////////////////////////////////////////////////////////////////
//
//                           HG_SDF
//
//     GLSL LIBRARY FOR BUILDING SIGNED DISTANCE BOUNDS
//
//     version 2021-07-28
//
//     Check https://mercury.sexy/hg_sdf for updates
//     and usage examples. Send feedback to spheretracing@mercury.sexy.
//
//     Brought to you by MERCURY https://mercury.sexy/
//
//
//
// Released dual-licensed under
//   Creative Commons Attribution-NonCommercial (CC BY-NC)
// or
//   MIT License
// at your choice.
//
// SPDX-License-Identifier: MIT OR CC-BY-NC-4.0
//
// /////

////////////////////////////////////////////////////////////////
//
//             HELPER FUNCTIONS/MACROS
//
////////////////////////////////////////////////////////////////

const float PI = 3.14159265;
const float TAU = (2. * PI);
const float PHI = sqrt(5.) * 0.5 + 0.5;

vec3 applyFog(vec3 col, float t, vec3 rd, vec3 lightDir, float b) {
    float fogAmount = 1.0 - exp(-t * b);
    float sunAmount = max(dot(rd, lightDir), 0.);
    vec3 fogColor = mix(vec3(0.1529, 0.1137, 0.2), // blue
    vec3(0.2588, 0.1765, 0.3529), // yellow
    pow(sunAmount, 1.0));
    return mix(col, fogColor, fogAmount);
}

mat2 scale(vec2 scale) {
    return mat2(1. / scale.x, 0.0, 0.0, 1. / scale.y);
}

// Sign function that doesn't return 0
float sgn(float x) {
    return (x < 0.) ? -1. : 1.;
}

vec2 sgn(vec2 v) {
    return vec2((v.x < 0.) ? -1. : 1., (v.y < 0.) ? -1. : 1.);
}

float square(float x) {
    return x * x;
}

vec2 square(vec2 x) {
    return x * x;
}

vec3 square(vec3 x) {
    return x * x;
}

float lengthSqr(vec3 x) {
    return dot(x, x);
}

// Maximum/minumum elements of a vector
float vmax(vec2 v) {
    return max(v.x, v.y);
}

float vmax(vec3 v) {
    return max(max(v.x, v.y), v.z);
}

float vmax(vec4 v) {
    return max(max(v.x, v.y), max(v.z, v.w));
}

float vmin(vec2 v) {
    return min(v.x, v.y);
}

float vmin(vec3 v) {
    return min(min(v.x, v.y), v.z);
}

float vmin(vec4 v) {
    return min(min(v.x, v.y), min(v.z, v.w));
}

// Hexagonal prism, circumcircle variant
float fHexagonCircumcircle(vec3 p, vec2 h) {
    vec3 q = abs(p);
    return max(q.y - h.y, max(q.x * sqrt(3.) * 0.5 + q.z * 0.5, q.z) - h.x);
	//this is mathematically equivalent to this line, but less efficient:
	//return max(q.y - h.y, max(dot(vec2(cos(PI/3), sin(PI/3)), q.zx), q.z) - h.x);
}

////////////////////////////////////////////////////////////////
//
//             PRIMITIVE DISTANCE FUNCTIONS
//
////////////////////////////////////////////////////////////////
//
// Conventions:
//
// Everything that is a distance function is called fSomething.
// The first argument is always a point in 2 or 3-space called <p>.
// Unless otherwise noted, (if the object has an intrinsic "up"
// side or direction) the y axis is "up" and the object is
// centered at the origin.
//
////////////////////////////////////////////////////////////////

float fSphere(vec3 p, float r) {
    return length(p) - r;
}

// Plane with normal n (n is normalized) at some distance from the origin
float fPlane(vec3 p, vec3 n, float distanceFromOrigin) {
    return dot(p, n) + distanceFromOrigin;
}

