luanti-extended-engine-features/leef-math-cd2025
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What ARE birds?

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We just don't know.
This commit is contained in:
karai17 2016-07-23 05:21:03 -03:00
parent fbf329264d
commit 481825cba4
3 changed files with 112 additions and 54 deletions
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57
modules/intersect.lua
View File

@ -58,6 +58,40 @@ function intersect.point_aabb(point, aabb)
aabb.max.z >= point.z
end
-- point is a vec3
-- frustum.left is a plane { a, b, c, d }
-- frustum.right is a plane { a, b, c, d }
-- frustum.bottom is a plane { a, b, c, d }
-- frustum.top is a plane { a, b, c, d }
-- frustum.near is a plane { a, b, c, d }
-- frustum.far is a plane { a, b, c, d }
function intersect.point_frustum(point, frustum)
local x, y, z = point:unpack()
local planes = {
frustum.left,
frustum.right,
frustum.bottom,
frustum.top,
frustum.near,
frustum.far or false
}
-- Skip the last test for infinite projections, it'll never fail.
if not planes[6] then
table.remove(planes)
end
local dot
for i = 1, #planes do
dot = planes[i].a * x + planes[i].b * y + planes[i].c * z + planes[i].d
if dot <= 0 then
return false
end
end
return true
end
-- http://www.lighthouse3d.com/tutorials/maths/ray-triangle-intersection/
-- ray.position is a vec3
-- ray.direction is a vec3
@ -413,10 +447,10 @@ end
-- aabb.min is a vec3
-- aabb.max is a vec3
-- frustum.top is a plane { a, b, c, d }
-- frustum.bottom is a plane { a, b, c, d }
-- frustum.left is a plane { a, b, c, d }
-- frustum.right is a plane { a, b, c, d }
-- frustum.bottom is a plane { a, b, c, d }
-- frustum.top is a plane { a, b, c, d }
-- frustum.near is a plane { a, b, c, d }
-- frustum.far is a plane { a, b, c, d }
function intersect.aabb_frustum(aabb, frustum)
@ -428,10 +462,10 @@ function intersect.aabb_frustum(aabb, frustum)
-- We have 6 planes defining the frustum, 5 if infinite.
local planes = {
frustum.top,
frustum.bottom,
frustum.left,
frustum.right,
frustum.bottom,
frustum.top,
frustum.near,
frustum.far or false
}
@ -493,20 +527,19 @@ end
-- sphere.position is a vec3
-- sphere.radius is a number
-- frustum.top is a plane { a, b, c, d }
-- frustum.bottom is a plane { a, b, c, d }
-- frustum.left is a plane { a, b, c, d }
-- frustum.right is a plane { a, b, c, d }
-- frustum.bottom is a plane { a, b, c, d }
-- frustum.top is a plane { a, b, c, d }
-- frustum.near is a plane { a, b, c, d }
-- frustum.far is a plane { a, b, c, d }
function intersect.sphere_frustum(sphere, frustum)
local x, y, z = sphere.position:unpack()
local planes = {
frustum.top,
frustum.bottom,
local planes = {
frustum.left,
frustum.right,
frustum.bottom,
frustum.top,
frustum.near
}
@ -515,8 +548,8 @@ function intersect.sphere_frustum(sphere, frustum)
end
local dot
for p = 1, #planes do
dot = planes[p].a * x + planes[p].b * y + planes[p].c * z + planes[p].d
for i = 1, #planes do
dot = planes[i].a * x + planes[i].b * y + planes[i].c * z + planes[i].d
if dot <= -sphere.radius then
return false

