Sergey Makeev SergeyMakeev

Realtime Fluid Simulation: Projection

The core of most real-time fluid simulators, like the one in EmberGen, are based on the "Stable Fluids" algorithm by Jos Stam, which to my knowledge was first presented at SIGGRAPH '99. This is a post about one part of this algorithm that's often underestimated: Projection

MG4_F32.mp4

Stable Fluids

The Stable Fluids algorithm solves a subset of the famous "Navier Stokes equations", which describe how fluids interact and move. In particular, it typically solves what's called the "incompressible Euler equations", where viscous forces are often ignored.

A metatable in Lua defines various extraneous behaviors for a table when indexed, modified, interacted with, etc. They are Lua's core metaprogramming feature; most well known for being useful to emulate classes much like an OOP language.

Any table (and userdata) may be assigned a metatable. You can define a metatable for a table as such:

-- Our sample table
local tab = {}
-- Our metatable
local metatable = {
 -- This table is then what holds the metamethods or metafields

CUSTOM GAME ENGINES: A Small Study

WARNING: Article moved to separate repo to allow users contributions: https://github.com/raysan5/custom_game_engines

A couple of weeks ago I played (and finished) A Plague Tale, a game by Asobo Studio. I was really captivated by the game, not only by the beautiful graphics but also by the story and the locations in the game. I decided to investigate a bit about the game tech and I was surprised to see it was developed with a custom engine by a relatively small studio. I know there are some companies using custom engines but it's very difficult to find a detailed market study with that kind of information curated and updated. So this article.

Nowadays lots of companies choose engines like [Unreal](https:

	def quat_from_xform(ts):

	return quat_normalize(
	torch.where((ts[...,2,2] < 0.0)[...,None],
	torch.where((ts[...,0,0] > ts[...,1,1])[...,None],
	torch.cat([
	(ts[...,2,1]-ts[...,1,2])[...,None],
	(1.0 + ts[...,0,0] - ts[...,1,1] - ts[...,2,2])[...,None],
	(ts[...,1,0]+ts[...,0,1])[...,None],
	(ts[...,0,2]+ts[...,2,0])[...,None]], dim=-1),

	--------------------------------------------------------------------------------------------------------------------------------------------------------------------
	-- Animate
	-- maximum_adhd
	-- September 21st, 2022
	--------------------------------------------------------------------------------------------------------------------------------------------------------------------
	--!strict

	local Players = game:GetService("Players")
	local RunService = game:GetService("RunService")

	//
	// Lookup Tables for Marching Cubes
	//
	// These tables differ from the original paper (Marching Cubes: A High Resolution 3D Surface Construction Algorithm)
	//
	// The co-ordinate system has the more convenient properties:
	//
	// i = cube index [0, 7]
	// x = (i & 1) >> 0
	// y = (i & 2) >> 1

	import numpy as np

	def sigmoid(x):
	return 1 / (1 + np.exp(-x))

	def neural_network(X, y):
	learning_rate = 0.1
	W1 = np.random.rand(2, 4)
	W2 = np.random.rand(4, 1)

	local CoreGui = game:GetService("CoreGui")
	local MIN_THICKNESS = 0.001
	local MAX_THICKNESS = 0.04
	local MIN_DIST = 2
	local MAX_DIST = 10

	game:GetService("RunService").Heartbeat:Connect(function()
	local hoverBox = CoreGui:FindFirstChild("HoverBox")
	if hoverBox and hoverBox:IsA("SelectionBox") then
	local adornee = hoverBox.Adornee

	string rpAsset = "";
	if (GraphicsSettings.renderPipelineAsset != null)
	rpAsset = GraphicsSettings.renderPipelineAsset.GetType().Name;

	if (rpAsset.Equals("HDRenderPipelineAsset"))
	renderPipeline = RenderPipeline.HDRP;
	else if (rpAsset.Equals("UniversalRenderPipelineAsset"))
	renderPipeline = RenderPipeline.URP;
	else
	renderPipeline = RenderPipeline.BuiltIn;

	local MockTree = {}

	local function addJointEdge(joints, joint, me, other)
	local edgeList = joints[me]
	if not edgeList then
	edgeList = {}
	joints[me] = edgeList
	end
	table.insert(edgeList, {joint, other})
	end