- find the adjacent points
switch tOne
case 1
put the number of lines in tPoints into tPrev
put 2 into tNext
break
case the number of lines in tPoints
put tOne-1 into tPrev
put 1 into tNext
-- special case where the poly is already closed !!
if line tOne of tPoints = line 1 of tPoints then put 2 into tNext
break
default
put tOne-1 into tPrev
put tOne+1 into tNext
break
end switch
if pDebug then put x && y && tPrev && tOne && tNext & CR after
field "F"
if pDebug then put line tPrev of tPoints && x && y && line tNext of
tPoints & CR after field "F"
-- now deal with the end-cases
if item 1 of line tPrev of tPoints = x then return false --
incoming edge is vertical, so counter
if item 1 of line tNext of tPoints = x then return true -- outgoing ...
-- so can safely that x-delta's are non-zero
put (y-item 2 of line tPrev of tPoints) / (x-item 1 of line tPrev
of tPoints) into yprev
put (y-item 2 of line tNext of tPoints) / (x-item 1 of line tNext
of tPoints) into ynext
if pDebug then put "ys are " && yprev && ynext & CR after field "F"
if yprev < ynext then return true
return false
end calculateflowusingpoint
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