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38 lines
1.3 KiB
Lua
38 lines
1.3 KiB
Lua
local function distance_to_segment(x1, y1, x2, y2, x, y)
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-- get the distance between point (x,y) and segment (x1,y1)-(x2,y2)
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local a = (x1-x2)^2 + (y1-y2)^2 -- square of distance
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local b = (x1-x)^2 + (y1-y)^2
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local c = (x2-x)^2 + (y2-y)^2
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if a + b < c then
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-- The closest point of the segment is the extremity 1
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return math.sqrt(b)
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elseif a + c < b then
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-- The closest point of the segment is the extremity 2
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return math.sqrt(c)
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else
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-- The closest point is on the segment
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return math.abs(x1 * (y2-y) + x2 * (y-y1) + x * (y1-y2)) / math.sqrt(a)
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end
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end
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local function transform_quadri(X, Y, x, y)
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-- To index points in an irregular quadrilateral, giving x and y between 0 (one edge) and 1 (opposite edge)
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-- X, Y 4-vectors giving the coordinates of the 4 vertices
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-- x, y position to index.
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local x1, x2, x3, x4 = unpack(X)
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local y1, y2, y3, y4 = unpack(Y)
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-- Compare distance to 2 opposite edges, they give the X coordinate
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local d23 = distance_to_segment(x2,y2,x3,y3,x,y)
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local d41 = distance_to_segment(x4,y4,x1,y1,x,y)
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local xc = d41 / (d23+d41)
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-- Same for the 2 other edges, they give the Y coordinate
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local d12 = distance_to_segment(x1,y1,x2,y2,x,y)
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local d34 = distance_to_segment(x3,y3,x4,y4,x,y)
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local yc = d12 / (d12+d34)
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return xc, yc
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end
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return transform_quadri
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