// Cheap Box: distance to corners is overestimated
float fBoxCheap(vec3 p, vec3 b) { //cheap box
    return vmax(abs(p) - b);
}

// Box: correct distance to corners
float fBox(vec3 p, vec3 b) {
    vec3 d = abs(p) - b;
    return length(max(d, vec3(0))) + vmax(min(d, vec3(0)));
}

// Same as above, but in two dimensions (an endless box)
float fBox2Cheap(vec2 p, vec2 b) {
    return vmax(abs(p) - b);
}

float fBox2(vec2 p, vec2 b) {
    vec2 d = abs(p) - b;
    return length(max(d, vec2(0.))) + vmax(min(d, vec2(0.)));
}

// Endless "corner"
float fCorner(vec2 p) {
    return length(max(p, vec2(0.))) + vmax(min(p, vec2(0.)));
}

// Cylinder standing upright on the xz plane
float fCylinder(vec3 p, float r, float height) {
    float d = length(p.xz) - r;
    d = max(d, abs(p.y) - height);
    return d;
}

// Capsule: A Cylinder with round caps on both sides
float fCapsule(vec3 p, float r, float c) {
    return mix(length(p.xz) - r, length(vec3(p.x, abs(p.y) - c, p.z)) - r, step(c, abs(p.y)));
}

// Distance to line segment between <a> and <b>, used for fCapsule() version 2below
float fLineSegment(vec3 p, vec3 a, vec3 b) {
    vec3 ab = b - a;
    float t = clamp(dot(p - a, ab) / dot(ab, ab), 0., 1.);
    return length((ab * t + a) - p);
}

// Capsule version 2: between two end points <a> and <b> with radius r
float fCapsule(vec3 p, vec3 a, vec3 b, float r) {
    return fLineSegment(p, a, b) - r;
}

// Torus in the XZ-plane
float fTorus(vec3 p, float smallRadius, float largeRadius) {
    return length(vec2(length(p.xz) - largeRadius, p.y)) - smallRadius;
}

// A circle line. Can also be used to make a torus by subtracting the smaller radius of the torus.
float fCircle(vec3 p, float r) {
    float l = length(p.xz) - r;
    return length(vec2(p.y, l));
}

// A circular disc with no thickness (i.e. a cylinder with no height).
// Subtract some value to make a flat disc with rounded edge.
float fDisc(vec3 p, float r) {
    float l = length(p.xz) - r;
    return l < 0. ? abs(p.y) : length(vec2(p.y, l));
}

// Hexagonal prism, incircle variant
float fHexagonIncircle(vec3 p, vec2 h) {
    return fHexagonCircumcircle(p, vec2(h.x * sqrt(3.) * 0.5, h.y));
}

// Cone with correct distances to tip and base circle. Y is up, 0 is in the middle of the base.
float fCone(vec3 p, float radius, float height) {
    vec2 q = vec2(length(p.xz), p.y);
    vec2 tip = q - vec2(0, height);
    vec2 mantleDir = normalize(vec2(height, radius));
    float mantle = dot(tip, mantleDir);
    float d = max(mantle, -q.y);
    float projected = dot(tip, vec2(mantleDir.y, -mantleDir.x));

	// distance to tip
    if((q.y > height) && (projected < 0.)) {
        d = max(d, length(tip));
    }

	// distance to base ring
    if((q.x > radius) && (projected > length(vec2(height, radius)))) {
        d = max(d, length(q - vec2(radius, 0)));
    }
    return d;
}

////////////////////////////////////////////////////////////////
//
//                DOMAIN MANIPULATION OPERATORS
//
////////////////////////////////////////////////////////////////
//
// Conventions:
//
// Everything that modifies the domain is named pSomething.
//
// Many operate only on a subset of the three dimensions. For those,
// you must choose the dimensions that you want manipulated
// by supplying e.g. <p.x> or <p.zx>
//
// <inout p> is always the first argument and modified in place.
//
// Many of the operators partition space into cells. An identifier
// or cell index is returned, if possible. This return value is
// intended to be optionally used e.g. as a random seed to change
// parameters of the distance functions inside the cells.
//
// Unless stated otherwise, for cell index 0, <p> is unchanged and cells
// are centered on the origin so objects don't have to be moved to fit.
//
//
////////////////////////////////////////////////////////////////

