bilbo/love-demo
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

_math: implement mat4.perspective_rh and mat4.look_at_rh

Browse Source
This commit is contained in:
Zack Buhman 2026-02-23 01:26:39 +00:00
parent 44a3c5b76e
commit 13d882d6df
2 changed files with 371 additions and 91 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

364
_math.lua
View File

@ -2,10 +2,24 @@ 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 scalar
local newmat4 = function(_t)
scalar = {
near_equal = function(s1, s2, epsilon)
local d = abs(s1 - s2)
return d <= epsilon
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())
@ -15,13 +29,37 @@ local newmat4 = function(_t)
}
setmetatable(value, mat4)
return value
end
end,
mat4 = {
__call = newmat4,
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 = newmat4()
local M = mat4()
M.m[0 * 4 + 0] = 1.0
--M.m[0 * 4 + 1] = 0.0
--M.m[0 * 4 + 2] = 0.0
@ -45,7 +83,7 @@ mat4 = {
end,
translation = function(x, y, z)
local M = newmat4()
local M = mat4()
M.m[0 * 4 + 0] = 1.0
--M.m[0 * 4 + 1] = 0.0
--M.m[0 * 4 + 2] = 0.0
@ -72,7 +110,7 @@ mat4 = {
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local M = newmat4()
local M = mat4()
M.m[0 * 4 + 0] = 1.0
--M.m[0 * 4 + 1] = 0.0
--M.m[0 * 4 + 2] = 0.0
@ -99,7 +137,7 @@ mat4 = {
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local M = newmat4()
local M = mat4()
M.m[0 * 4 + 0] = cos_angle
--M.m[0 * 4 + 1] = 0.0
M.m[0 * 4 + 2] = -sin_angle
@ -126,7 +164,7 @@ mat4 = {
local sin_angle = sin(angle)
local cos_angle = cos(angle)
local M = newmat4()
local M = mat4()
M.m[0 * 4 + 0] = cos_angle
M.m[0 * 4 + 1] = sin_angle
--M.m[0 * 4 + 2] = 0.0
@ -149,13 +187,313 @@ mat4 = {
return M
end,
dot = function(a, b)
print("dot" .. tostring(a) .. tostring(b))
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,
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,
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)
return {
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,
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,
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)
----------------------------------------------------------------------
-- 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(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))
return {
scalar = scalar,
mat4 = mat4,
vec3 = vec3,
}

82
main.lua
View File

@ -3,6 +3,9 @@ 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
@ -55,27 +58,6 @@ local vertexformat = {
{ name = 'VertexTexture', format = 'floatvec3', location = 2 },
}
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(1024, 1024, {depth=true})
@ -122,59 +104,19 @@ 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 print_matrix(ptr)
for i=0,15 do
io.write(tostring(ptr[i]))
io.write(" ")
if i % 4 == 3 then
io.write("\n")
end
end
end
local math = require '_math'
local mat4 = math.mat4
function love.draw()
local radius = 100
local mx, my = love.mouse.getPosition()
shader:send("projection", projection(1, 1))
shader:send("view", "column", mat4.translation(0, 0, -2).data)
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)
shader:send("texture_sampler", texture)