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base: bilbo:955a3e09aadf056f804f0de793e0297863bc5185
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bilbo:main
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compare: bilbo:64d959ed81f2b1f7acd9ddcb54cac454a957e07e
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bilbo:main

4 Commits
955a3e09aa ... 64d959ed81

Author SHA1 Message Date
Zack Buhman
64d959ed81 _math: add rotation_axis, rotation_normal, load_table 2026-02-24 01:21:11 +00:00
Zack Buhman
cf05436514 _math: implement matrix multiplication 2026-02-23 02:11:02 +00:00
Zack Buhman
13d882d6df _math: implement mat4.perspective_rh and mat4.look_at_rh 2026-02-23 01:26:39 +00:00
Zack Buhman
44a3c5b76e _math: initial matrix/vector math library 2026-02-22 21:28:08 +00:00
4 changed files with 867 additions and 72 deletions
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4
.gitignore vendored Normal file
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_math.lua Normal file
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local ffi = require 'ffi'
local sin = math.sin
local cos = math.cos
local sqrt = math.sqrt
local abs = math.abs
local mat4
local vec3
local vec4
local scalar
scalar = {
near_equal = function(s1, s2, epsilon)
local d = abs(s1 - s2)
return d <= epsilon
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)
mat4 = {
__call = function(_t)
-- newByteData is zero-initialized
local data = love.data.newByteData(16 * 4)
local m = ffi.cast('float*', data:getFFIPointer())
value = {
data = data,
m = m,
}
setmetatable(value, mat4)
return value
end,
__mul = function(M1, M2)
return mat4.multiply(M1, M2)
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,
m10, m11, m12, m13,
m20, m21, m22, m23,
m30, m31, m32, m33)
local M = mat4()
M.m[0 * 4 + 0] = m00
M.m[0 * 4 + 1] = m01
M.m[0 * 4 + 2] = m02
M.m[0 * 4 + 3] = m03
M.m[1 * 4 + 0] = m10
M.m[1 * 4 + 1] = m11
M.m[1 * 4 + 2] = m12
M.m[1 * 4 + 3] = m13
M.m[2 * 4 + 0] = m20
M.m[2 * 4 + 1] = m21
M.m[2 * 4 + 2] = m22
M.m[2 * 4 + 3] = m23
M.m[3 * 4 + 0] = m30
M.m[3 * 4 + 1] = m31
M.m[3 * 4 + 2] = m32
M.m[3 * 4 + 3] = m33
return M
end,
identity = function()
local M = mat4()
M.m[0 * 4 + 0] = 1.0
--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] = 1.0
--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] = 1.0
--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,
translation = function(x, y, z)
local M = mat4()
M.m[0 * 4 + 0] = 1.0
--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] = 1.0
--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] = 1.0
--M.m[2 * 4 + 3] = 0.0
M.m[3 * 4 + 0] = x
M.m[3 * 4 + 1] = y
M.m[3 * 4 + 2] = z
M.m[3 * 4 + 3] = 1.0
return M
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)
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local M = mat4()
M.m[0 * 4 + 0] = 1.0