// Rotate around a coordinate axis (i.e. in a plane perpendicular to that axis) by angle <a>.
// Read like this: R(p.xz, a) rotates "x towards z".
// This is fast if <a> is a compile-time constant and slower (but still practical) if not.
void pR(inout vec2 p, float a) {
    p = cos(a) * p + sin(a) * vec2(p.y, -p.x);
}

// Shortcut for 45-degrees rotation
void pR45(inout vec2 p) {
    p = (p + vec2(p.y, -p.x)) * sqrt(0.5);
}

// Repeat space along one axis. Use like this to repeat along the x axis:
// <float cell = pMod1(p.x,5);> - using the return value is optional.
float pMod1(inout float p, float size) {
    float halfsize = size * 0.5;
    float c = floor((p + halfsize) / size);
    p = mod(p + halfsize, size) - halfsize;
    return c;
}

// Same, but mirror every second cell so they match at the boundaries
float pModMirror1(inout float p, float size) {
    float halfsize = size * 0.5;
    float c = floor((p + halfsize) / size);
    p = mod(p + halfsize, size) - halfsize;
    p *= mod(c, 2.0) * 2. - 1.;
    return c;
}

// Repeat the domain only in positive direction. Everything in the negative half-space is unchanged.
float pModSingle1(inout float p, float size) {
    float halfsize = size * 0.5;
    float c = floor((p + halfsize) / size);
    if(p >= 0.)
        p = mod(p + halfsize, size) - halfsize;
    return c;
}

// Repeat only a few times: from indices <start> to <stop> (similar to above, but more flexible)
float pModInterval1(inout float p, float size, float start, float stop) {
    float halfsize = size * 0.5;
    float c = floor((p + halfsize) / size);
    p = mod(p + halfsize, size) - halfsize;
    if(c > stop) { //yes, this might not be the best thing numerically.
        p += size * (c - stop);
        c = stop;
    }
    if(c < start) {
        p += size * (c - start);
        c = start;
    }
    return c;
}

// Repeat around the origin by a fixed angle.
// For easier use, num of repetitions is use to specify the angle.
float pModPolar(inout vec2 p, float repetitions) {
    float angle = 2. * PI / repetitions;
    float a = atan(p.y, p.x) + angle / 2.;
    float r = length(p);
    float c = floor(a / angle);
    a = mod(a, angle) - angle / 2.;
    p = vec2(cos(a), sin(a)) * r;
	// For an odd number of repetitions, fix cell index of the cell in -x direction
	// (cell index would be e.g. -5 and 5 in the two halves of the cell):
    if(abs(c) >= (repetitions / 2.))
        c = abs(c);
    return c;
}

// Repeat in two dimensions
vec2 pMod2(inout vec2 p, vec2 size) {
    vec2 c = floor((p + size * 0.5) / size);
    p = mod(p + size * 0.5, size) - size * 0.5;
    return c;
}

// Same, but mirror every second cell so all boundaries match
vec2 pModMirror2(inout vec2 p, vec2 size) {
    vec2 halfsize = size * 0.5;
    vec2 c = floor((p + halfsize) / size);
    p = mod(p + halfsize, size) - halfsize;
    p *= mod(c, vec2(2.)) * 2. - vec2(1);
    return c;
}

// Same, but mirror every second cell at the diagonal as well
vec2 pModGrid2(inout vec2 p, vec2 size) {
    vec2 c = floor((p + size * 0.5) / size);
    p = mod(p + size * 0.5, size) - size * 0.5;
    p *= mod(c, vec2(2.)) * 2. - vec2(1.);
    p -= size / 2.;
    if(p.x > p.y)
        p.xy = p.yx;
    return floor(c / 2.);
}

