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feat: Application prototype (#14)

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Creates a prototype user interface for dyna3 in the `app-proto` folder. The interface is dynamically constructed using [Sycamore](https://sycamore.dev).

The prototype includes:

  * An application state model (the `AppState` type)
    * A constraint problem model (the `Assembly` type), used in the application state
  * Two views
    * A 3D rendering of the assembly (the `Display` component)
    * A list of elements and constraints (the `Outline` component)

The following features confirm that the views can reflect and send input to the model:

  * You can select elements by clicking and shift-clicking them in the outline. The selected elements are highlighted in the display.
  * You can add elements using a button above the outline. The new elements appear in the display.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: glen/dyna3#14
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>
This commit is contained in:
Vectornaut 2024-10-21 23:38:27 +00:00 • committed by Glen Whitney
parent b92be312e8
commit 86fa682b31
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app-proto/src/inversive.frag Normal file
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#version 300 es
precision highp float;
out vec4 outColor;
// --- inversive geometry ---
struct vecInv {
vec3 sp;
vec2 lt;
};
// --- uniforms ---
// assembly
const int SPHERE_MAX = 200;
uniform int sphere_cnt;
uniform vecInv sphere_list[SPHERE_MAX];
uniform vec3 color_list[SPHERE_MAX];
uniform float highlight_list[SPHERE_MAX];
// view
uniform vec2 resolution;
uniform float shortdim;
// controls
uniform float opacity;
uniform int layer_threshold;
uniform bool debug_mode;
// light and camera
const float focal_slope = 0.3;
const vec3 light_dir = normalize(vec3(2., 2., 1.));
const float ixn_threshold = 0.005;
const float INTERIOR_DIMMING = 0.7;
// --- sRGB ---
// map colors from RGB space to sRGB space, as specified in the sRGB standard
// (IEC 61966-2-1:1999)
//
// https://www.color.org/sRGB.pdf
// https://www.color.org/chardata/rgb/srgb.xalter
//
// in RGB space, color value is proportional to light intensity, so linear
// color-vector interpolation corresponds to physical light mixing. in sRGB
// space, the color encoding used by many monitors, we use more of the value
// interval to represent low intensities, and less of the interval to represent
// high intensities. this improves color quantization
float sRGB(float t) {
if (t <= 0.0031308) {
return 12.92*t;
} else {
return 1.055*pow(t, 5./12.) - 0.055;
}
}
vec3 sRGB(vec3 color) {
return vec3(sRGB(color.r), sRGB(color.g), sRGB(color.b));
}
// --- shading ---
struct Fragment {
vec3 pt;
vec3 normal;
vec4 color;
};
Fragment sphere_shading(vecInv v, vec3 pt, vec3 base_color) {
// the expression for normal needs to be checked. it's supposed to give the
// negative gradient of the lorentz product between the impact point vector
// and the sphere vector with respect to the coordinates of the impact
// point. i calculated it in my head and decided that the result looked good
// enough for now
vec3 normal = normalize(-v.sp + 2.*v.lt.s*pt);
float incidence = dot(normal, light_dir);
float illum = mix(0.4, 1.0, max(incidence, 0.0));
return Fragment(pt, normal, vec4(illum * base_color, opacity));
}
float intersection_dist(Fragment a, Fragment b) {
float intersection_sin = length(cross(a.normal, b.normal));
vec3 disp = a.pt - b.pt;
return max(
abs(dot(a.normal, disp)),
abs(dot(b.normal, disp))
) / intersection_sin;
}
// --- ray-casting ---
struct TaggedDepth {
float depth;
float dimming;
int id;
};
// if `a/b` is less than this threshold, we approximate `a*u^2 + b*u + c` by
// the linear function `b*u + c`
const float DEG_THRESHOLD = 1e-9;
// the depths, represented as multiples of `dir`, where the line generated by
