voxelcore/res/modules/animation.lua

local this = {}

local CH_TRANSLATE = 1
local CH_ROTATE = 2

local AX_X = 1
local AX_Y = 2
local AX_Z = 3

local INT_CONST = 1
local INT_LINEAR = 2
local INT_BEZIER = 3

local function bezier(a, b, c, d, u)
    local s = 1 - u
    return s * s * s * a +
        3 * s * s * u * b +
        3 * s * u * u * c +
        u * u * u * d
end

local function bezier_derivative(a, b, c, d, u)
    local s = 1 - u
    return
        3 * s * s * (b - a) +
        6 * s * u * (c - b) +
        3 * u * u * (d - c)
end

local function bezier_interpolation(k0, k1, t)
    local frame = k0.frame + t * (k1.frame - k0.frame)
    local u = t

    for i=1,8 do
        local x = bezier(
            k0.frame,
            k0.rx,
            k1.lx,
            k1.frame,
            u
        )
        local dx = bezier_derivative(
            k0.frame,
            k0.rx,
            k1.lx,
            k1.frame,
            u
        )
        if math.abs(dx) < 1e-8 then
            break
        end

        u = u - (x - frame) / dx

        if u < 0 then u = 0 end
        if u > 1 then u = 1 end
    end

    return bezier(k0.value, k0.ry, k1.ly, k1.value, u)
end

local patterns =  {
    {name="sint", pattern="sin(t)"},
    {name="sint2", pattern="sin(t * 2)"},
}

local function process_expression(src, memoised)
    for i, pattern in ipairs(patterns) do
        local pattern_safe = string.pattern_safe(pattern.pattern)
        if src:find(pattern_safe) then
            memoised[pattern.name] = pattern.pattern
            src = src:gsub(pattern_safe, pattern.name)
        end
    end
    return src
end

local function key_neighbors(keys, frame)
    local left = 1
    local right = #keys

    while left <= right do
        local mid = math.floor((left + right) / 2)

        if keys[mid].frame < frame then
            left = mid + 1
        elseif keys[mid].frame > frame then
            right = mid - 1
        else
            return mid, mid
        end
    end
    if left > #keys then
        left = #keys
    end
    return right, left
end

local env = {
    mat4 = mat4,
    X = {1, 0, 0},
    Y = {0, 1, 0},
    Z = {0, 0, 1},
    DST = mat4.idt(),
    value_at = function(keys, frame, interp)
        local left, right = key_neighbors(keys, frame)
        if left == right then
            return keys[left].value
        end
        left = keys[left]
        if interp == INT_CONST then
            return left.value
        end
        right = keys[right]
        local t = (frame - left.frame) / (right.frame - left.frame)
        if interp == INT_BEZIER then
            return bezier_interpolation(left, right, t)
        end
        return left.value * (1.0 - t) + right.value * t
    end,
}
table.extend(env, math)

local function codegen_track(lines, memoised, keysets)
    local code = ""
    local translation = {false, false, false}
    local rotation = {false, false, false}
    for i, line in ipairs(lines) do
        if line.expression then
            code = code .. "\n  local l" .. i .. " = (" ..
                process_expression(line.expression, memoised) .. ")"
        elseif line.keys then
            keysets[i] = line.keys
            code = code .. string.format(
                "\n  local l%d = value_at(keysets[%d], t * 3 %% 60, %s)",
                i, i, line.interp)
        end

        if line.channel == CH_TRANSLATE then
            translation[line.axis] = i
        elseif line.channel == CH_ROTATE then
            rotation[line.axis] = i
        end
    end

    code = code .. "\n  mat4.idt(dst)"
    if translation[1] or translation[2] or translation[3] then
        code = code .. "\n  mat4.translate(dst, {" ..
        (translation[1] and ("l" .. translation[1]) or '0').. ", " ..
        (translation[2] and ("l" .. translation[2]) or '0').. ", " ..
        (translation[3] and ("l" .. translation[3]) or '0').. "}, dst)"
    end

    local axis_names = {"X", "Y", "Z"}
    for axis, var in ipairs(rotation) do
        if var then
            code = code .. "\n  mat4.rotate(dst, " .. axis_names[axis] ..
                ",l" ..  var .. ", dst)"
        end
    end

    return code
end

local action_to_channel = {
    move = CH_TRANSLATE,
    rotate = CH_ROTATE
}

function this.parse_track(root)
    local linesets = {}
    for i, node in ipairs(root) do
        if type(node) == "string" then
            goto continue
        end
        local tag = node['#']
        local bone = node.bone

        local lineset = linesets[bone]
        if not lineset then
            lineset = {lines = {}}
            linesets[bone] = lineset
        end

        local line
        if node.func then
            line = {
                axis = ("xyz"):find(node.by),
                channel = action_to_channel[tag],
                expression = node.func,
            }
        elseif #node > 0 then
            error("not implemented")
        end

        table.insert(lineset.lines, line)
        ::continue::
    end
    return linesets
end


function this.compile_track(linesets)
    local code = ""
    local memoised = {}
    local keysets = {}

    for bone, lineset in pairs(linesets) do
        local lineset_code = codegen_track(lineset.lines, memoised, keysets)
        code = code .. "\n do" .. lineset_code .. "\n end\n" ..
            " rig:set_matrix(rig:index(" .. string.escape(bone) .. "), dst)\n"
    end

    local memoised_code = ""
    for name, expression in pairs(memoised) do
        memoised_code = memoised_code .. "\n local " .. name .. " = " .. expression
    end

    if #memoised_code > 0 then
        code = memoised_code .. "\n" .. code
    end

    local src = "return function(rig, t, m)\n local dst = DST\n" .. code .. "\nend"
    local generator, err = load(src, "<expr>", "bt", table.extend({keysets = keysets}, env))
    if not generator then
        error(err)
    end
    return generator()
end

return this