// Repeat in three dimensions
vec3 pMod3(inout vec3 p, vec3 size) {
    vec3 c = floor((p + size * 0.5) / size);
    p = mod(p + size * 0.5, size) - size * 0.5;
    return c;
}

// Mirror at an axis-aligned plane which is at a specified distance <dist> from the origin.
float pMirror(inout float p, float dist) {
    float s = sgn(p);
    p = abs(p) - dist;
    return s;
}

// Mirror in both dimensions and at the diagonal, yielding one eighth of the space.
// translate by dist before mirroring.
vec2 pMirrorOctant(inout vec2 p, vec2 dist) {
    vec2 s = sgn(p);
    pMirror(p.x, dist.x);
    pMirror(p.y, dist.y);
    if(p.y > p.x)
        p.xy = p.yx;
    return s;
}

// Reflect space at a plane
float pReflect(inout vec3 p, vec3 planeNormal, float offset) {
    float t = dot(p, planeNormal) + offset;
    if(t < 0.) {
        p = p - (2. * t) * planeNormal;
    }
    return sgn(t);
}

////////////////////////////////////////////////////////////////
//
//             OBJECT COMBINATION OPERATORS
//
////////////////////////////////////////////////////////////////
//
// We usually need the following boolean operators to combine two objects:
// Union: OR(a,b)
// Intersection: AND(a,b)
// Difference: AND(a,!b)
// (a and b being the distances to the objects).
//
// The trivial implementations are min(a,b) for union, max(a,b) for intersection
// and max(a,-b) for difference. To combine objects in more interesting ways to
// produce rounded edges, chamfers, stairs, etc. instead of plain sharp edges we
// can use combination operators. It is common to use some kind of "smooth minimum"
// instead of min(), but we don't like that because it does not preserve Lipschitz
// continuity in many cases.
//
// Naming convention: since they return a distance, they are called fOpSomething.
// The different flavours usually implement all the boolean operators above
// and are called fOpUnionRound, fOpIntersectionRound, etc.
//
// The basic idea: Assume the object surfaces intersect at a right angle. The two
// distances <a> and <b> constitute a new local two-dimensional coordinate system
// with the actual intersection as the origin. In this coordinate system, we can
// evaluate any 2D distance function we want in order to shape the edge.
//
// The operators below are just those that we found useful or interesting and should
// be seen as examples. There are infinitely more possible operators.
//
// They are designed to actually produce correct distances or distance bounds, unlike
// popular "smooth minimum" operators, on the condition that the gradients of the two
// SDFs are at right angles. When they are off by more than 30 degrees or so, the
// Lipschitz condition will no longer hold (i.e. you might get artifacts). The worst
// case is parallel surfaces that are close to each other.
//
// Most have a float argument <r> to specify the radius of the feature they represent.
// This should be much smaller than the object size.
//
// Some of them have checks like "if ((-a < r) && (-b < r))" that restrict
// their influence (and computation cost) to a certain area. You might
// want to lift that restriction or enforce it. We have left it as comments
// in some cases.
//
// usage example:
//
// float fTwoBoxes(vec3 p) {
//   float box0 = fBox(p, vec3(1));
//   float box1 = fBox(p-vec3(1), vec3(1));
//   return fOpUnionChamfer(box0, box1, 0.2);
// }
//
////////////////////////////////////////////////////////////////

// The "Chamfer" flavour makes a 45-degree chamfered edge (the diagonal of a square of size <r>):
float fOpUnionChamfer(float a, float b, float r) {
    return min(min(a, b), (a - r + b) * sqrt(0.5));
}

// Intersection has to deal with what is normally the inside of the resulting object
// when using union, which we normally don't care about too much. Thus, intersection
// implementations sometimes differ from union implementations.
float fOpIntersectionChamfer(float a, float b, float r) {
    return max(max(a, b), (a + r + b) * sqrt(0.5));
}