--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] = cos_angle
M.m[1 * 4 + 2] = sin_angle
--M.m[1 * 4 + 3] = 0.0
--M.m[2 * 4 + 0] = 0.0
M.m[2 * 4 + 1] = -sin_angle
M.m[2 * 4 + 2] = cos_angle
--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_y = function(angle)
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local M = mat4()
M.m[0 * 4 + 0] = cos_angle
--M.m[0 * 4 + 1] = 0.0
M.m[0 * 4 + 2] = -sin_angle
--M.m[0 * 4 + 3] = 0.0
--M.m[1 * 4 + 0] = 0.0
M.m[1 * 4 + 1] = 1.0
--M.m[1 * 4 + 2] = 0.0
--M.m[1 * 4 + 3] = 0.0
M.m[2 * 4 + 0] = sin_angle
--M.m[2 * 4 + 1] = 0.0
M.m[2 * 4 + 2] = cos_angle
--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_z = function(angle)
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local M = mat4()
M.m[0 * 4 + 0] = cos_angle
M.m[0 * 4 + 1] = sin_angle
--M.m[0 * 4 + 2] = 0.0
--M.m[0 * 4 + 3] = 0.0
M.m[1 * 4 + 0] = -sin_angle
M.m[1 * 4 + 1] = cos_angle
--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] = 1.0
--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,
transpose = function(M)
local MT = mat4()
--MT.m[0 * 4 + 0] = M.m[0 * 4 + 0]
MT.m[0 * 4 + 1] = M.m[1 * 4 + 0]
MT.m[0 * 4 + 2] = M.m[2 * 4 + 0]
MT.m[0 * 4 + 3] = M.m[3 * 4 + 0]
MT.m[1 * 4 + 0] = M.m[0 * 4 + 1]
--MT.m[1 * 4 + 1] = M.m[1 * 4 + 1]
MT.m[1 * 4 + 2] = M.m[2 * 4 + 1]
MT.m[1 * 4 + 3] = M.m[3 * 4 + 1]
MT.m[2 * 4 + 0] = M.m[0 * 4 + 2]
MT.m[2 * 4 + 1] = M.m[1 * 4 + 2]
--MT.m[2 * 4 + 2] = M.m[2 * 4 + 2]
MT.m[2 * 4 + 3] = M.m[3 * 4 + 2]
MT.m[3 * 4 + 0] = M.m[0 * 4 + 3]
MT.m[3 * 4 + 1] = M.m[1 * 4 + 3]
MT.m[3 * 4 + 2] = M.m[2 * 4 + 3]
--MT.m[3 * 4 + 3] = M.m[3 * 4 + 3]
return MT
end,
multiply = function(M1, M2)
local M = mat4()
local x = M1.m[0 * 4 + 0]
local y = M1.m[0 * 4 + 1]
local z = M1.m[0 * 4 + 2]
local w = M1.m[0 * 4 + 3]
M.m[0 * 4 + 0] = (M2.m[0 * 4 + 0] * x) + (M2.m[1 * 4 + 0] * y) + (M2.m[2 * 4 + 0] * z) + (M2.m[3 * 4 + 0] * w)
M.m[0 * 4 + 1] = (M2.m[0 * 4 + 1] * x) + (M2.m[1 * 4 + 1] * y) + (M2.m[2 * 4 + 1] * z) + (M2.m[3 * 4 + 1] * w)
M.m[0 * 4 + 2] = (M2.m[0 * 4 + 2] * x) + (M2.m[1 * 4 + 2] * y) + (M2.m[2 * 4 + 2] * z) + (M2.m[3 * 4 + 2] * w)
M.m[0 * 4 + 3] = (M2.m[0 * 4 + 3] * x) + (M2.m[1 * 4 + 3] * y) + (M2.m[2 * 4 + 3] * z) + (M2.m[3 * 4 + 3] * w)
x = M1.m[1 * 4 + 0]
y = M1.m[1 * 4 + 1]
z = M1.m[1 * 4 + 2]
w = M1.m[1 * 4 + 3]
M.m[1 * 4 + 0] = (M2.m[0 * 4 + 0] * x) + (M2.m[1 * 4 + 0] * y) + (M2.m[2 * 4 + 0] * z) + (M2.m[3 * 4 + 0] * w)
M.m[1 * 4 + 1] = (M2.m[0 * 4 + 1] * x) + (M2.m[1 * 4 + 1] * y) + (M2.m[2 * 4 + 1] * z) + (M2.m[3 * 4 + 1] * w)
M.m[1 * 4 + 2] = (M2.m[0 * 4 + 2] * x) + (M2.m[1 * 4 + 2] * y) + (M2.m[2 * 4 + 2] * z) + (M2.m[3 * 4 + 2] * w)
M.m[1 * 4 + 3] = (M2.m[0 * 4 + 3] * x) + (M2.m[1 * 4 + 3] * y) + (M2.m[2 * 4 + 3] * z) + (M2.m[3 * 4 + 3] * w)
x = M1.m[2 * 4 + 0]
y = M1.m[2 * 4 + 1]
z = M1.m[2 * 4 + 2]
w = M1.m[2 * 4 + 3]
M.m[2 * 4 + 0] = (M2.m[0 * 4 + 0] * x) + (M2.m[1 * 4 + 0] * y) + (M2.m[2 * 4 + 0] * z) + (M2.m[3 * 4 + 0] * w)
