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Imported/adapted Mercury's lib

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Emmanuel BENOîT 2017-10-05 20:29:39 +02:00
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////////////////////////////////////////////////////////////////
//
// HG_SDF
//
// GLSL LIBRARY FOR BUILDING SIGNED DISTANCE BOUNDS
//
// version 2016-01-10
//
// Check http://mercury.sexy/hg_sdf for updates
// and usage examples. Send feedback to spheretracing@mercury.sexy.
//
// Brought to you by MERCURY http://mercury.sexy
//
//
//
// Released as Creative Commons Attribution-NonCommercial (CC BY-NC)
//
////////////////////////////////////////////////////////////////
//
// How to use this:
//
// 1. Build some system to #include glsl files in each other.
// Include this one at the very start. Or just paste everywhere.
// 2. Build a sphere tracer. See those papers:
// * "Sphere Tracing" http://graphics.cs.illinois.edu/sites/default/files/zeno.pdf
// * "Enhanced Sphere Tracing" http://lgdv.cs.fau.de/get/2234
// The Raymnarching Toolbox Thread on pouet can be helpful as well
// http://www.pouet.net/topic.php?which=7931&page=1
// and contains links to many more resources.
// 3. Use the tools in this library to build your distance bound f().
// 4. ???
// 5. Win a compo.
//
// (6. Buy us a beer or a good vodka or something, if you like.)
//
////////////////////////////////////////////////////////////////
//
// Table of Contents:
//
// * Helper functions and macros
// * Collection of some primitive objects
// * Domain Manipulation operators
// * Object combination operators
//
////////////////////////////////////////////////////////////////
//
// Why use this?
//
// The point of this lib is that everything is structured according
// to patterns that we ended up using when building geometry.
// It makes it more easy to write code that is reusable and that somebody
// else can actually understand. Especially code on Shadertoy (which seems
// to be what everybody else is looking at for "inspiration") tends to be
// really ugly. So we were forced to do something about the situation and
// release this lib ;)
//
// Everything in here can probably be done in some better way.
// Please experiment. We'd love some feedback, especially if you
// use it in a scene production.
//
// The main patterns for building geometry this way are:
// * Stay Lipschitz continuous. That means: don't have any distance
// gradient larger than 1. Try to be as close to 1 as possible -
// Distances are euclidean distances, don't fudge around.
// Underestimating distances will happen. That's why calling
// it a "distance bound" is more correct. Don't ever multiply
// distances by some value to "fix" a Lipschitz continuity
// violation. The invariant is: each fSomething() function returns
// a correct distance bound.
// * Use very few primitives and combine them as building blocks
// using combine opertors that preserve the invariant.
// * Multiply objects by repeating the domain (space).
// If you are using a loop inside your distance function, you are
// probably doing it wrong (or you are building boring fractals).
// * At right-angle intersections between objects, build a new local
// coordinate system from the two distances to combine them in
// interesting ways.
// * As usual, there are always times when it is best to not follow
// specific patterns.
//
////////////////////////////////////////////////////////////////
//
// FAQ
//
// Q: Why is there no sphere tracing code in this lib?
// A: Because our system is way too complex and always changing.
// This is the constant part. Also we'd like everyone to
// explore for themselves.
//
// Q: This does not work when I paste it into Shadertoy!!!!
// A: Yes. It is GLSL, not GLSL ES. We like real OpenGL
// because it has way more features and is more likely
// to work compared to browser-based WebGL. We recommend
// you consider using OpenGL for your productions. Most
// of this can be ported easily though.
//
// Q: How do I material?
// A: We recommend something like this:
// Write a material ID, the distance and the local coordinate
// p into some global variables whenever an object's distance is
// smaller than the stored distance. Then, at the end, evaluate
// the material to get color, roughness, etc., and do the shading.
//
// Q: I found an error. Or I made some function that would fit in
// in this lib. Or I have some suggestion.
// A: Awesome! Drop us a mail at spheretracing@mercury.sexy.
//
// Q: Why is this not on github?
// A: Because we were too lazy. If we get bugged about it enough,
// we'll do it.
//
// Q: Your license sucks for me.
// A: Oh. What should we change it to?
//
// Q: I have trouble understanding what is going on with my distances.
// A: Some visualization of the distance field helps. Try drawing a
// plane that you can sweep through your scene with some color
// representation of the distance field at each point and/or iso
// lines at regular intervals. Visualizing the length of the
// gradient (or better: how much it deviates from being equal to 1)
// is immensely helpful for understanding which parts of the
// distance field are broken.
//
////////////////////////////////////////////////////////////////
//! type library
//! include lib/utils.glsl
////////////////////////////////////////////////////////////////
//
// 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 HG_fSphere(vec3 p, float r) {
return length(p) - r;
}
// Plane with normal n (n is normalized) at some distance from the origin
float HG_fPlane(vec3 p, vec3 n, float distanceFromOrigin) {
return dot(p, n) + distanceFromOrigin;
}
// Cheap Box: distance to corners is overestimated
float HG_fBoxCheap(vec3 p, vec3 b) { //cheap box
return M_VecMax(abs(p) - b);
}
// Box: correct distance to corners
float HG_fBox(vec3 p, vec3 b) {
vec3 d = abs(p) - b;
return length(max(d, vec3(0))) + M_VecMax(min(d, vec3(0)));
}
// Same as above, but in two dimensions (an endless box)
float HG_fBox2Cheap(vec2 p, vec2 b) {
return M_VecMax(abs(p)-b);
}
float HG_fBox2(vec2 p, vec2 b) {
vec2 d = abs(p) - b;
return length(max(d, vec2(0))) + M_VecMax(min(d, vec2(0)));
}
// Endless "corner"
float HG_fCorner (vec2 p) {
return length(max(p, vec2(0))) + M_VecMax(min(p, vec2(0)));
}
// Blobby ball object. You've probably seen it somewhere. This is not a correct distance bound, beware.
float HG_fBlob(vec3 p) {
p = abs(p);
if (p.x < max(p.y, p.z)) p = p.yzx;
if (p.x < max(p.y, p.z)) p = p.yzx;
float b = max(max(max(
dot(p, normalize(vec3(1, 1, 1))),
dot(p.xz, normalize(vec2(PHI+1, 1)))),
dot(p.yx, normalize(vec2(1, PHI)))),
dot(p.xz, normalize(vec2(1, PHI))));
