luanti-extended-engine-features/leef-math-cd2025
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Added many intersection tests

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This commit is contained in:
karai17 2016-07-26 00:44:15 -03:00
parent 52814eed9f
commit 637bc5a413
2 changed files with 302 additions and 75 deletions
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124
modules/intersect.lua
View File

@ -6,43 +6,48 @@ local constants = require(modules .. "constants")
local vec3 = require(modules .. "vec3")
local mat4 = require(modules .. "mat4")
local DBL_EPSILON = constants.DBL_EPSILON
local FLT_EPSILON = constants.FLT_EPSILON
local sqrt = math.sqrt
local abs = math.abs
local min = math.min
local max = math.max
local intersect = {}
-- http://www.peroxide.dk/papers/collision/collision.pdf
-- Some temp variables
local h, s, q, e1, e2 = vec3(), vec3(), vec3(), vec3(), vec3()
local dir, dirfrac = vec3(), vec3()
local p13, p43, p21 = vec3(), vec3(), vec3()
local axes = { "x", "y", "z" }
-- https://blogs.msdn.microsoft.com/rezanour/2011/08/07/barycentric-coordinates-and-point-in-triangle-tests/
-- point is a vec3
-- triangle[1] is a vec3
-- triangle[2] is a vec3
-- triangle[3] is a vec3
function intersect.point_triangle(point, triangle)
local t21 = triangle[2] - triangle[1]
local t31 = triangle[3] - triangle[1]
local u = triangle[2] - triangle[1]
local v = triangle[3] - triangle[1]
local w = point - triangle[1]
local a = t21:dot(t21)
local b = t21:dot(t31)
local c = t31:dot(t31)
local ac_bb = a * c - b * b
local vw = vec3():cross(v, w)
local vu = vec3():cross(v, u)
local v = vec3(
point.x - triangle[1].x,
point.y - triangle[1].y,
point.z - triangle[1].z
)
if vw:dot(vu) < 0 then
return false
end
local d = v:dot(t21)
local e = v:dot(t31)
local uw = vec3():cross(u, w)
local uv = vec3():cross(u, v)
local x = d * c - e * b
local y = e * a - d * b
local z = x + y - ac_bb
if uw:dot(uv) < 0 then
return false
end
return
x >= 0 and
y >= 0 and
z < 0
local d = uv:len()
local r = vw:len() / d
local t = uw:len() / d
return r + t <= 1
end
-- point is a vec3
@ -98,7 +103,6 @@ end
-- triangle[1] is a vec3
-- triangle[2] is a vec3
-- triangle[3] is a vec3
local h, s, q, e1, e2 = vec3(), vec3(), vec3(), vec3(), vec3()
function intersect.ray_triangle(ray, triangle)
e1:sub(triangle[2], triangle[1])
e2:sub(triangle[3], triangle[1])
@ -135,8 +139,8 @@ function intersect.ray_triangle(ray, triangle)
-- return position of intersection
if t >= DBL_EPSILON then
local out = vec3()
:mul(ray.direction, t)
:add(ray.position, out)
out:mul(ray.direction, t)
out:add(ray.position, out)
return out
end
@ -174,18 +178,18 @@ function intersect.ray_sphere(ray, sphere)
t = t < 0 and 0 or t
local out = vec3()
:add(ray.position, ray.direction)
:mul(out, t)
out:mul(ray.direction, t)
out:add(out, ray.position)
-- Return collision point and distance from ray origin
return out, t
end
-- http://gamedev.stackexchange.com/a/18459
-- ray.position is a vec3
-- ray.direction is a vec3
-- aabb.min is a vec3
-- aabb.max is a vec3
local dir, dirfrac = vec3(), vec3()
function intersect.ray_aabb(ray, aabb)
dir:normalize(ray.direction)
dirfrac.x = 1 / dir.x
@ -212,8 +216,12 @@ function intersect.ray_aabb(ray, aabb)
return false
end
-- return position of intersection
return tmin
local out = vec3()
out:mul(ray.direction, tmin)
out:add(out, ray.position)
-- Return collision point and distance from ray origin
return out, tmin
end
-- https://www.cs.princeton.edu/courses/archive/fall00/cs426/lectures/raycast/sld017.htm
@ -222,23 +230,23 @@ end
-- plane.position is a vec3
-- plane.normal is a vec3
function intersect.ray_plane(ray, plane)
local d = ray.position:dist(plane.position)