M.m[2 * 4 + 1] = (M2.m[0 * 4 + 1] * x) + (M2.m[1 * 4 + 1] * y) + (M2.m[2 * 4 + 1] * z) + (M2.m[3 * 4 + 1] * w)
M.m[2 * 4 + 2] = (M2.m[0 * 4 + 2] * x) + (M2.m[1 * 4 + 2] * y) + (M2.m[2 * 4 + 2] * z) + (M2.m[3 * 4 + 2] * w)
M.m[2 * 4 + 3] = (M2.m[0 * 4 + 3] * x) + (M2.m[1 * 4 + 3] * y) + (M2.m[2 * 4 + 3] * z) + (M2.m[3 * 4 + 3] * w)
x = M1.m[3 * 4 + 0]
y = M1.m[3 * 4 + 1]
z = M1.m[3 * 4 + 2]
w = M1.m[3 * 4 + 3]
M.m[3 * 4 + 0] = (M2.m[0 * 4 + 0] * x) + (M2.m[1 * 4 + 0] * y) + (M2.m[2 * 4 + 0] * z) + (M2.m[3 * 4 + 0] * w)
M.m[3 * 4 + 1] = (M2.m[0 * 4 + 1] * x) + (M2.m[1 * 4 + 1] * y) + (M2.m[2 * 4 + 1] * z) + (M2.m[3 * 4 + 1] * w)
M.m[3 * 4 + 2] = (M2.m[0 * 4 + 2] * x) + (M2.m[1 * 4 + 2] * y) + (M2.m[2 * 4 + 2] * z) + (M2.m[3 * 4 + 2] * w)
M.m[3 * 4 + 3] = (M2.m[0 * 4 + 3] * x) + (M2.m[1 * 4 + 3] * y) + (M2.m[2 * 4 + 3] * z) + (M2.m[3 * 4 + 3] * w)
return M
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)
assert(not vec3.equal(eye_direction, vec3._zero))
assert(not vec3.isinfinite(eye_direction))
assert(not vec3.equal(up_direction, vec3._zero))
assert(not vec3.isinfinite(up_direction))
local r2 = vec3.normalize(eye_direction)
local r0 = vec3.cross(up_direction, r2)
r0 = vec3.normalize(r0)
local r1 = vec3.cross(r2, r0)
local neg_eye_position = vec3.negate(eye_position)
local d0 = vec3.dot(r0, neg_eye_position)
local d1 = vec3.dot(r1, neg_eye_position)
local d2 = vec3.dot(r2, neg_eye_position)
local M = mat4()
M.m[0 * 4 + 0] = r0.f[0]
M.m[1 * 4 + 0] = r0.f[1]
M.m[2 * 4 + 0] = r0.f[2]
M.m[3 * 4 + 0] = d0
M.m[0 * 4 + 1] = r1.f[0]
M.m[1 * 4 + 1] = r1.f[1]
M.m[2 * 4 + 1] = r1.f[2]
M.m[3 * 4 + 1] = d1
M.m[0 * 4 + 2] = r2.f[0]
M.m[1 * 4 + 2] = r2.f[1]
M.m[2 * 4 + 2] = r2.f[2]
M.m[3 * 4 + 2] = d2
--M.m[0 * 4 + 3] = 0
--M.m[1 * 4 + 3] = 0
--M.m[2 * 4 + 3] = 0
M.m[3 * 4 + 3] = 1
return M
end,
look_at_lh = function(eye_position, focus_position, up_direction)
local eye_direction = vec3.subtract(focus_position, eye_position)
return mat4.look_to_lh(eye_position, eye_direction, up_direction)
end,
look_at_rh = function(eye_position, focus_position, up_direction)
local neg_eye_direction = vec3.subtract(eye_position, focus_position)
return mat4.look_to_lh(eye_position, neg_eye_direction, up_direction)
end,
perspective_rh = function(view_width, view_height, near_z, far_z)
assert(near_z > 0.0 and far_z > 0.0)
assert(not scalar.near_equal(view_width, 0.0, 0.00001))
assert(not scalar.near_equal(view_height, 0.0, 0.00001))
assert(not scalar.near_equal(far_z, near_z, 0.00001))
local two_near_z = near_z + near_z;
local f_range = far_z / (near_z - far_z);
local M = mat4()
M.m[0 * 4 + 0] = two_near_z / view_width
--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] = two_near_z / view_height
--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] = f_range
M.m[2 * 4 + 3] = -1.0
--M.m[3 * 4 + 0] = 0.0
