local sin = math.sin
local cos = math.cos
local sqrt = math.sqrt
local rad = math.rad

-- =================================================== --
-- ====================== vec3 ======================= --
-- =================================================== --
function vec3.add(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] + b[1]
            dst[2] = a[2] + b[2]
            dst[3] = a[3] + b[3]
        else
            dst[1] = a[1] + b
            dst[2] = a[2] + b
            dst[3] = a[3] + b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] + b[1], a[2] + b[2], a[3] + b[3]}
        else
            return {a[1] + b, a[2] + b, a[3] + b}
        end
    end
end

function vec3.sub(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] - b[1]
            dst[2] = a[2] - b[2]
            dst[3] = a[3] - b[3]
        else
            dst[1] = a[1] - b
            dst[2] = a[2] - b
            dst[3] = a[3] - b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] - b[1], a[2] - b[2], a[3] - b[3]}
        else
            return {a[1] - b, a[2] - b, a[3] - b}
        end
    end
end

function vec3.mul(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] * b[1]
            dst[2] = a[2] * b[2]
            dst[3] = a[3] * b[3]
        else
            dst[1] = a[1] * b
            dst[2] = a[2] * b
            dst[3] = a[3] * b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] * b[1], a[2] * b[2], a[3] * b[3]}
        else
            return {a[1] * b, a[2] * b, a[3] * b}
        end
    end
end

function vec3.div(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] / b[1]
            dst[2] = a[2] / b[2]
            dst[3] = a[3] / b[3]
        else
            dst[1] = a[1] / b
            dst[2] = a[2] / b
            dst[3] = a[3] / b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] / b[1], a[2] / b[2], a[3] / b[3]}
        else
            return {a[1] / b, a[2] / b, a[3] / b}
        end
    end
end

function vec3.abs(a, dst)
    local x = a[1]
    local y = a[2]
    local z = a[3]
    if dst then
        dst[1] = x < 0.0 and -x or x
        dst[2] = y < 0.0 and -y or y
        dst[3] = z < 0.0 and -z or z
    else
        return {
            x < 0.0 and -x or x,
            y < 0.0 and -y or y,
            z < 0.0 and -z or z,
        }
    end
end

function vec3.dot(a, b)
    return a[1] * b[1] + a[2] * b[2] + a[3] * b[3]
end

function vec3.mix(a, b, t, dest)
    if dest then
        dest[1] = a[1] * (1.0 - t) + b[1] * t
        dest[2] = a[2] * (1.0 - t) + b[2] * t
        dest[3] = a[3] * (1.0 - t) + b[3] * t
        return dest
    else
        return {
            a[1] * (1.0 - t) + b[1] * t,
            a[2] * (1.0 - t) + b[2] * t,
            a[3] * (1.0 - t) + b[3] * t,
        }
    end
end

-- =================================================== --
-- ====================== vec2 ======================= --
-- =================================================== --
function vec2.add(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] + b[1]
            dst[2] = a[2] + b[2]
        else
            dst[1] = a[1] + b
            dst[2] = a[2] + b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] + b[1], a[2] + b[2]}
        else
            return {a[1] + b, a[2] + b}
        end
    end
end

function vec2.sub(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] - b[1]
            dst[2] = a[2] - b[2]
        else
            dst[1] = a[1] - b
            dst[2] = a[2] - b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] - b[1], a[2] - b[2]}
        else
            return {a[1] - b, a[2] - b}
        end
    end
end

function vec2.mul(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] * b[1]
            dst[2] = a[2] * b[2]
        else
            dst[1] = a[1] * b
            dst[2] = a[2] * b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] * b[1], a[2] * b[2]}
        else
            return {a[1] * b, a[2] * b}
        end
    end
end

