modules/flui2d: add 2D fluid dynamics simulation

This implements near verbatim the code found in the paper titled:
Real-Time Fluid Dynamics for Games
By Jos Stam

It sometimes has the filename GDC03.PDF, or Stam_fluids_GDC03.pdf

The density field is rendered using simple linear interpolation of
the samples, in a grayscale palette.  No gamma correction is being
performed.

There are three configurable defines of interest:
VISCOSITY, DIFFUSION, and ROOT.

This module is only threaded in the drawing stage, so basically the
linear interpolation uses multiple cores.  The simulation itself is
not threaded, the implementation from the paper made no such
considerations.

It would be nice to reimplement this in a threaded fashion with a
good generalized API, then move it into libs.  Something where a unit
square can be sampled for interpolated densities would be nice.

Then extend it into 3 dimensions for volumetric effects...

2 files changed, 294 insertions, 0 deletions

diff --git a/src/modules/flui2d/Makefile.am b/src/modules/flui2d/Makefile.am
new file mode 100644
index 0000000..239de9e
--- /dev/null
+++ b/src/modules/flui2d/Makefile.am
@@ -0,0 +1,3 @@
+noinst_LIBRARIES = libflui2d.a
+libflui2d_a_SOURCES = flui2d.c
+libflui2d_a_CPPFLAGS = -I@top_srcdir@/src
diff --git a/src/modules/flui2d/flui2d.c b/src/modules/flui2d/flui2d.c
new file mode 100644
index 0000000..2f0a472
--- /dev/null
+++ b/src/modules/flui2d/flui2d.c
@@ -0,0 +1,291 @@
+#include <stdint.h>
+#include <inttypes.h>
+#include <math.h>
+#include <stdlib.h>
+
+#include "fb.h"
+#include "rototiller.h"
+
+
+/* This code is almost entirely taken from the paper:
+ * Real-Time Fluid Dynamics for Games
+ * Joe Stam - Alias | Wavefront
+ *
+ * I take zero credit for it, I only wrote the rototiller integration.
+ *   - Vito Caputo <vcaputo@pengaru.com> 10/13/2019
+ */
+
+#if 1
+	/* These knobs affect how the simulated fluid behaves */
+#define VISCOSITY	.000000001f
+#define DIFFUSION	.00001f
+#else
+#define VISCOSITY	.00001f
+#define DIFFUSION	.000001f
+#endif
+
+#define ROOT		128	// Change this to vary the density field resolution
+#define SIZE		((ROOT + 2) * (ROOT + 2))
+#define IX(i, j)	((i) + (ROOT + 2) * (j))
+#define SWAP(x0, x)	{float *tmp = x0; x0 = x; x = tmp;}
+
+typedef struct flui2d_t {
+	float	u[SIZE], v[SIZE], u_prev[SIZE], v_prev[SIZE];
+	float	dens[SIZE], dens_prev[SIZE];
+	float	visc, diff;
+} flui2d_t;
+
+static void set_bnd(int N, int b, float *x)
+{
+	for (int i = 1; i <= N; i++) {
+		x[IX(0, i)] = b == 1 ? -x[IX(1, i)] : x[IX(1, i)];
+		x[IX(N + 1, i)] = b == 1 ? -x[IX(N, i)] : x[IX(N, i)];
+		x[IX(i, 0)] = b == 2 ? -x[IX(i, 1)] : x[IX(i, 1)];
+		x[IX(i, N + 1)] = b == 2 ? -x[IX(i, N)] : x[IX(i, N)];
+	}
+
+	x[IX(0 , 0)] = 0.5 * (x[IX(1, 0)] + x[IX(0, 1)]);
+	x[IX(0 , N + 1)] = 0.5 * (x[IX(1, N + 1)] + x[IX(0, N)]);
+	x[IX(N + 1, 0)] = 0.5 * (x[IX(N, 0)] + x[IX(N + 1, 1)]);
+	x[IX(N + 1, N + 1)] = 0.5 * (x[IX(N, N + 1)] + x[IX(N + 1, N)]);
+}
+
+static void add_source(int N, float *x, float *s, float dt)
+{
+	int	size = (N + 2) * (N + 2);
+
+	for (int i = 0; i < size; i++)
+		x[i] += dt * s[i];
+}
+
+static void diffuse(int N, int b, float *x, float *x0, float diff, float dt)
