Shining-in-the-Darkness-Lua-Remake-abandoned/g3d/matrices.lua

-- written by groverbuger for g3d
-- september 2021
-- MIT license

local vectors = require(g3d.path .. "/vectors")
local vectorCrossProduct = vectors.crossProduct
local vectorDotProduct = vectors.dotProduct
local vectorNormalize = vectors.normalize

----------------------------------------------------------------------------------------------------
-- matrix class
----------------------------------------------------------------------------------------------------
-- matrices are 16 numbers in table, representing a 4x4 matrix like so:
--
-- |  1   2   3   4  |
-- |                 |
-- |  5   6   7   8  |
-- |                 |
-- |  9   10  11  12 |
-- |                 |
-- |  13  14  15  16 |

local matrix = {}
matrix.__index = matrix

local function newMatrix()
    local self = setmetatable({}, matrix)

    -- initialize a matrix as the identity matrix
    self[1],  self[2],  self[3],  self[4]  = 1, 0, 0, 0
    self[5],  self[6],  self[7],  self[8]  = 0, 1, 0, 0
    self[9],  self[10], self[11], self[12] = 0, 0, 1, 0
    self[13], self[14], self[15], self[16] = 0, 0, 0, 1

    return self
end

-- automatically converts a matrix to a string
-- for printing to console and debugging
function matrix:__tostring()
    return ("%f\t%f\t%f\t%f\n%f\t%f\t%f\t%f\n%f\t%f\t%f\t%f\n%f\t%f\t%f\t%f"):format(unpack(self))
end

----------------------------------------------------------------------------------------------------
-- transformation, projection, and rotation matrices
----------------------------------------------------------------------------------------------------
-- the three most important matrices for 3d graphics
-- these three matrices are all you need to write a simple 3d shader

-- returns a transformation matrix
-- translation, rotation, and scale are all 3d vectors
function matrix:setTransformationMatrix(translation, rotation, scale)
    -- translations
    self[4]  = translation[1]
    self[8]  = translation[2]
    self[12] = translation[3]

    -- rotations
    if #rotation == 3 then
        -- use 3D rotation vector as euler angles
        -- source: https://en.wikipedia.org/wiki/Rotation_matrix
        local ca, cb, cc = math.cos(rotation[3]), math.cos(rotation[2]), math.cos(rotation[1])
        local sa, sb, sc = math.sin(rotation[3]), math.sin(rotation[2]), math.sin(rotation[1])
        self[1], self[2],  self[3]  = ca*cb, ca*sb*sc - sa*cc, ca*sb*cc + sa*sc
        self[5], self[6],  self[7]  = sa*cb, sa*sb*sc + ca*cc, sa*sb*cc - ca*sc
        self[9], self[10], self[11] = -sb, cb*sc, cb*cc
    else
        -- use 4D rotation vector as a quaternion
        local qx, qy, qz, qw = rotation[1], rotation[2], rotation[3], rotation[4]
        self[1], self[2],  self[3]  = 1 - 2*qy^2 - 2*qz^2, 2*qx*qy - 2*qz*qw,   2*qx*qz + 2*qy*qw
        self[5], self[6],  self[7]  = 2*qx*qy + 2*qz*qw,   1 - 2*qx^2 - 2*qz^2, 2*qy*qz - 2*qx*qw
        self[9], self[10], self[11] = 2*qx*qz - 2*qy*qw,   2*qy*qz + 2*qx*qw,   1 - 2*qx^2 - 2*qy^2
    end

    -- scale
    local sx, sy, sz = scale[1], scale[2], scale[3]
    self[1], self[2],  self[3]  = self[1] * sx, self[2]  * sy, self[3]  * sz
    self[5], self[6],  self[7]  = self[5] * sx, self[6]  * sy, self[7]  * sz
    self[9], self[10], self[11] = self[9] * sx, self[10] * sy, self[11] * sz

    -- fourth row is not used, just set it to the fourth row of the identity matrix
    self[13], self[14], self[15], self[16] = 0, 0, 0, 1
end

-- returns a perspective projection matrix
-- (things farther away appear smaller)
-- all arguments are scalars aka normal numbers
-- aspectRatio is defined as window width divided by window height
function matrix:setProjectionMatrix(fov, near, far, aspectRatio)
    local top = near * math.tan(fov/2)
    local bottom = -1*top
    local right = top * aspectRatio
    local left = -1*right

    self[1],  self[2],  self[3],  self[4]  = 2*near/(right-left), 0, (right+left)/(right-left), 0
    self[5],  self[6],  self[7],  self[8]  = 0, 2*near/(top-bottom), (top+bottom)/(top-bottom), 0
    self[9],  self[10], self[11], self[12] = 0, 0, -1*(far+near)/(far-near), -2*far*near/(far-near)
    self[13], self[14], self[15], self[16] = 0, 0, -1, 0
end

-- returns an orthographic projection matrix
-- (things farther away are the same size as things closer)
-- all arguments are scalars aka normal numbers
-- aspectRatio is defined as window width divided by window height
function matrix:setOrthographicMatrix(fov, size, near, far, aspectRatio)
    local top = size * math.tan(fov/2)
    local bottom = -1*top
    local right = top * aspectRatio
    local left = -1*right

    self[1],  self[2],  self[3],  self[4]  = 2/(right-left), 0, 0, -1*(right+left)/(right-left)
    self[5],  self[6],  self[7],  self[8]  = 0, 2/(top-bottom), 0, -1*(top+bottom)/(top-bottom)
    self[9],  self[10], self[11], self[12] = 0, 0, -2/(far-near), -(far+near)/(far-near)
    self[13], self[14], self[15], self[16] = 0, 0, 0, 1
end

-- returns a view matrix
-- eye, target, and up are all 3d vectors
function matrix:setViewMatrix(eye, target, up)
    local z1, z2, z3 = vectorNormalize(eye[1] - target[1], eye[2] - target[2], eye[3] - target[3])
    local x1, x2, x3 = vectorNormalize(vectorCrossProduct(up[1], up[2], up[3], z1, z2, z3))
    local y1, y2, y3 = vectorCrossProduct(z1, z2, z3, x1, x2, x3)

    self[1],  self[2],  self[3],  self[4]  = x1, x2, x3, -1*vectorDotProduct(x1, x2, x3, eye[1], eye[2], eye[3])
    self[5],  self[6],  self[7],  self[8]  = y1, y2, y3, -1*vectorDotProduct(y1, y2, y3, eye[1], eye[2], eye[3])
    self[9],  self[10], self[11], self[12] = z1, z2, z3, -1*vectorDotProduct(z1, z2, z3, eye[1], eye[2], eye[3])
    self[13], self[14], self[15], self[16] = 0, 0, 0, 1
end

return newMatrix