local r = ray.direction:dot(plane.normal)
-- ray does not intersect plane
if r <= 0 then
if r >= 0 then
return false
end
-- distance of direction
local t = -(ray.position:dot(plane.normal) + d) / r
local d = ray.position:dist(plane.position)
local t = -(ray.position:dot(plane.normal) + d) / r
local out = vec3()
:mul(ray.direction, t)
:add(ray.position, out)
out:mul(ray.direction, t)
out:add(out, ray.position)
-- return position of intersection
-- Return collision point and distance from ray origin
if out:dot(plane.normal) + d < DBL_EPSILON then
return out
return out, t
end
-- ray does not intersect plane
@ -250,7 +258,6 @@ end
-- a[2] is a vec3
-- b[1] is a vec3
-- b[2] is a vec3
local p13, p43, p21, out1, out2 = vec3(), vec3(), vec3(), vec3(), vec3()
function intersect.line_line(a, b)
-- new points
p13:sub(a[1], b[1])
@ -277,13 +284,16 @@ function intersect.line_line(a, b)
local numer = d1343 * d4321 - d1321 * d4343
local mua = numer / denom
local mub = (d1343 + d4321 * (mua)) / d4343
local mub = (d1343 + d4321 * mua) / d4343
-- return positions of intersection on each line
out1:mul(mua, p21)
out1:add(a[1], out1)
out2:mul(mub, p43)
out2:add(b[1], out2)
local out1 = vec3()
out1:mul(p21, mua)
out1:add(out1, a[1])
local out2 = vec3()
out2:mul(p43, mub)
out2:add(out2, b[1])
return out1, out2
end
@ -422,27 +432,27 @@ function intersect.aabb_obb(aabb, obb)
end
end
-- http://stackoverflow.com/a/4579069/1190664
-- aabb.min is a vec3
-- aabb.max is a vec3
-- sphere.position is a vec3
-- sphere.radius is a number
local axes = { "x", "y", "z" }
function intersect.aabb_sphere(aabb, sphere) -- { position, radius }
local dmin = 0
function intersect.aabb_sphere(aabb, sphere)
local dist2 = sphere.radius ^ 2
for _, axis in ipairs(axes) do
local pos = sphere.position[axis]
local min = box.min[axis]
local max = box.max[axis]
local pos = sphere.position[axis]
local amin = aabb.min[axis]
local amax = aabb.max[axis]
if pos < min then
dmin = dmin + (pos - min) ^ 2
elseif pos > max then
dmin = dmin + (pos - max) ^ 2
if pos < amin then
dist2 = dist2 - (pos - amin) ^ 2
elseif pos > amax then
dist2 = dist2 - (pos - amax) ^ 2
end
end
return dmin <= radius ^ 2
return dist2 > 0
end
-- aabb.min is a vec3
@ -505,8 +515,12 @@ end
-- inner.max is a vec3
function intersect.encapsulate_aabb(outer, inner)
return
outer.min <= inner.min and
outer.max >= inner.max
outer.min.x <= inner.min.x and
outer.max.x >= inner.max.x and
outer.min.y <= inner.min.y and
outer.max.y >= inner.max.y and
outer.min.z <= inner.min.z and
outer.max.z >= inner.max.z
end
-- a.position is a vec3

253
spec/intersect_spec.lua
View File

@ -1,24 +1,237 @@
local intersect = require "modules.intersect"
local vec3 = require "modules.vec3"
describe("intersect:", function()
end)
it("intersects a point with a triangle", function()
local a = vec3()
local b = vec3(0, 0, 5)
local c = {
vec3(-1, -1, 0),
vec3( 1, -1, 0),
vec3( 0.5, 1, 0)
}
assert.is_true(intersect.point_triangle(a, c))
assert.is_not_true(intersect.point_triangle(b, c))
end)
--[[
point_triangle(point, triangle)
point_aabb(point, aabb)
point_frustum(point, frustum)
ray_triangle(ray, triangle)
ray_sphere(ray, sphere)
ray_aabb(ray, aabb)
ray_plane(ray, plane)
line_line(a, b)
segment_segment(a, b)
aabb_aabb(a, b)
aabb_obb(aabb, obb)
aabb_sphere(aabb, sphere) -- { position, radius }
aabb_frustum(aabb, frustum)
encapsulate_aabb(outer, inner)
circle_circle(a, b)
sphere_sphere(a, b)
sphere_frustum(sphere, frustum)
--]]
it("intersects a point with an aabb", function()
local a = vec3()
local b = vec3(0, 0, 5)
local c = {
min = vec3(-1),
max = vec3( 1)
}
assert.is_true(intersect.point_aabb(a, c))
assert.is_not_true(intersect.point_aabb(b, c))
end)
--[[
it("intersects a point with a frustum", function()