+{
+	float a = dt * diff * (float)N * (float)N;
+	int i, j, k;
+	float z = 1.f / (1.f + 4.f * a);
+
+	for (k = 0; k < 20; k++) {
+		for (i = 1; i <= N; i++) {
+			for (j = 1; j <= N; j++) {
+				x[IX(i, j)] = (x0[IX(i, j)] + a * (x[IX(i - 1, j)] + x[IX(i + 1, j)] + x[IX(i, j - 1)] + x[IX(i, j + 1)])) * z;
+			}
+		}
+		set_bnd(N, b, x);
+	}
+}
+
+static void advect(int N, int b, float *d, float *d0, float *u, float *v, float dt)
+{
+	float x, y, s0, t0, s1, t1, dt0;
+	int i, j, i0, j0, i1, j1;
+
+	dt0 = dt * (float)N;
+	for (i = 1 ; i <= N ; i++) {
+		for (j = 1 ; j <= N; j++) {
+			x = (float)i - dt0 * u[IX(i, j)];
+			y = (float)j - dt0 * v[IX(i, j)];
+
+			if (x < .5f)
+				x = .5f;
+			if (x > (float)N + .5f)
+				x = (float)N + .5f;
+
+			i0 = (int)x;
+			i1 = i0 + 1;
+
+			if (y < .5f)
+				y = .5f;
+			if (y > (float)N + .5f)
+				y = (float)N + .5f;
+
+			j0 = (int)y;
+			j1 = j0 + 1;
+
+			s1 = x - (float)i0;
+			s0 = 1.f - s1;
+			t1 = y - (float)j0;
+			t0 = 1.f - t1;
+
+			d[IX(i, j)] = s0 * (t0 * d0[IX(i0, j0)] + t1 * d0[IX(i0, j1)]) + s1 * (t0 * d0[IX(i1, j0)] + t1 * d0[IX(i1, j1)]);
+		}
+	}
+	set_bnd(N, b, d);
+}
+
+static void project(int N, float *u, float *v, float *p, float *div)
+{
+	float h = 1.f / (float)N;
+	int i, j, k;
+
+	for (i = 1; i <= N ; i++) {
+		for (j = 1; j <= N; j++) {
+			div[IX(i, j)] = -0.5 * h *(u[IX(i + 1, j)] - u[IX(i - 1, j)] + v[IX(i, j + 1)] - v[IX(i, j - 1)]);
+			p[IX(i, j)] = 0;
+		}
+	}
+
+	set_bnd(N, 0, div);
+	set_bnd(N, 0, p);
+
+	for (k = 0; k < 20; k++) {
+		for (i = 1; i <= N; i++) {
+			for (j = 1; j <= N; j++) {
+				p[IX(i, j)] = (div[IX(i, j)] + p[IX(i - 1, j)] + p[IX(i + 1, j)] + p[IX(i, j - 1)] + p[IX(i, j + 1)]) * .25f;
+			}
+		}
+		set_bnd(N, 0, p);
+	}
+
+	for (i = 1; i <= N; i++) {
+		for (j = 1; j <= N; j++) {
+			u[IX(i, j)] -= 0.5 * (p[IX(i + 1, j)] - p[IX(i - 1, j)]) / h;
+			v[IX(i, j)] -= 0.5 * (p[IX(i, j + 1)] - p[IX(i, j - 1)]) / h;
+		}
+	}
+
+	set_bnd(N, 1, u);
+	set_bnd(N, 2, v);
+}
+
+static void dens_step(int N, float *x, float *x0, float *u, float *v, float diff, float dt)
+{
+
+	/*
+	 * The paper includes this, but it blows up the simulation.
+	 * add_source(N, x, x0, dt);
+	 * SWAP(x0, x);
+	 */
+	diffuse(N, 0, x, x0, diff, dt);
+	SWAP(x0, x);
+	advect(N, 0, x, x0, u, v, dt);
+}
+
+static void vel_step(int N, float *u, float *v, float *u0, float *v0, float visc, float dt)
+{
+	add_source(N, u, u0, dt);
+	add_source(N, v, v0, dt);
+	SWAP(u0, u);
+	diffuse(N, 1, u, u0, visc, dt);
+	SWAP(v0, v);
+	diffuse(N, 2, v, v0, visc, dt);
+	project(N, u, v, u0, v0);
+	SWAP(u0, u);
+	SWAP(v0, v);
+	advect(N, 1, u, u0, u0, v0, dt);
+	advect(N, 2, v, v0, u0, v0, dt);
+	project(N, u, v, u0, v0);
+}
+
+
+typedef struct flui2d_context_t {
+	flui2d_t	fluid;
+	float		xf, yf;
+} flui2d_context_t;
+
+
+static void * flui2d_create_context(void)
+{
+	flui2d_context_t	*ctxt;
+
+	ctxt = calloc(1, sizeof(flui2d_context_t));
+	if (!ctxt)
+		return NULL;
+
+	ctxt->fluid.visc = VISCOSITY;
+	ctxt->fluid.diff = DIFFUSION;
+
+	return ctxt;
+}
+
+
+static void flui2d_destroy_context(void *context)
+{
+	free(context);
+}
+
+
