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@ -0,0 +1,791 @@ |
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//////////////////////////////////////////////////////////////// |
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// |
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// HG_SDF |
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// |
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// GLSL LIBRARY FOR BUILDING SIGNED DISTANCE BOUNDS |
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// |
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// version 2016-01-10 |
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// |
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// Check http://mercury.sexy/hg_sdf for updates |
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// and usage examples. Send feedback to spheretracing@mercury.sexy. |
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// |
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// Brought to you by MERCURY http://mercury.sexy |
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// |
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// |
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// |
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// Released as Creative Commons Attribution-NonCommercial (CC BY-NC) |
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// |
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//////////////////////////////////////////////////////////////// |
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// |
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// How to use this: |
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// |
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// 1. Build some system to #include glsl files in each other. |
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// Include this one at the very start. Or just paste everywhere. |
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// 2. Build a sphere tracer. See those papers: |
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// * "Sphere Tracing" http://graphics.cs.illinois.edu/sites/default/files/zeno.pdf |
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// * "Enhanced Sphere Tracing" http://lgdv.cs.fau.de/get/2234 |
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// The Raymnarching Toolbox Thread on pouet can be helpful as well |
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// http://www.pouet.net/topic.php?which=7931&page=1 |
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// and contains links to many more resources. |
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// 3. Use the tools in this library to build your distance bound f(). |
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// 4. ??? |
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// 5. Win a compo. |
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// |
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// (6. Buy us a beer or a good vodka or something, if you like.) |
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// |
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//////////////////////////////////////////////////////////////// |
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// |
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// Table of Contents: |
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// |
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// * Helper functions and macros |
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// * Collection of some primitive objects |
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// * Domain Manipulation operators |
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// * Object combination operators |
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// |
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//////////////////////////////////////////////////////////////// |
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// |
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// Why use this? |
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// |
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// The point of this lib is that everything is structured according |
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// to patterns that we ended up using when building geometry. |
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// It makes it more easy to write code that is reusable and that somebody |
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// else can actually understand. Especially code on Shadertoy (which seems |
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// to be what everybody else is looking at for "inspiration") tends to be |
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// really ugly. So we were forced to do something about the situation and |
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// release this lib ;) |
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// |
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// Everything in here can probably be done in some better way. |
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// Please experiment. We'd love some feedback, especially if you |
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// use it in a scene production. |
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// |
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// The main patterns for building geometry this way are: |
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// * Stay Lipschitz continuous. That means: don't have any distance |
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// gradient larger than 1. Try to be as close to 1 as possible - |
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// Distances are euclidean distances, don't fudge around. |
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// Underestimating distances will happen. That's why calling |
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// it a "distance bound" is more correct. Don't ever multiply |
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// distances by some value to "fix" a Lipschitz continuity |
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// violation. The invariant is: each fSomething() function returns |
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// a correct distance bound. |
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// * Use very few primitives and combine them as building blocks |
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// using combine opertors that preserve the invariant. |
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// * Multiply objects by repeating the domain (space). |
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// If you are using a loop inside your distance function, you are |
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// probably doing it wrong (or you are building boring fractals). |
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// * At right-angle intersections between objects, build a new local |
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// coordinate system from the two distances to combine them in |
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// interesting ways. |
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// * As usual, there are always times when it is best to not follow |
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// specific patterns. |
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// |
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//////////////////////////////////////////////////////////////// |
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// |
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// FAQ |
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// |
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// Q: Why is there no sphere tracing code in this lib? |
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// A: Because our system is way too complex and always changing. |
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// This is the constant part. Also we'd like everyone to |
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// explore for themselves. |
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// |
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// Q: This does not work when I paste it into Shadertoy!!!! |
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// A: Yes. It is GLSL, not GLSL ES. We like real OpenGL |
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// because it has way more features and is more likely |
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// to work compared to browser-based WebGL. We recommend |
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// you consider using OpenGL for your productions. Most |
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// of this can be ported easily though. |
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// |
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// Q: How do I material? |
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// A: We recommend something like this: |
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// Write a material ID, the distance and the local coordinate |
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// p into some global variables whenever an object's distance is |
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// smaller than the stored distance. Then, at the end, evaluate |
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// the material to get color, roughness, etc., and do the shading. |
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// |
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// Q: I found an error. Or I made some function that would fit in |
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// in this lib. Or I have some suggestion. |
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// A: Awesome! Drop us a mail at spheretracing@mercury.sexy. |
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// |
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// Q: Why is this not on github? |
