vassvik

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.

h3r2tic

A quick breakdown of lighting in the restir-meets-surfel branch of my renderer, where I revive some olde surfel experiments, and generously sprinkle ReSTIR on top.

General remarks

Please note that this is all based on work-in-progress experimental software, and represents a single snapshot in development history. Things will certainly change 😛

Due to how I'm capturing this, there's frame-to-frame variability, e.g. different rays being shot, TAA shimmering slightly. Some of the images come from a dedicated visualization pass, and are anti-aliased, and some show internal buffers which are not anti-aliased.

Final images

pixelsnafu

Volumetric Clouds Resources List

1. A. Schneider, "Real-Time Volumetric Cloudscapes," in GPU Pro 7: Advanced Rendering Techniques, 2016, pp. 97-127. (Follow up presentations here, and here.)

2. S. Hillaire, "Physically Based Sky, Atmosphere and Cloud Rendering in Frostbite" in Physically Based Shading in Theory and Practice course, SIGGRAPH 2016. [video] [course notes] [scatter integral shadertoy]

3. [R. Högfeldt, "Convincing Cloud Rendering – An Implementation of Real-Time Dynamic Volumetric Clouds in Frostbite"](https://odr.chalmers.se/hand

pervognsen

A quadratic space is a real vector space V with a quadratic form Q(x), e.g. V = R^n with Q as the squared length. The Clifford algebra Cl(V) of a quadratic space is the associative algebra that contains V and satisfies x^2 = Q(x) for all x in V. We're imposing by fiat that the square of a vector should be the quadratic form's value and seeing where it takes us. Treat x^2 = Q(x) as a symbolic rewriting rule that lets you replace x^2 or x x with Q(x) and vice versa whenever x is a vector. Beyond that Cl(V) satisfies the standard axioms of an algebra: it lets you multiply by scalars, it's associative and distributive, but not necessarily commutative.

Remarkably, this is all you need to derive everything about Clifford algebras.

Let me show you how easy it is to bootstrap the theory from nothing.

We know Cl(V) contains a copy of V. Since x^2 = Q(x) for all x, it must also contain a copy of some nonnegative reals.

rygorous

 Directory of C:\devel\projects\bink\src\tools\shadergen

06/02/2014  05:16 PM    <DIR>          .
06/02/2014  05:16 PM    <DIR>          ..
05/28/2014  03:14 PM             3,639 codegen_d3d.cpp
05/27/2014  07:04 PM             6,799 codegen_d3d10.cpp
12/17/2013  06:27 PM             3,590 codegen_gl.c
05/28/2014  06:33 PM             4,751 codegen_orbis.cpp
05/28/2014  12:16 PM             9,305 codegen_ps3cg.cpp
06/02/2014  05:16 PM             4,170 codegen_psp2.cpp

dubik

// Vectormath https://github.com/erwincoumans/sce_vectormath
class Ray
{
public:
    Ray();
public:
    Vectormath::Aos::Vector3 m_pos;
    Vectormath::Aos::Vector3 m_dir;
    Vectormath::Aos::Vector3 m_invDir; // 1.0f / m_dir per elem
    float m_min;

adamgit

##########################################
#
# c.f. http://stackoverflow.com/questions/3520977/build-fat-static-library-device-simulator-using-xcode-and-sdk-4
#
# Version 2.82
#
# Latest Change:
# - MORE tweaks to get the iOS 10+ and 9- working
# - Support iOS 10+
# - Corrected typo for iOS 1-10+ (thanks @stuikomma)

rygorous

// float->sRGB8 conversions - two variants.
// by Fabian "ryg" Giesen
//
// I hereby place this code in the public domain.
//
// Both variants come with absolute error bounds and a reversibility and monotonicity
// guarantee (see test driver code below). They should pass D3D10 conformance testing
// (not that you can verify this, but still). They are verified against a clean reference
// implementation provided below, and the test driver checks all floats exhaustively.
//

rygorous

// float->half variants.
// by Fabian "ryg" Giesen.
//
// I hereby place this code in the public domain, as per the terms of the
// CC0 license:
//
//   https://creativecommons.org/publicdomain/zero/1.0/
//
// float_to_half_full: This is basically the ISPC stdlib code, except
// I preserve the sign of NaNs (any good reason not to?)

castano

#include <intrin.h> // __rdtsc
#include <stdio.h>

typedef unsigned int uint;
typedef unsigned short uint16;
typedef unsigned long long uint64;

// ISPC functions:
extern "C" void half_to_float_test(const uint16 * vin, float * vout, int count);
extern "C" void half_to_float_test_fast(const uint16 * vin, float * vout, int count);