// Difference can be built from Intersection or Union:
float fOpDifferenceChamfer(float a, float b, float r) {
    return fOpIntersectionChamfer(a, -b, r);
}

// The "Round" variant uses a quarter-circle to join the two objects smoothly:
float fOpUnionRound(float a, float b, float r) {
    vec2 u = max(vec2(r - a, r - b), vec2(0));
    return max(r, min(a, b)) - length(u);
}

float fOpIntersectionRound(float a, float b, float r) {
    vec2 u = max(vec2(r + a, r + b), vec2(0));
    return min(-r, max(a, b)) + length(u);
}

float fOpDifferenceRound(float a, float b, float r) {
    return fOpIntersectionRound(a, -b, r);
}

// The "Columns" flavour makes n-1 circular columns at a 45 degree angle:
float fOpUnionColumns(float a, float b, float r, float n) {
    if((a < r) && (b < r)) {
        vec2 p = vec2(a, b);
        float columnradius = r * sqrt(2.) / ((n - 1.) * 2. + sqrt(2.));
        pR45(p);
        p.x -= sqrt(2.) / 2. * r;
        p.x += columnradius * sqrt(2.);
        if(mod(n, 2.) == 1.) {
            p.y += columnradius;
        }
		// At this point, we have turned 45 degrees and moved at a point on the
		// diagonal that we want to place the columns on.
		// Now, repeat the domain along this direction and place a circle.
        pMod1(p.y, columnradius * 2.);
        float result = length(p) - columnradius;
        result = min(result, p.x);
        result = min(result, a);
        return min(result, b);
    } else {
        return min(a, b);
    }
}

float fOpDifferenceColumns(float a, float b, float r, float n) {
    a = -a;
    float m = min(a, b);
	//avoid the expensive computation where not needed (produces discontinuity though)
    if((a < r) && (b < r)) {
        vec2 p = vec2(a, b);
        float columnradius = r * sqrt(2.) / n / 2.0;
        columnradius = r * sqrt(2.) / ((n - 1.) * 2. + sqrt(2.));

        pR45(p);
        p.y += columnradius;
        p.x -= sqrt(2.) / 2. * r;
        p.x += -columnradius * sqrt(2.) / 2.;

        if(mod(n, 2.) == 1.) {
            p.y += columnradius;
        }
        pMod1(p.y, columnradius * 2.);

        float result = -length(p) + columnradius;
        result = max(result, p.x);
        result = min(result, a);
        return -min(result, b);
    } else {
        return -m;
    }
}

float fOpIntersectionColumns(float a, float b, float r, float n) {
    return fOpDifferenceColumns(a, -b, r, n);
}

// The "Stairs" flavour produces n-1 steps of a staircase:
// much less stupid version by paniq
float fOpUnionStairs(float a, float b, float r, float n) {
    float s = r / n;
    float u = b - r;
    return min(min(a, b), 0.5 * (u + a + abs((mod(u - a + s, 2. * s)) - s)));
}

// We can just call Union since stairs are symmetric.
float fOpIntersectionStairs(float a, float b, float r, float n) {
    return -fOpUnionStairs(-a, -b, r, n);
}

float fOpDifferenceStairs(float a, float b, float r, float n) {
    return -fOpUnionStairs(-a, b, r, n);
}

// Similar to fOpUnionRound, but more lipschitz-y at acute angles
// (and less so at 90 degrees). Useful when fudging around too much
// by MediaMolecule, from Alex Evans' siggraph slides
float fOpUnionSoft(float a, float b, float r) {
    float e = max(r - abs(a - b), 0.);
    return min(a, b) - e * e * 0.25 / r;
}

// produces a cylindical pipe that runs along the intersection.
// No objects remain, only the pipe. This is not a boolean operator.
float fOpPipe(float a, float b, float r) {
    return length(vec2(a, b)) - r;
}