57
modules/mat4.lua
View File

@ -520,6 +520,7 @@ function mat4.to_vec4s(a)
}
end
-- http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
function mat4.to_quat(a)
identity(tmp):transpose(a)
@ -541,34 +542,6 @@ function mat4.to_frustum(a, infinite)
local t
local frustum = {}
-- Extract the TOP plane
frustum.top = {}
frustum.top.a = a[4] - a[2]
frustum.top.b = a[8] - a[6]
frustum.top.c = a[12] - a[10]
frustum.top.d = a[16] - a[14]
-- Normalize the result
t = sqrt(frustum.top.a * frustum.top.a + frustum.top.b * frustum.top.b + frustum.top.c * frustum.top.c)
frustum.top.a = frustum.top.a / t
frustum.top.b = frustum.top.b / t
frustum.top.c = frustum.top.c / t
frustum.top.d = frustum.top.d / t
-- Extract the BOTTOM plane
frustum.bottom = {}
frustum.bottom.a = a[4] + a[2]
frustum.bottom.b = a[8] + a[6]
frustum.bottom.c = a[12] + a[10]
frustum.bottom.d = a[16] + a[14]
-- Normalize the result
t = sqrt(frustum.bottom.a * frustum.bottom.a + frustum.bottom.b * frustum.bottom.b + frustum.bottom.c * frustum.bottom.c)
frustum.bottom.a = frustum.bottom.a / t
frustum.bottom.b = frustum.bottom.b / t
frustum.bottom.c = frustum.bottom.c / t
frustum.bottom.d = frustum.bottom.d / t
-- Extract the LEFT plane
frustum.left.a = a[4] + a[1]
frustum.left.b = a[8] + a[5]
@ -596,6 +569,34 @@ function mat4.to_frustum(a, infinite)
frustum.right.c = frustum.right.c / t
frustum.right.d = frustum.right.d / t
-- Extract the BOTTOM plane
frustum.bottom = {}
frustum.bottom.a = a[4] + a[2]
frustum.bottom.b = a[8] + a[6]
frustum.bottom.c = a[12] + a[10]
frustum.bottom.d = a[16] + a[14]
-- Normalize the result
t = sqrt(frustum.bottom.a * frustum.bottom.a + frustum.bottom.b * frustum.bottom.b + frustum.bottom.c * frustum.bottom.c)
frustum.bottom.a = frustum.bottom.a / t
frustum.bottom.b = frustum.bottom.b / t
frustum.bottom.c = frustum.bottom.c / t
frustum.bottom.d = frustum.bottom.d / t
-- Extract the TOP plane
frustum.top = {}
frustum.top.a = a[4] - a[2]
frustum.top.b = a[8] - a[6]
frustum.top.c = a[12] - a[10]
frustum.top.d = a[16] - a[14]
-- Normalize the result
t = sqrt(frustum.top.a * frustum.top.a + frustum.top.b * frustum.top.b + frustum.top.c * frustum.top.c)
frustum.top.a = frustum.top.a / t
frustum.top.b = frustum.top.b / t
frustum.top.c = frustum.top.c / t
frustum.top.d = frustum.top.d / t
-- Extract the NEAR plane
frustum.near = {}
frustum.near.a = a[4] + a[3]

52
spec/mat4_spec.lua
View File

@ -100,8 +100,18 @@ describe("mat4:", function()
it("tests multiplication", function()
do
local a = mat4 { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 }
local b = mat4 { 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 8, 12, 16 }
local a = mat4 {
1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16
}
local b = mat4 {
1, 5, 9, 13,
2, 6, 10, 14,
3, 7, 11, 15,
4, 8, 12, 16
}
local c = mat4():mul(a, b)
assert.is.equal(c[1], 30)
assert.is.equal(c[2], 70)
@ -125,13 +135,18 @@ describe("mat4:", function()
end
do
local a = mat4 { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 , 13, 14, 15, 16 }
local a = mat4 {
1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16
}
local b = { 10, 20, 30, 40 }
local c = mat4.mul_mat4x1({}, a, b)
assert.is.equal(c[1], 900)
assert.is.equal(c[2], 1000)
assert.is.equal(c[3], 1100)
assert.is.equal(c[4], 1200)
assert.is.equal(c[1], 900)
assert.is.equal(c[2], 1000)
assert.is.equal(c[3], 1100)
assert.is.equal(c[4], 1200)
end
end)
@ -172,7 +187,12 @@ describe("mat4:", function()
end)
it("tests transpose", function()
local a = mat4 { 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3 ,3 ,4, 4 ,4 ,4 }
local a = mat4 {
1, 1, 1, 1,
2, 2, 2, 2,
3, 3, 3, 3,
4, 4, 4, 4
}
local b = mat4():transpose(a)
assert.is.equal(b[1], 1)
assert.is.equal(b[2], 2)
@ -211,8 +231,6 @@ describe("mat4:", function()
it("tests convertions", function()
local a = mat4()
local b = mat4 { 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4 }
local v = a:to_vec4s()
assert.is_true(type(v) == "table")
assert.is_true(type(v[1]) == "table")
@ -236,11 +254,17 @@ describe("mat4:", function()
assert.is.equal(v[4][3], 0)
assert.is.equal(v[4][4], 1)
local b = mat4 {
0, 0, 1, 0,
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 0, 0
}
local q = b:to_quat()
--assert.is.equal(q.x, 0)
--assert.is.equal(q.y, 0)
--assert.is.equal(q.z, 0)
--assert.is.equal(q.w, 0)
assert.is.equal(q.x, -0.5)
assert.is.equal(q.y, -0.5)
assert.is.equal(q.z, -0.5)
assert.is.equal(q.w, 0.5)
end)
end)