// `dir` hits the sphere represented by `v`. if both depths are positive, the
// smaller one is returned in the first component. if only one depth is
// positive, it could be returned in either component
vec2 sphere_cast(vecInv v, vec3 dir) {
float a = -v.lt.s * dot(dir, dir);
float b = dot(v.sp, dir);
float c = -v.lt.t;
float adjust = 4.*a*c/(b*b);
if (adjust < 1.) {
// as long as `b` is non-zero, the linear approximation of
//
// a*u^2 + b*u + c
//
// at `u = 0` will reach zero at a finite depth `u_lin`. the root of the
// quadratic adjacent to `u_lin` is stored in `lin_root`. if both roots
// have the same sign, `lin_root` will be the one closer to `u = 0`
float square_rect_ratio = 1. + sqrt(1. - adjust);
float lin_root = -(2.*c)/b / square_rect_ratio;
if (abs(a) > DEG_THRESHOLD * abs(b)) {
return vec2(lin_root, -b/(2.*a) * square_rect_ratio);
} else {
return vec2(lin_root, -1.);
}
} else {
// the line through `dir` misses the sphere completely
return vec2(-1., -1.);
}
}
void main() {
vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim;
vec3 dir = vec3(focal_slope * scr, -1.);
// cast rays through the spheres
const int LAYER_MAX = 12;
TaggedDepth top_hits [LAYER_MAX];
int layer_cnt = 0;
for (int id = 0; id < sphere_cnt; ++id) {
// find out where the ray hits the sphere
vec2 hit_depths = sphere_cast(sphere_list[id], dir);
// insertion-sort the points we hit into the hit list
float dimming = 1.;
for (int side = 0; side < 2; ++side) {
float depth = hit_depths[side];
if (depth > 0.) {
for (int layer = layer_cnt; layer >= 0; --layer) {
if (layer < 1 || top_hits[layer-1].depth <= depth) {
// we're not as close to the screen as the hit before
// the empty slot, so insert here
if (layer < LAYER_MAX) {
top_hits[layer] = TaggedDepth(depth, dimming, id);
}
break;
} else {
// we're closer to the screen than the hit before the
// empty slot, so move that hit into the empty slot
top_hits[layer] = top_hits[layer-1];
}
}
layer_cnt = min(layer_cnt + 1, LAYER_MAX);
dimming = INTERIOR_DIMMING;
}
}
}
/* DEBUG */
// in debug mode, show the layer count instead of the shaded image
if (debug_mode) {
// at the bottom of the screen, show the color scale instead of the
// layer count
if (gl_FragCoord.y < 10.) layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
// convert number to color
ivec3 bits = layer_cnt / ivec3(1, 2, 4);
vec3 color = mod(vec3(bits), 2.);
if (layer_cnt % 16 >= 8) {
color = mix(color, vec3(0.5), 0.5);
}
outColor = vec4(color, 1.);
return;
}
// composite the sphere fragments
vec3 color = vec3(0.);
int layer = layer_cnt - 1;
TaggedDepth hit = top_hits[layer];
Fragment frag_next = sphere_shading(
sphere_list[hit.id],
hit.depth * dir,
hit.dimming * color_list[hit.id]
);
float highlight_next = highlight_list[hit.id];
--layer;
for (; layer >= layer_threshold; --layer) {
// load the current fragment
Fragment frag = frag_next;
float highlight = highlight_next;
// shade the next fragment
hit = top_hits[layer];
frag_next = sphere_shading(
sphere_list[hit.id],
hit.depth * dir,
hit.dimming * color_list[hit.id]
);
highlight_next = highlight_list[hit.id];
// highlight intersections
float ixn_dist = intersection_dist(frag, frag_next);
float max_highlight = max(highlight, highlight_next);
float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
frag.color = mix(frag.color, vec4(1.), ixn_highlight);
frag_next.color = mix(frag_next.color, vec4(1.), ixn_highlight);
// highlight cusps
float cusp_cos = abs(dot(dir, frag.normal));
float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[hit.id].lt.s);
float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
frag.color = mix(frag.color, vec4(1.), cusp_highlight);
// composite the current fragment
color = mix(color, frag.color.rgb, frag.color.a);
}
color = mix(color, frag_next.color.rgb, frag_next.color.a);
outColor = vec4(sRGB(color), 1.);
}