94 lines
2.4 KiB
Lua
94 lines
2.4 KiB
Lua
local current_folder = (...):gsub('%.[^%.]+$', '') .. "."
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local vec3 = require(current_folder .. "vec3")
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local constants = require(current_folder .. "constants")
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local intersect = {}
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-- http://www.lighthouse3d.com/tutorials/maths/ray-triangle-intersection/
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function intersect.ray_triangle(ray, triangle)
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assert(ray.point ~= nil)
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assert(ray.direction ~= nil)
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assert(#triangle == 3)
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local p, d = ray.point, ray.direction
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local h, s, q = vec3(), vec3(), vec3()
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local a, f, u, v
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local e1 = triangle[2] - triangle[1]
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local e2 = triangle[3] - triangle[1]
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h = d:clone():cross(e2)
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a = (e1*h) -- dot product
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if a > -0.00001 and a < 0.00001 then
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return false
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end
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f = 1/a
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s = p - triangle[1]
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u = f * (s*h)
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if u < 0 or u > 1 then
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return false
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end
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q = s:clone():cross(e1)
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v = f * (d*q)
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if v < 0 or u + v > 1 then
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return false
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end
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-- at this stage we can compute t to find out where
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-- the intersection point is on the line
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t = f * (e2*q)
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if t > constants.FLT_EPSILON then
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return p + t * d -- we've got a hit!
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else
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return false -- the line intersects, but it's behind the point
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end
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end
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-- Algorithm is ported from the C algorithm of
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-- Paul Bourke at http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline3d/
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-- Archive.org am hero \o/
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function intersect.line_line(p1, p2, p3, p4)
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local epsilon = constants.FLT_EPSILON
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local resultSegmentPoint1 = vec3(0,0,0)
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local resultSegmentPoint2 = vec3(0,0,0)
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local p13 = p1 - p3
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local p43 = p4 - p3
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local p21 = p2 - p1
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if p43:len2() < epsilon then return false end
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if p21:len2() < epsilon then return false end
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local d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z
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local d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z
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local d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z
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local d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z
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local d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z
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local denom = d2121 * d4343 - d4321 * d4321
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if math.abs(denom) < epsilon then return false end
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local numer = d1343 * d4321 - d1321 * d4343
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local mua = numer / denom
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local mub = (d1343 + d4321 * (mua)) / d4343
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resultSegmentPoint1.x = p1.x + mua * p21.x
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resultSegmentPoint1.y = p1.y + mua * p21.y
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resultSegmentPoint1.z = p1.z + mua * p21.z
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resultSegmentPoint2.x = p3.x + mub * p43.x
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resultSegmentPoint2.y = p3.y + mub * p43.y
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resultSegmentPoint2.z = p3.z + mub * p43.z
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return true, resultSegmentPoint1, resultSegmentPoint2
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end
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return intersect
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