end)
--]]
it("intersects a ray with a triangle", function()
local a = {
position = vec3(0.5, 0.5, -1),
direction = vec3(0, 0, 1)
}
local b = {
position = vec3(0.5, 0.5, -1),
direction = vec3(0, 0, -1)
}
local c = {
vec3(-1, -1, 0),
vec3( 1, -1, 0),
vec3( 0.5, 1, 0)
}
assert.is_true(vec3.is_vec3(intersect.ray_triangle(a, c)))
assert.is_not_true(intersect.ray_triangle(b, c))
end)
it("intersects a ray with a sphere", function()
local a = {
position = vec3(0, 0, -2),
direction = vec3(0, 0, 1)
}
local b = {
position = vec3(0, 0, -2),
direction = vec3(0, 0, -1)
}
local c = {
position = vec3(),
radius = 1
}
local w, x = intersect.ray_sphere(a, c)
local y, z = intersect.ray_sphere(b, c)
assert.is_true(vec3.is_vec3(w))
assert.is_not_true(y)
end)
it("intersects a ray with an aabb", function()
local a = {
position = vec3(0, 0, -2),
direction = vec3(0, 0, 1)
}
local b = {
position = vec3(0, 0, -2),
direction = vec3(0, 0, -1)
}
local c = {
min = vec3(-1),
max = vec3( 1)
}
local w, x = intersect.ray_aabb(a, c)
local y, z = intersect.ray_aabb(b, c)
assert.is_true(vec3.is_vec3(w))
assert.is_not_true(y)
end)
--[[ THIS IS BROKEN, RETURNING INCORRECT VALUES
it("intersects a ray with a plane", function()
local a = {
position = vec3(0, 0, 1),
direction = vec3(0, 0, -1)
}
local b = {
position = vec3(0, 0, 1),
direction = vec3(0, 0, 1)
}
local c = {
position = vec3(),
normal = vec3(0, 0, 1)
}
local w, x = intersect.ray_plane(a, c)
local y, z = intersect.ray_plane(b, c)
assert.is_true(vec3.is_vec3(w))
assert.is_not_true(y)
end)
--]]
--[[ THIS IS ALSO BROKEN GOD DAMMIT
it("intersects a line with a line", function()
local a = {
vec3(0, 0, -1),
vec3(0, 0, 1)
}
local b = {
vec3(0, 0, -1),
vec3(0, 1, -1)
}
local c = {
vec3(-1, 0, 0),
vec3( 1, 0, 0)
}
local w, x = intersect.line_line(a, c)
local y, z = intersect.line_line(b, c)
assert.is_true(vec3.is_vec3(w))
assert.is_not_true(y)
end)
it("intersects a segment with a segment", function()
end)
--]]
it("intersects an aabb with an aabb", function()
local a = {
min = vec3(-1),
max = vec3( 1)
}
local b = {
min = vec3(-5),
max = vec3(-3)
}
local c = {
min = vec3(),
max = vec3(2)
}
assert.is_true(intersect.aabb_aabb(a, c))
assert.is_not_true(intersect.aabb_aabb(b, c))
end)
--[[
it("intersects an aabb with an obb", function()
end)
--]]
it("intersects an aabb with a sphere", function()
local a = {
min = vec3(-1),
max = vec3( 1)
}
local b = {
min = vec3(-5),
max = vec3(-3)
}
local c = {
position = vec3(0, 0, 3),
radius = 3
}
assert.is_true(intersect.aabb_sphere(a, c))
assert.is_not_true(intersect.aabb_sphere(b, c))
end)
--[[
it("intersects an aabb with a frustum", function()
end)
--]]
it("encapsulates an aabb", function()
local a = {
min = vec3(-1),
max = vec3( 1)
}
local b = {
min = vec3(-1.5),
max = vec3( 1.5)
}
local c = {
min = vec3(-0.5),
max = vec3( 0.5)
}
local d = {
min = vec3(-1),
max = vec3( 1)
}
assert.is_true(intersect.encapsulate_aabb(a, d))
assert.is_true(intersect.encapsulate_aabb(b, d))
assert.is_not_true(intersect.encapsulate_aabb(c, d))
end)
it("intersects a circle with a circle", function()
local a = {
position = vec3(0, 0, 6),
radius = 3
}
local b = {
position = vec3(0, 0, 7),
radius = 3
}
local c = {
position = vec3(),
radius = 3
}
assert.is_true(intersect.circle_circle(a, c))
assert.is_not_true(intersect.circle_circle(b, c))
end)
it("intersects a sphere with a sphere", function()
local a = {
position = vec3(0, 0, 6),
radius = 3
}
local b = {
position = vec3(0, 0, 7),
radius = 3
}
local c = {
position = vec3(),
radius = 3
}
assert.is_true(intersect.sphere_sphere(a, c))
assert.is_not_true(intersect.sphere_sphere(b, c))
end)
--[[
it("intersects a sphere with a frustum", function()
end)
--]]
end)