float l = length(p);
return l - 1.5 - 0.2 * (1.5 / 2)* cos(min(sqrt(1.01 - b / l)*(PI / 0.25), PI));
}
// Cylinder standing upright on the xz plane
float HG_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 HG_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 HG_fLineSegment(vec3 p, vec3 a, vec3 b) {
vec3 ab = b - a;
float t = M_Saturate(dot(p - a, ab) / dot(ab, ab));
return length((ab*t + a) - p);
}
// Capsule version 2: between two end points <a> and <b> with radius r
float HG_fCapsule(vec3 p, vec3 a, vec3 b, float r) {
return HG_fLineSegment(p, a, b) - r;
}
// Torus in the XZ-plane
float HG_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 HG_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 HG_fDisc(vec3 p, float r) {
float l = length(p.xz) - r;
return l < 0 ? abs(p.y) : length(vec2(p.y, l));
}
// Hexagonal prism, circumcircle variant
float HG_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);
}
// Hexagonal prism, incircle variant
float HG_fHexagonIncircle(vec3 p, vec2 h) {
return HG_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 HG_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;
}
//
// "Generalized Distance Functions" by Akleman and Chen.
// see the Paper at https://www.viz.tamu.edu/faculty/ergun/research/implicitmodeling/papers/sm99.pdf
//
// This set of constants is used to construct a large variety of geometric primitives.
// Indices are shifted by 1 compared to the paper because we start counting at Zero.
// Some of those are slow whenever a driver decides to not unroll the loop,
// which seems to happen for fIcosahedron und fTruncatedIcosahedron on nvidia 350.12 at least.
// Specialized implementations can well be faster in all cases.
//
const vec3 HG_GDFVectors[19] = vec3[](
normalize(vec3(1, 0, 0)),
normalize(vec3(0, 1, 0)),
normalize(vec3(0, 0, 1)),
normalize(vec3(1, 1, 1 )),
normalize(vec3(-1, 1, 1)),
normalize(vec3(1, -1, 1)),
normalize(vec3(1, 1, -1)),
normalize(vec3(0, 1, PHI+1)),
normalize(vec3(0, -1, PHI+1)),
normalize(vec3(PHI+1, 0, 1)),
normalize(vec3(-PHI-1, 0, 1)),
normalize(vec3(1, PHI+1, 0)),
normalize(vec3(-1, PHI+1, 0)),
normalize(vec3(0, PHI, 1)),
normalize(vec3(0, -PHI, 1)),
normalize(vec3(1, 0, PHI)),
normalize(vec3(-1, 0, PHI)),
normalize(vec3(PHI, 1, 0)),
normalize(vec3(-PHI, 1, 0))
);
// Version with variable exponent.
// This is slow and does not produce correct distances, but allows for bulging of objects.
float HG_fGDF(vec3 p, float r, float e, int begin, int end) {
float d = 0;
for (int i = begin; i <= end; ++i)
d += pow(abs(dot(p, HG_GDFVectors[i])), e);
return pow(d, 1/e) - r;
}
// Version with without exponent, creates objects with sharp edges and flat faces
float HG_fGDF(vec3 p, float r, int begin, int end) {
float d = 0;
for (int i = begin; i <= end; ++i)
d = max(d, abs(dot(p, HG_GDFVectors[i])));
return d - r;
}
// Primitives follow:
float HG_fOctahedron(vec3 p, float r, float e) {
return HG_fGDF(p, r, e, 3, 6);
}
float HG_fDodecahedron(vec3 p, float r, float e) {
return HG_fGDF(p, r, e, 13, 18);
}
float HG_fIcosahedron(vec3 p, float r, float e) {
return HG_fGDF(p, r, e, 3, 12);
}
float HG_fTruncatedOctahedron(vec3 p, float r, float e) {
return HG_fGDF(p, r, e, 0, 6);
}
float HG_fTruncatedIcosahedron(vec3 p, float r, float e) {
return HG_fGDF(p, r, e, 3, 18);
}
float HG_fOctahedron(vec3 p, float r) {
return HG_fGDF(p, r, 3, 6);
}
float HG_fDodecahedron(vec3 p, float r) {
return HG_fGDF(p, r, 13, 18);
}
float HG_fIcosahedron(vec3 p, float r) {
return HG_fGDF(p, r, 3, 12);
}
float HG_fTruncatedOctahedron(vec3 p, float r) {
return HG_fGDF(p, r, 0, 6);
}
float HG_fTruncatedIcosahedron(vec3 p, float r) {
return HG_fGDF(p, r, 3, 18);
}
////////////////////////////////////////////////////////////////
//
// 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 HG_pR(inout vec2 p, float a) {
p = cos(a)*p + sin(a)*vec2(p.y, -p.x);
}
// Shortcut for 45-degrees rotation
void HG_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 = HG_pMod1(p.x,5);> - using the return value is optional.
float HG_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 HG_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 HG_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 HG_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 HG_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 HG_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 HG_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 HG_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 HG_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 HG_pMirror (inout float p, float dist) {
float s = M_Sign(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 HG_pMirrorOctant (inout vec2 p, vec2 dist) {
vec2 s = M_Sign(p);
HG_pMirror(p.x, dist.x);
HG_pMirror(p.y, dist.y);
if (p.y > p.x)
p.xy = p.yx;
return s;
}
// Reflect space at a plane
float HG_pReflect(inout vec3 p, vec3 planeNormal, float offset) {
float t = dot(p, planeNormal)+offset;
if (t < 0) {
p = p - (2*t)*planeNormal;
}
return M_Sign(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 HG_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 HG_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 HG_fOpDifferenceChamfer (float a, float b, float r) {
return HG_fOpIntersectionChamfer(a, -b, r);
}
// The "Round" variant uses a quarter-circle to join the two objects smoothly:
float HG_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 HG_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 HG_fOpDifferenceRound (float a, float b, float r) {
return HG_fOpIntersectionRound(a, -b, r);
}
// The "Columns" flavour makes n-1 circular columns at a 45 degree angle:
float HG_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));
HG_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.
HG_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 HG_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));
HG_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;
}
HG_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 HG_fOpDifferenceColumns(a,-b,r, n);
}
// The "Stairs" flavour produces n-1 steps of a staircase:
// much less stupid version by paniq
float HG_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 -HG_fOpUnionStairs(-a, -b, r, n);
}
float fOpDifferenceStairs(float a, float b, float r, float n) {
return -HG_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 HG_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 HG_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 HG_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 HG_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 HG_fOpTongue(float a, float b, float ra, float rb) {
return min(a, max(a - ra, abs(b) - rb));
}