--M.m[3 * 4 + 1] = 0.0
M.m[3 * 4 + 2] = f_range * near_z
--M.m[3 * 4 + 3] = 0.0
return M
end,
near_equal = function(M1, M2, epsilon)
local d00 = abs(M1.m[0 * 4 + 0] - M2.m[0 * 4 + 0])
local d01 = abs(M1.m[0 * 4 + 1] - M2.m[0 * 4 + 1])
local d02 = abs(M1.m[0 * 4 + 2] - M2.m[0 * 4 + 2])
local d03 = abs(M1.m[0 * 4 + 3] - M2.m[0 * 4 + 3])
local d10 = abs(M1.m[1 * 4 + 0] - M2.m[1 * 4 + 0])
local d11 = abs(M1.m[1 * 4 + 1] - M2.m[1 * 4 + 1])
local d12 = abs(M1.m[1 * 4 + 2] - M2.m[1 * 4 + 2])
local d13 = abs(M1.m[1 * 4 + 3] - M2.m[1 * 4 + 3])
local d20 = abs(M1.m[2 * 4 + 0] - M2.m[2 * 4 + 0])
local d21 = abs(M1.m[2 * 4 + 1] - M2.m[2 * 4 + 1])
local d22 = abs(M1.m[2 * 4 + 2] - M2.m[2 * 4 + 2])
local d23 = abs(M1.m[2 * 4 + 3] - M2.m[2 * 4 + 3])
local d30 = abs(M1.m[3 * 4 + 0] - M2.m[3 * 4 + 0])
local d31 = abs(M1.m[3 * 4 + 1] - M2.m[3 * 4 + 1])
local d32 = abs(M1.m[3 * 4 + 2] - M2.m[3 * 4 + 2])
local d33 = abs(M1.m[3 * 4 + 3] - M2.m[3 * 4 + 3])
return (
(d00 <= epsilon) and (d01 <= epsilon) and (d02 <= epsilon) and (d03 <= epsilon) and
(d10 <= epsilon) and (d11 <= epsilon) and (d12 <= epsilon) and (d13 <= epsilon) and
(d20 <= epsilon) and (d21 <= epsilon) and (d22 <= epsilon) and (d23 <= epsilon) and
(d30 <= epsilon) and (d31 <= epsilon) and (d32 <= epsilon) and (d33 <= epsilon)
)
end,
equal = function(M1, M2)
return (
M1.m[0 * 4 + 0] == M2.m[0 * 4 + 0] and
M1.m[0 * 4 + 1] == M2.m[0 * 4 + 1] and
M1.m[0 * 4 + 2] == M2.m[0 * 4 + 2] and
M1.m[0 * 4 + 3] == M2.m[0 * 4 + 3] and
M1.m[1 * 4 + 0] == M2.m[1 * 4 + 0] and
M1.m[1 * 4 + 1] == M2.m[1 * 4 + 1] and
M1.m[1 * 4 + 2] == M2.m[1 * 4 + 2] and
M1.m[1 * 4 + 3] == M2.m[1 * 4 + 3] and
M1.m[2 * 4 + 0] == M2.m[2 * 4 + 0] and
M1.m[2 * 4 + 1] == M2.m[2 * 4 + 1] and
M1.m[2 * 4 + 2] == M2.m[2 * 4 + 2] and
M1.m[2 * 4 + 3] == M2.m[2 * 4 + 3] and
M1.m[3 * 4 + 0] == M2.m[3 * 4 + 0] and
M1.m[3 * 4 + 1] == M2.m[3 * 4 + 1] and
M1.m[3 * 4 + 2] == M2.m[3 * 4 + 2] and
M1.m[3 * 4 + 3] == M2.m[3 * 4 + 3]
)
end,
print = function(M)
for i = 0, 15 do
io.write(tostring(M.m[i]))
io.write(" ")
if i % 4 == 3 then
io.write("\n")
end
end
end
}
setmetatable(mat4, mat4)
vec3 = {
__call = function(_t, x, y, z)
-- newByteData is zero-initialized
local data = love.data.newByteData(3 * 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
setmetatable(value, vec3)
return value
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)
local value = (
v1.f[0] * v2.f[0] +
v1.f[1] * v2.f[1] +
v1.f[2] * v2.f[2]
)
return value
end,
length_sq = function(v)
return vec3.dot(v, v)
end,
reciprocal_length = function(v)
local result
result = vec3.length_sq(v)
result = 1.0 / sqrt(result)
return result
end,
length = function(v)
local result
result = vec3.length_sq(v)
result = sqrt(result)
return result
end,
add = function(v1, v2)
local result = vec3(
v1.f[0] + v2.f[0],
v1.f[1] + v2.f[1],
v1.f[2] + v2.f[2]
)
return result
end,
