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_math: add rotation_axis, rotation_normal, load_table

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This commit is contained in:
Zack Buhman 2026-02-24 01:21:11 +00:00
parent cf05436514
commit 64d959ed81
1 changed files with 216 additions and 0 deletions
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216
_math.lua
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@ -7,6 +7,7 @@ local abs = math.abs
local mat4 local mat4
local vec3 local vec3
local vec4
local scalar local scalar
scalar = { scalar = {
@ -14,6 +15,14 @@ scalar = {
local d = abs(s1 - s2) local d = abs(s1 - s2)
return d <= epsilon return d <= epsilon
end, end,
convert_to_radians = function(degrees)
return degrees * (math.pi / 180.0)
end,
convert_to_degrees = function(radians)
return radians * (180.0 / math.pi)
end,
} }
setmetatable(scalar, scalar) setmetatable(scalar, scalar)
@ -35,6 +44,30 @@ mat4 = {
return mat4.multiply(M1, M2) return mat4.multiply(M1, M2)
end, end,
load_table = function(t)
assert(#t == 16)
assert(t[1] ~= nil)
assert(t[2] ~= nil)
assert(t[3] ~= nil)
assert(t[4] ~= nil)
assert(t[5] ~= nil)
assert(t[6] ~= nil)
assert(t[7] ~= nil)
assert(t[8] ~= nil)
assert(t[9] ~= nil)
assert(t[10] ~= nil)
assert(t[11] ~= nil)
assert(t[12] ~= nil)
assert(t[13] ~= nil)
assert(t[14] ~= nil)
assert(t[15] ~= nil)
assert(t[16] ~= nil)
return mat4.set(t[1], t[2], t[3], t[4],
t[5], t[6], t[7], t[8],
t[9], t[10], t[11], t[12],
t[13], t[14], t[15], t[16])
end,
set = function(m00, m01, m02, m03, set = function(m00, m01, m02, m03,
m10, m11, m12, m13, m10, m11, m12, m13,
m20, m21, m22, m23, m20, m21, m22, m23,
@ -110,6 +143,38 @@ mat4 = {
return M return M
end, end,
translation_from_vector = function(v)
return translation(v.f[0], v.f[1], v.f[2])
end,
scaling = function(x, y, z)
local M = mat4()
M.m[0 * 4 + 0] = x
--M.m[0 * 4 + 1] = 0.0
--M.m[0 * 4 + 2] = 0.0
--M.m[0 * 4 + 3] = 0.0
--M.m[1 * 4 + 0] = 0.0
M.m[1 * 4 + 1] = y
--M.m[1 * 4 + 2] = 0.0
--M.m[1 * 4 + 3] = 0.0
--M.m[2 * 4 + 0] = 0.0
--M.m[2 * 4 + 1] = 0.0
M.m[2 * 4 + 2] = z
--M.m[2 * 4 + 3] = 0.0
--M.m[3 * 4 + 0] = 0.0
--M.m[3 * 4 + 1] = 0.0
--M.m[3 * 4 + 2] = 0.0
M.m[3 * 4 + 3] = 1.0
return M
end,
scaling_from_vector = function(v)
return scaling(v.f[0], v.f[1], v.f[2])
end,
rotation_x = function(angle) rotation_x = function(angle)
local sin_angle = sin(angle) local sin_angle = sin(angle)
local cos_angle = cos(angle) local cos_angle = cos(angle)
@ -254,6 +319,54 @@ mat4 = {
return M return M
end, end,
rotation_normal = function(normal_axis, angle)
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local c2 = vec3.replicate(1.0 - cos_angle)
local c1 = vec3.replicate(cos_angle)
local c0 = vec3.replicate(sin_angle)
local n0 = vec3(normal_axis.f[1], normal_axis.f[2], normal_axis.f[0])
local n1 = vec3(normal_axis.f[2], normal_axis.f[0], normal_axis.f[1])
local v0 = vec3.multiply(c2, n0)
v0 = vec3.multiply(v0, n1)
local r0 = vec3.multiply(c2, normal_axis)
r0 = vec3.multiply_add(r0, normal_axis, c1)
local r1 = vec3.multiply_add(c0, normal_axis, v0)
local r2 = vec3.negative_multiply_subtract(c0, normal_axis, v0)
local M = mat4()
M.m[0 * 4 + 0] = r0.f[0]
M.m[0 * 4 + 1] = r1.f[2]
M.m[0 * 4 + 2] = r2.f[1]
--M.m[0 * 4 + 3] = 0.0
M.m[1 * 4 + 0] = r2.f[2]
M.m[1 * 4 + 1] = r0.f[1]
M.m[1 * 4 + 2] = r1.f[0]
--M.m[1 * 4 + 3] = 0.0
M.m[2 * 4 + 0] = r1.f[1]
M.m[2 * 4 + 1] = r2.f[0]
M.m[2 * 4 + 2] = r0.f[2]
--M.m[2 * 4 + 3] = 0.0
--M.m[3 * 4 + 0] = 0.0
--M.m[3 * 4 + 1] = 0.0
--M.m[3 * 4 + 2] = 0.0
M.m[3 * 4 + 3] = 1.0
return M
end,
rotation_axis = function(axis, angle)
local normal = vec3.normalize(axis)
return mat4.rotation_normal(normal, angle)
end,
look_to_lh = function(eye_position, eye_direction, up_direction) look_to_lh = function(eye_position, eye_direction, up_direction)
assert(not vec3.equal(eye_direction, vec3._zero)) assert(not vec3.equal(eye_direction, vec3._zero))
assert(not vec3.isinfinite(eye_direction)) assert(not vec3.isinfinite(eye_direction))
@ -419,6 +532,18 @@ vec3 = {
return value return value
