← geometric-flows

Lattice flow (plane)

A planar lattice flowing under geodesic and horocyclic flows, tracing the orbit of its shortest vectors.

Source

// 2dFlow: a unimodular lattice in the plane under a linear flow. The shared
// lattice driver (_visualisers/lattice/script.js) integrates the flow chosen
// by uFlow at speed uSpeed and pushes the basis as uLattice each frame;
// uScale comes from the UI slider. Buffers: gridTrace accumulates the paths
// of every lattice point; image.glsl draws the current dots on top.

#include "../shared/2d_utils.glsl"
#include "../shared/coord_utils.glsl"

// Compile-time toggles.
bool showDots = true;
bool showBasis = false;
float traceLevel = 0.3;  // Strength of the accumulated path trace.
float backFade = .999;   // Per-frame retention of the trace buffer.

vec4 dotCol = vec4(.8,.05,.04,1.);
vec4 backCol = vec4(1.,1.,1.,0);
vec4 traceCol = vec4(0.,0.,0.,1.);
vec4 basisCol = vec4(.651,.669,.95,1.);

// Background and full path record: each frame the current lattice dots are
// stamped faintly over the old frame (backFade keeps almost all of it), so
// the trace of every dot's path accumulates. Cleared on the first frame or
// while the pointer is down.

void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    vec2 p = coords(fragCoord, iResolution, uScale, iResolution.xy * 0.5);
	vec2 uv = fragCoord / iResolution.xy;

    vec4 col = mix(backCol,vec4(texture(gridTrace,uv).xyz,1),backFade);

    col = drGrid(col, p, mat2(uLattice), 0.075, mix(col,traceCol,traceLevel), 2.);

    if(iFrame == 0 || iMouse.z > 0.)
    { col = backCol; }

    fragColor = col;
}

// Composite: the current lattice dots (and optional basis markers) drawn
// directly over the accumulated path trace.

void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    vec2 p = coords(fragCoord, iResolution, uScale, iResolution.xy * 0.5);
	vec2 uv = fragCoord.xy / iResolution.xy;

    vec4 col = vec4(texture(gridTrace,uv).xyz,1);

    if(showDots)
    {
        col = drGrid(col, p, mat2(uLattice), 0.2, dotCol, 0.15);
    }

    // Mark the two basis vectors of the current lattice.
    if(showBasis)
    {
    	col = drPt(col, p, uLattice, .4, basisCol, .75);
    	col = drPt(col, p, vec4(uLattice.zw,0,0), .4, basisCol, .75);
    }

    fragColor = col;
}

// 2dFlowJS: the plain lattice-flow shader UI. All the driving logic lives in
// the shared lattice driver; this script is just its instantiation, so state
// is per-instance and other shaders can layer their own UI on the same core.
import { createLatticeDriver } from '../shared/lattice_driver.js';

const driver = createLatticeDriver();

export const setup = driver.setup;
export const onFrame = driver.onFrame;
export const onSetLattice = driver.onSetLattice;