subtract = function(v1, v2)
local result = vec3(
v1.f[0] - v2.f[0],
v1.f[1] - v2.f[1],
v1.f[2] - v2.f[2]
)
return result
end,
multiply = function(v1, v2)
local result = vec3(
v1.f[0] * v2.f[0],
v1.f[1] * v2.f[1],
v1.f[2] * v2.f[2]
)
return result
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)
local length = vec3.reciprocal_length(v)
local result = vec3(
v.f[0] * length,
v.f[1] * length,
v.f[2] * length
)
return result
end,
cross = function(v1, v2)
local result = vec3(
(v1.f[1] * v2.f[2]) - (v1.f[2] * v2.f[1]),
(v1.f[2] * v2.f[0]) - (v1.f[0] * v2.f[2]),
(v1.f[0] * v2.f[1]) - (v1.f[1] * v2.f[0])
)
return result
end,
negate = function(v)
local result = vec3(
-v.f[0],
-v.f[1],
-v.f[2]
)
return result
end,
equal = function(v1, v2)
return (
(v1.f[0] == v2.f[0]) and
(v1.f[1] == v2.f[1]) and
(v1.f[2] == v2.f[2])
)
end,
near_equal = function(v1, v2, epsilon)
local dx = abs(v1.f[0] - v2.f[0])
local dy = abs(v1.f[1] - v2.f[1])
local dz = abs(v1.f[2] - v2.f[2])
return (dx <= epsilon) and (dy <= epsilon) and (dz <= epsilon)
end,
isinfinite = function(v)
return (
(v.f[0] == -math.huge or v.f[0] == math.huge) or
(v.f[1] == -math.huge or v.f[1] == math.huge) or
(v.f[2] == -math.huge or v.f[2] == math.huge)
)
end,
print = function(v)
print(tostring(v.f[0]) .. " " .. tostring(v.f[1]) .. " " .. tostring(v.f[2]))
end,
}
setmetatable(vec3, vec3)
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
----------------------------------------------------------------------
assert(vec3.dot(vec3(1, 3, -5), vec3(4, -2, -1)) == 3)
assert(vec3.dot(vec3(1, 3, -5), vec3(1, 3, -5)) == 35)
assert(vec3.length_sq(vec3(1, 3, -5)) == 35)
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.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),
vec3(5, 6, 7),
vec3(9, 10, 11)),
mat4.set( 0.408249, 0.778499, 0.476731, 0.000000,
-0.816496, 0.077850, 0.572078, 0.000000,
0.408248, -0.622799, 0.667424, 0.000000,
-0.000001, 0.934199, -3.623158, 1.000000),
0.00001))
assert(mat4.near_equal(mat4.perspective_rh(2, 3, 4, 5),
mat4.set(4.000000, 0.000000, 0.000000, 0.000000,
0.000000, 2.666667, 0.000000, 0.000000,
0.000000, 0.000000, -5.000000, -1.000000,
0.000000, 0.000000, -20.000000, 0.000000),
0.00001))
assert(mat4.equal(mat4.multiply(mat4.set(1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16),
mat4.set(17, 18, 19, 20,
21, 22, 23, 24,
25, 26, 27, 29,
30, 31, 32, 33)),
mat4.set(254, 264, 274, 287,
626, 652, 678, 711,
998, 1040, 1082, 1135,
1370, 1428, 1486, 1559)))
assert(mat4.equal(mat4.set(1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16)
*
mat4.set(17, 18, 19, 20,
21, 22, 23, 24,
25, 26, 27, 29,
30, 31, 32, 33),
mat4.set(254, 264, 274, 287,
626, 652, 678, 711,
998, 1040, 1082, 1135,
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 {
scalar = scalar,
mat4 = mat4,
vec3 = vec3,
}

BIN
bird.dds Normal file
View File

Binary file not shown.