end, end,
load_table = function(t)
assert(#t == 3)
assert(t[1] ~= nil)
assert(t[2] ~= nil)
assert(t[3] ~= nil)
return vec3(t[1], t[2], t[3])
end,
replicate = function(value)
return vec3(value, value, value)
end,
dot = function(v1, v2) dot = function(v1, v2)
local value = ( local value = (
v1.f[0] * v2.f[0] + v1.f[0] * v2.f[0] +
@ -473,6 +598,24 @@ vec3 = {
return result return result
end, end,
multiply_add = function(v1, v2, v3)
local result = vec3(
v1.f[0] * v2.f[0] + v3.f[0],
v1.f[1] * v2.f[1] + v3.f[1],
v1.f[2] * v2.f[2] + v3.f[2]
)
return result
end,
negative_multiply_subtract = function(v1, v2, v3)
local result = vec3(
v3.f[0] - (v1.f[0] * v2.f[0]),
v3.f[1] - (v1.f[1] * v2.f[1]),
v3.f[2] - (v1.f[2] * v2.f[2])
)
return result
end,
normalize = function(v) normalize = function(v)
local length = vec3.reciprocal_length(v) local length = vec3.reciprocal_length(v)
local result = vec3( local result = vec3(
@ -532,6 +675,39 @@ vec3 = {
setmetatable(vec3, vec3) setmetatable(vec3, vec3)
vec3._zero = vec3(0, 0, 0) vec3._zero = vec3(0, 0, 0)
vec4 = {
__call = function(_t, x, y, z, w)
-- newByteData is zero-initialized
local data = love.data.newByteData(4 * 4)
local f = ffi.cast('float*', data:getFFIPointer())
value = {
data = data,
f = f,
}
f[0] = x or 0
f[1] = y or 0
f[2] = z or 0
f[3] = w or 0
setmetatable(value, vec4)
return value
end,
load_table = function(t)
assert(#t == 4)
assert(t[1] ~= nil)
assert(t[2] ~= nil)
assert(t[3] ~= nil)
assert(t[4] ~= nil)
return vec4(t[1], t[2], t[3], t[4])
end,
print = function(v)
print(tostring(v.f[0]) .. " " .. tostring(v.f[1]) .. " " .. tostring(v.f[2]) .. " " .. tostring(v.f[3]))
end,
}
setmetatable(vec4, vec4)
---------------------------------------------------------------------- ----------------------------------------------------------------------
-- tests -- tests
---------------------------------------------------------------------- ----------------------------------------------------------------------
@ -543,6 +719,9 @@ assert(vec3.equal(vec3.multiply(vec3(1, 3, -5), vec3(2, 3, 4)), vec3(2, 9, -20))
assert(vec3.near_equal(vec3.normalize(vec3(1, 3, -5)), vec3(0.16903, 0.50709, -0.84515), 0.0001)) assert(vec3.near_equal(vec3.normalize(vec3(1, 3, -5)), vec3(0.16903, 0.50709, -0.84515), 0.0001))
assert(vec3.equal(vec3.cross(vec3(1, 2, 3), vec3(4, 5, 6)), vec3(-3, 6, -3))) assert(vec3.equal(vec3.cross(vec3(1, 2, 3), vec3(4, 5, 6)), vec3(-3, 6, -3)))
assert(vec3.equal(vec3.load_table({1, 2, 3}),
vec3(1, 2, 3)))
assert(mat4.near_equal(mat4.look_to_lh(vec3(1, 2, 3), assert(mat4.near_equal(mat4.look_to_lh(vec3(1, 2, 3),
vec3(5, 6, 7), vec3(5, 6, 7),
vec3(9, 10, 11)), vec3(9, 10, 11)),
@ -586,6 +765,43 @@ assert(mat4.equal(mat4.set(1, 2, 3, 4,
998, 1040, 1082, 1135, 998, 1040, 1082, 1135,
1370, 1428, 1486, 1559))) 1370, 1428, 1486, 1559)))
assert(mat4.equal(mat4.load_table({1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16}),
mat4.set(1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16)))
assert(mat4.near_equal(mat4.rotation_normal(vec3(1, 0, 0), 33.0),
mat4.set(1.000000, 0.000000, 0.000000, 0.000000,
0.000000, -0.013275, 0.999912, 0.000000,
0.000000, -0.999912, -0.013275, 0.000000,
0.000000, 0.000000, 0.000000, 1.000000),
0.00001))
assert(mat4.near_equal(mat4.rotation_normal(vec3(0, 1, 0), 78.0),
mat4.set(-0.857803, 0.000000, -0.513979, 0.000000,
0.000000, 1.000000, 0.000000, 0.000000,
0.513979, 0.000000, -0.857803, 0.000000,
0.000000, 0.000000, 0.000000, 1.000000),
0.00001))
assert(mat4.near_equal(mat4.rotation_normal(vec3(0, 0, 1), 135.0),
mat4.set(-0.996087, 0.088377, 0.000000, 0.000000,
-0.088377, -0.996087, 0.000000, 0.000000,
0.000000, 0.000000, 1.000000, 0.000000,
0.000000, 0.000000, 0.000000, 1.000000),
0.00001))
assert(mat4.near_equal(mat4.rotation_axis(vec3(1, 2, 3), 17.0),
mat4.set(-0.184080, -0.588667, 0.787138, 0.000000,
0.952999, 0.089169, 0.289554, 0.000000,
-0.240639, 0.803443, 0.544584, 0.000000,
0.000000, 0.000000, 0.000000, 1.000000),
0.00001))
return { return {
scalar = scalar, scalar = scalar,
mat4 = mat4, mat4 = mat4,