+static int flui2d_fragmenter(void *context, const fb_fragment_t *fragment, unsigned num, fb_fragment_t *res_fragment)
+{
+	return fb_fragment_tile_single(fragment, 64, num, res_fragment);
+}
+
+
+/* Prepare a frame for concurrent drawing of fragment using multiple fragments */
+static void flui2d_prepare_frame(void *context, unsigned n_cpus, fb_fragment_t *fragment, rototiller_fragmenter_t *res_fragmenter)
+{
+	flui2d_context_t	*ctxt = context;
+	static float		r;
+	int			x = (cos(r += .01f) * .4f + .5f) * (float)ROOT;	/* figure eight pattern for the added densities */
+	int			y = (sin(r * 2.f) * .4f + .5f) * (float)ROOT;
+
+	*res_fragmenter = flui2d_fragmenter;
+
+	ctxt->fluid.dens_prev[IX(x, y)] = 1.f;
+
+	/* This orientation for the added velocities at the added densities isn't trying to
+	 * emulate any sort of physical relationship to the movement - it's just creating a variety
+	 * of turbulence.  It'd be trivial to make it look like a rocket's jetstream or something.
+	 */
+	ctxt->fluid.u_prev[IX(x, y)] = cos(r * 3.f) * 10.f;
+	ctxt->fluid.v_prev[IX(x, y)] = sin(r * 3.f) * 10.f;
+
+	/* These are the core of the simulation, and can't currently be threaded using the paper's implementation, so they
+	 * must occur serialized here in prepare_frame.  It would be interesting to try refactor the API and tweak the
+	 * implementation for threading, as it would really open up larger field sizes as well as map more naturally to
+	 * a GLSL implementation for a fragment shader.
+	 */
+	vel_step(ROOT, ctxt->fluid.u, ctxt->fluid.v, ctxt->fluid.u_prev, ctxt->fluid.v_prev, ctxt->fluid.visc, .1f);
+	dens_step(ROOT, ctxt->fluid.dens, ctxt->fluid.dens_prev, ctxt->fluid.u, ctxt->fluid.v, ctxt->fluid.diff, .1f);
+
+	ctxt->xf = 1.f / fragment->frame_width;
+	ctxt->yf = 1.f / fragment->frame_height;
+}
+
+
+/* Draw a the flui2d densities */
+static void flui2d_render_fragment(void *context, fb_fragment_t *fragment)
+{
+	flui2d_context_t	*ctxt = context;
+
+	for (int y = fragment->y; y < fragment->y + fragment->height; y++) {
+		int	y0, y1;
+		float	Y;
+
+		Y = (float)y * ctxt->yf * (float)ROOT;
+		y0 = (int)Y;
+		y1 = y0 + 1;
+
+		for (int x = fragment->x; x < fragment->x + fragment->width; x++) {
+			float		X, dens, dx0, dx1;
+			int		x0, x1;
+			uint32_t	pixel;
+
+			X = (float)x * ctxt->xf * (float)ROOT;
+			x0 = (int)X;
+			x1 = x0 + 1;
+
+			/* linear interpolation of density samples */
+			dx0 = ctxt->fluid.dens[(int)IX(x0, y0)] * (1.f - (X - x0));
+			dx0 += ctxt->fluid.dens[(int)IX(x1, y0)] * (X - x0);
+			dx1 = ctxt->fluid.dens[(int)IX(x0, y1)] * (1.f - (X - x0));
+			dx1 += ctxt->fluid.dens[(int)IX(x1, y1)] * (X - x0);
+			dens = dx0 * (1.f - (Y - y0)) + dx1 * (Y - y0);
+
+			pixel = ((float)dens * 256.f);
+			pixel = pixel << 16 | pixel << 8 | pixel;
+			fb_fragment_put_pixel_unchecked(fragment, x, y, pixel);
+		}
+	}
+}
+
+
+rototiller_module_t	flui2d_module = {
+	.create_context = flui2d_create_context,
+	.destroy_context = flui2d_destroy_context,
+	.prepare_frame = flui2d_prepare_frame,
+	.render_fragment = flui2d_render_fragment,
+	.name = "flui2d",
+	.description = "Fluid dynamics simulation in 2D (threaded (poorly))",
+	.author = "Vito Caputo <vcaputo@pengaru.com>",
+	.license = "Unknown",
+};