// first object gets a v-shaped engraving where it intersect the second
float fOpEngrave(float a, float b, float r) {
    return max(a, (a + r - abs(b)) * sqrt(0.5));
}

// first object gets a capenter-style groove cut out
float fOpGroove(float a, float b, float ra, float rb) {
    return max(a, min(a + ra, rb - abs(b)));
}

// first object gets a capenter-style tongue attached
float fOpTongue(float a, float b, float ra, float rb) {
    return min(a, max(a - ra, abs(b) - rb));
}

//#endSection End of library

// https://stackoverflow.com/questions/4200224/random-noise-functions-for-glsl
// golden_noise
float noise(in vec2 xy, in float seed) {
    return fract(tan(distance(xy * PHI, xy) * seed) * xy.x);
}

vec3 rnd23(vec2 p) {
    vec3 p3 = fract(p.xyx * vec3(.1031, .1030, .0973));
    p3 += dot(p3, p3.yxz + 33.33);
    return fract((p3.xxy + p3.yzz) * p3.zyx);
}

mat2 Rot(float a) {
    float s = sin(a), c = cos(a);
    return mat2(c, -s, s, c);
}

float opExtrusion(in vec3 p, in float sdf, in float h) {
    vec2 w = vec2(sdf, abs(p.z) - h);
    return min(max(w.x, w.y), 0.0) + length(max(w, 0.0));
}

float sdCog2d(vec2 pos) {
    float r = length(pos) * 2.;
    float a = atan(pos.y, pos.x);
    float f = 1. - smoothstep(-0.2, .8, sin(a * 12.)) * 0.14;
    f = smoothstep(f, f + 2., r);
    return f;
}

float sdCog(vec3 pos, float angle) {
    pos.xy *= Rot(angle);
    float d1 = opExtrusion(pos, sdCog2d(pos.xy), 0.05);
    float d2 = fCapsule(pos, vec3(0., 0.0, 0.), vec3(0., 0., 1.), 0.2);
    return 0.8 * fOpDifferenceRound(d1, d2, 0.05) - 0.003;
}

float sdCapsule(vec3 p, vec3 a, vec3 b, float r) {
    vec3 pa = p - a, ba = b - a;
    float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);
    return length(pa - ba * h) - r;
}

float sdCylinder(vec3 p, vec3 a, vec3 b, float r) {

    vec3 ba = b - a;
    vec3 pa = p - a;
    float baba = dot(ba, ba);
    float paba = dot(pa, ba);
    float x = length(pa * baba - ba * paba) - r * baba;
    float y = abs(paba - baba * 0.5) - baba * 0.5;
    float x2 = x * x;
    float y2 = y * y * baba;
    float d = (max(x, y) < 0.0) ? -min(x2, y2) : (((x > 0.0) ? x2 : 0.0) + ((y > 0.0) ? y2 : 0.0));

    return sign(d) * sqrt(abs(d)) / baba;
}

float sdPlane(vec3 p, vec4 n) {
  // n must be normalized
    return dot(p, n.xyz) + n.w;
}

// Add this function before mapScene
float rippleEffect(vec3 p, vec3 center, float time) {
    float dist = length(p.xz - center.xz);
    float wave = sin(dist * 2.0 - time * 8.0) * exp(-dist * 0.3);
    return wave * 0.5; // Adjust amplitude as needed
}

/*// Hexagonal prism, circumcircle variant
float fHexagonCircumcircle(vec3 p, vec2 h) {
    vec3 q = abs(p);
    return max(q.y - h.y, max(q.x * sqrt(3.) * 0.5 + q.z * 0.5, q.z) - h.x);
	//this is mathematically equivalent to this line, but less efficient:
	//return max(q.y - h.y, max(dot(vec2(cos(PI/3), sin(PI/3)), q.zx), q.z) - h.x);
}*/