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More numerically stable point-in-triangle test

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This commit is contained in:
Matthias Richter 2012-06-29 12:21:47 +02:00
parent ea49f9df8b
commit 6b23a5c4c4
1 changed files with 14 additions and 13 deletions
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27
polygon.lua
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@ -44,7 +44,7 @@ end
-- returns true if three vertices lie on a line
local function areCollinear(p, q, r, eps)
return math.abs(vector.det(q.x-p.x, q.y-p.y, r.x-p.x,r.y-p.y)) <= (eps or 1e-20)
return math.abs(vector.det(q.x-p.x, q.y-p.y, r.x-p.x,r.y-p.y)) <= (eps or 1e-32)
end
-- remove vertices that lie on a line
local function removeCollinear(vertices)
@ -75,18 +75,16 @@ local function ccw(p, q, r)
return vector.det(q.x-p.x, q.y-p.y, r.x-p.x, r.y-p.y) >= 0
end
-- test if a point lies inside of a triangle using cramers rule
local function pointInTriangle(q, p1,p2,p3)
local v1x,v1y = p2.x-p1.x, p2.y-p1.y
local v2x,v2y = p3.x-p1.x, p3.y-p1.y
local qpx,qpy = q.x-p1.x, q.y-p1.y
local l = vector.det(qpx,qpy, v2x,v2y)
if l <= 0 then return false end
-- test wether a and b lie on the same side of the line c->d
local function onSameSide(a,b, c,d)
local px, py = d.x-c.x, d.y-c.y
local l = vector.det(px,py, a.x-c.x, a.y-c.y)
local m = vector.det(px,py, b.x-c.x, b.y-c.y)
return l*m >= 0
end
local m = vector.det(v1x,v1y, qpx,qpy)
if m <= 0 then return false end
local dv = vector.det(v1x,v2y, v2x,v2y)
return (l+m)/dv < 1
local function pointInTriangle(p, a,b,c)
return onSameSide(p,a, b,c) and onSameSide(p,b, a,c) and onSameSide(p,c, a,b)
end
-- returns starting indices of shared edge, i.e. if p and q share the
@ -259,7 +257,9 @@ function Polygon:triangulate()
local function isEar(p1,p2,p3)
if not ccw(p1,p2,p3) then return false end
for q,_ in pairs(concave) do
if pointInTriangle(q, p1,p2,p3) then return false end
if q ~= p1 and q ~= p2 and q ~= p3 and pointInTriangle(q, p1,p2,p3) then
return false
end
end
return true
end
@ -274,6 +274,7 @@ function Polygon:triangulate()
-- the polygon constructor throws an error.
if not areCollinear(p.l, p.p, p.r) then
triangles[#triangles+1] = newPolygon(p.l.x,p.l.y, p.p.x,p.p.y, p.r.x,p.r.y)
skipped = 0
end
if concave[p.l] and ccw(adj[p.l].l, p.l, p.r) then