function vec2.div(a, b, dst)
    local btype = type(b)
    if dst then
        if btype == "table" then
            dst[1] = a[1] / b[1]
            dst[2] = a[2] / b[2]
        else
            dst[1] = a[1] / b
            dst[2] = a[2] / b
        end
        return dst
    else
        if btype == "table" then
            return {a[1] / b[1], a[2] / b[2]}
        else
            return {a[1] / b, a[2] / b}
        end
    end
end

function vec2.abs(a, dst)
    local x = a[1]
    local y = a[2]
    if dst then
        dst[1] = x < 0.0 and -x or x
        dst[2] = y < 0.0 and -y or y
    else
        return {
            x < 0.0 and -x or x,
            y < 0.0 and -y or y,
        }
    end
end

function vec2.dot(a, b)
    return a[1] * b[1] + a[2] * b[2]
end

function vec2.mix(a, b, t, dest)
    if dest then
        dest[1] = a[1] * (1.0 - t) + b[1] * t
        dest[2] = a[2] * (1.0 - t) + b[2] * t
        return dest
    else
        return {
            a[1] * (1.0 - t) + b[1] * t,
            a[2] * (1.0 - t) + b[2] * t,
        }
    end
end

function mat4.idt(dst)
    if dst then
        for i=1,16 do
            dst[i] = (i % 5 == 1) and 1 or 0
        end
    end
    return {
        1, 0, 0, 0,
        0, 1, 0, 0,
        0, 0, 1, 0,
        0, 0, 0, 1
    }
end

function mat4.rotate(...)
    local argc = select("#", ...)

    local matrix, axis, angle, dst

    if argc == 2 then
        axis, angle = ...
        matrix = mat4.idt()
    elseif argc == 3 then
        matrix, axis, angle = ...
    elseif argc == 4 then
        matrix, axis, angle, dst = ...
    else
        error("invalid arguments number (2, 3 or 4 expected)")
    end

    angle = rad(angle)

    local x, y, z = axis[1], axis[2], axis[3]

    local len = sqrt(x * x + y * y + z * z)
    if len == 0 then
        error("rotation axis has zero length")
    end

    x = x / len
    y = y / len
    z = z / len

    local c = cos(angle)
    local s = sin(angle)
    local t = 1 - c

    local r00 = t * x * x + c
    local r01 = t * x * y - s * z
    local r02 = t * x * z + s * y

    local r10 = t * x * y + s * z
    local r11 = t * y * y + c
    local r12 = t * y * z - s * x

    local r20 = t * x * z - s * y
    local r21 = t * y * z + s * x
    local r22 = t * z * z + c

    local out = dst or {}

    local m1,  m2,  m3,  m4  = matrix[1],  matrix[2],  matrix[3],  matrix[4]
    local m5,  m6,  m7,  m8  = matrix[5],  matrix[6],  matrix[7],  matrix[8]
    local m9,  m10, m11, m12 = matrix[9],  matrix[10], matrix[11], matrix[12]
    local m13, m14, m15, m16 = matrix[13], matrix[14], matrix[15], matrix[16]

    out[1]  = m1 * r00 + m5 * r10 + m9  * r20
    out[2]  = m2 * r00 + m6 * r10 + m10 * r20
    out[3]  = m3 * r00 + m7 * r10 + m11 * r20
    out[4]  = m4 * r00 + m8 * r10 + m12 * r20

    out[5]  = m1 * r01 + m5 * r11 + m9  * r21
    out[6]  = m2 * r01 + m6 * r11 + m10 * r21
    out[7]  = m3 * r01 + m7 * r11 + m11 * r21
    out[8]  = m4 * r01 + m8 * r11 + m12 * r21

    out[9]  = m1 * r02 + m5 * r12 + m9  * r22
    out[10] = m2 * r02 + m6 * r12 + m10 * r22
    out[11] = m3 * r02 + m7 * r12 + m11 * r22
    out[12] = m4 * r02 + m8 * r12 + m12 * r22

    out[13] = m13
    out[14] = m14
    out[15] = m15
    out[16] = m16

    return out
end