126
main.lua
View File

@ -1,15 +1,28 @@
local mesh
local rotation
local texture
local ffi = require 'ffi'
local _math = require '_math'
local mat4 = _math.mat4
local vec3 = _math.vec3
local pixelcode = [[
#pragma language glsl3
varying vec4 PixelColor;
varying vec4 PixelNormal;
varying vec4 PixelTexture;
uniform sampler2D texture_sampler;
out vec4 outData;
void pixelmain()
{
outData = PixelColor;
vec4 texColor = texture(texture_sampler, PixelTexture.xy);
float intensity = min(max(dot(vec3(1, 1, 1), PixelNormal.xyz), 0), 1);
outData = vec4(texColor.xyz * (0.1 + intensity * intensity), 1.0);
}
]]
@ -20,18 +33,16 @@ local vertexcode = [[
layout (location = 1) in vec4 VertexNormal;
layout (location = 2) in vec4 VertexTexture;
uniform mat4 projection;
uniform mat4 view;
uniform mat4 model;
uniform mat4 model2;
uniform mat4 transform;
varying vec4 PixelColor;
varying vec4 PixelNormal;
varying vec4 PixelTexture;
void vertexmain()
{
PixelColor = VertexNormal * 0.5 + 0.5;
mat4 trans = projection * view * model * model2;
love_Position = trans * vec4(VertexPosition.xyz, 1);
PixelNormal = VertexNormal * 0.5 + 0.5;
PixelTexture = VertexTexture;
love_Position = transform * vec4(VertexPosition.xyz, 1);
}
]]
@ -43,31 +54,8 @@ local vertexformat = {
{ name = 'VertexTexture', format = 'floatvec3', location = 2 },
}
local rotation
function look_at()
local m = {
1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, 0.000000,
0.000000, 0.000000, 1.000000, -2.000000,
0.000000, 0.000000, 0.000000, 1.000000,
}
return m;
end
function projection()
local m = {
1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, 0.000000,
0.000000, 0.000000, -1.002002, -0.200200,
0.000000, 0.000000, -1.000000, 0.000000,
}
return m
end
function love.load(args)
love.window.setMode(600, 600, {depth=true})
love.window.setMode(1024, 1024, {depth=true})
local vertexdata = love.filesystem.newFileData("position_normal_texture.vtx")
local indexdata = love.filesystem.newFileData("index.idx")
@ -105,52 +93,46 @@ function love.load(args)
mesh = love.graphics.newMesh(attributelist, drawmode)
mesh:setIndexBuffer(indexbuffer)
local image_data = love.image.newCompressedData('bird.dds')
texture = love.graphics.newTexture(image_data)
end
local rotation = 0.0
function rotate_x(t)
local cos = math.cos
local sin = math.sin
return {
1, 0, 0, 0,
0, cos(t), -sin(t), 0,
0, sin(t), cos(t), 0,
0, 0, 0, 1
}
end
function rotate_y(t)
local cos = math.cos
local sin = math.sin
return {
cos(t), 0, sin(t), 0,
0, 1, 0, 0,
-sin(t), 0, cos(t), 0,
0, 0, 0, 1
}
end
function rotate_z(t)
local cos = math.cos
local sin = math.sin
return {
cos(t), -sin(t), 0, 0,
sin(t), cos(t), 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
}
end
function love.draw()
local radius = 100
local mx, my = love.mouse.getPosition()
shader:send("projection", projection(1, 1))
shader:send("view", look_at())
shader:send("model", rotate_x(rotation))
shader:send("model2", rotate_z(rotation * 0.5))
width, height = love.graphics.getDimensions()
-- shader:send("projection", "column", mat4.perspective_rh(width / width * 0.25,
-- height / width * 0.25,
-- 0.1,
-- 1000.0).data)
-- shader:send("view", "column", mat4.look_at_rh(vec3(0, -2, 0),
-- vec3(0, 0, 0),
-- vec3(0, 0, 1)).data)
-- shader:send("model", "column", mat4.rotation_x(rotation).data)
-- shader:send("model2", "column", mat4.rotation_z(rotation * 0.5).data)
local projection = mat4.perspective_rh(width / width * 0.25,
height / width * 0.25,
0.1,
1000.0)
local view = mat4.look_at_rh(vec3(0, -2, 0),
vec3(0, 0, 0),
vec3(0, 0, 1))
local world1 = mat4.rotation_x(rotation)
local world2 = mat4.rotation_z(rotation * 0.5)
local world3 = mat4.translation(0, 0, -0.5)
local transform = world3 * world2 * world1 * view * projection
shader:send("transform", "column", transform.data)
shader:send("texture_sampler", texture)
rotation = rotation + 0.01
love.graphics.setShader(shader)
love.graphics.setDepthMode("less", true)