72
shaders/lib/utils.glsl
View file

@ -1,7 +1,9 @@
//! type library
const float PI = 3.14159265;
const float PI = 3.1415926535;
const float TAU = 2 * PI;
const float PHI = sqrt( 5 ) * .5 + .5;
// -----------------------------------------------------------------------------
@ -42,3 +44,71 @@ float M_LengthSqr(
{
return dot( x , x );
}
float M_Sqr(
in float x )
{
return x * x;
}
vec2 M_Sqr(
in vec2 x )
{
return x * x;
}
vec3 M_Sqr(
in vec3 x )
{
return x * x;
}
float M_Sign(
in float x )
{
return ( x < 0 ) ? -1 : 1;
}
vec2 M_Sign(
in vec2 v )
{
return vec2( M_Sign( v.x ) , M_Sign( v.y ) );
}
float M_VecMax(
in vec2 v )
{
return max( v.x , v.y );
}
float M_VecMax(
in vec3 v )
{
return max( M_VecMax( v.xy ) , v.z );
}
float M_VecMax(
in vec4 v )
{
return max( M_VecMax( v.xy ) , M_VecMax( v.zw ) );
}
float M_VecMin(
in vec2 v )
{
return min( v.x , v.y );
}
float M_VecMin(
in vec3 v )
{
return min( M_VecMin( v.xy ) , v.z );
}
float M_VecMin(
in vec4 v )
{
return min( M_VecMin( v.xy ) , M_VecMin( v.zw ) );
}

2
shaders/scene.f.glsl
View file

@ -2,6 +2,8 @@
//! type fragment
//! include chunks/raymarcher.glsl
//! include lib/hg_sdf.glsl
//! include lib/shading-pbr.glsl
//! include lib/shading-blinnphong.glsl
//! include lib/fog.glsl