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// A: Because we were too lazy. If we get bugged about it enough, |
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// we'll do it. |
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// |
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// Q: Your license sucks for me. |
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// A: Oh. What should we change it to? |
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// |
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// Q: I have trouble understanding what is going on with my distances. |
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// A: Some visualization of the distance field helps. Try drawing a |
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// plane that you can sweep through your scene with some color |
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// representation of the distance field at each point and/or iso |
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// lines at regular intervals. Visualizing the length of the |
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// gradient (or better: how much it deviates from being equal to 1) |
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// is immensely helpful for understanding which parts of the |
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// distance field are broken. |
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// |
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//////////////////////////////////////////////////////////////// |
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//////////////////////////////////////////////////////////////// |
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// |
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// HELPER FUNCTIONS/MACROS |
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// |
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//////////////////////////////////////////////////////////////// |
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#define PI 3.14159265 |
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#define TAU (2*PI) |
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#define PHI (sqrt(5)*0.5 + 0.5) |
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// Clamp to [0,1] - this operation is free under certain circumstances. |
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// For further information see |
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// http://www.humus.name/Articles/Persson_LowLevelThinking.pdf and |
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// http://www.humus.name/Articles/Persson_LowlevelShaderOptimization.pdf |
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#define saturate(x) clamp(x, 0, 1) |
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// Sign function that doesn't return 0 |
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float sgn(float x) { |
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return (x<0)?-1.:1.; |
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} |
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vec2 sgn(vec2 v) { |
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return vec2((v.x<0)?-1:1, (v.y<0)?-1:1); |
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} |
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float square (float x) { |
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return x*x; |
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} |
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vec2 square (vec2 x) { |
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return x*x; |
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} |
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vec3 square (vec3 x) { |
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return x*x; |
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} |
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float lengthSqr(vec3 x) { |
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return dot(x, x); |
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} |
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// Maximum/minumum elements of a vector |
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float vmax(vec2 v) { |
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return max(v.x, v.y); |
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} |
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float vmax(vec3 v) { |
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return max(max(v.x, v.y), v.z); |
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} |
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float vmax(vec4 v) { |
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return max(max(v.x, v.y), max(v.z, v.w)); |
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} |
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float vmin(vec2 v) { |
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return min(v.x, v.y); |
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} |
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float vmin(vec3 v) { |
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return min(min(v.x, v.y), v.z); |
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} |
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float vmin(vec4 v) { |
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return min(min(v.x, v.y), min(v.z, v.w)); |
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} |
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//////////////////////////////////////////////////////////////// |
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// |
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// PRIMITIVE DISTANCE FUNCTIONS |
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// |
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//////////////////////////////////////////////////////////////// |
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// |
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// Conventions: |
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// |
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// Everything that is a distance function is called fSomething. |
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// The first argument is always a point in 2 or 3-space called <p>. |
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// Unless otherwise noted, (if the object has an intrinsic "up" |
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// side or direction) the y axis is "up" and the object is |
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// centered at the origin. |
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// |
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//////////////////////////////////////////////////////////////// |
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float fSphere(vec3 p, float r) { |
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return length(p) - r; |
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} |
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// Plane with normal n (n is normalized) at some distance from the origin |
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float fPlane(vec3 p, vec3 n, float distanceFromOrigin) { |
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return dot(p, n) + distanceFromOrigin; |
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} |
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// Cheap Box: distance to corners is overestimated |
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float fBoxCheap(vec3 p, vec3 b) { //cheap box |
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return vmax(abs(p) - b); |
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} |
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// Box: correct distance to corners |
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float fBox(vec3 p, vec3 b) { |
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vec3 d = abs(p) - b; |
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return length(max(d, vec3(0))) + vmax(min(d, vec3(0))); |
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} |
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// Same as above, but in two dimensions (an endless box) |
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float fBox2Cheap(vec2 p, vec2 b) { |
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return vmax(abs(p)-b); |
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} |
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float fBox2(vec2 p, vec2 b) { |
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vec2 d = abs(p) - b; |
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return length(max(d, vec2(0))) + vmax(min(d, vec2(0))); |
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} |
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// Endless "corner" |
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float fCorner (vec2 p) { |
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return length(max(p, vec2(0))) + vmax(min(p, vec2(0))); |
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} |
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// Blobby ball object. You've probably seen it somewhere. This is not a correct distance bound, beware. |
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float fBlob(vec3 p) { |
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p = abs(p); |
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if (p.x < max(p.y, p.z)) p = p.yzx; |
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if (p.x < max(p.y, p.z)) p = p.yzx; |
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float b = max(max(max( |
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dot(p, normalize(vec3(1, 1, 1))), |
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dot(p.xz, normalize(vec2(PHI+1, 1)))), |
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dot(p.yx, normalize(vec2(1, PHI)))), |
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dot(p.xz, normalize(vec2(1, PHI)))); |
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float l = length(p); |
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return l - 1.5 - 0.2 * (1.5 / 2)* cos(min(sqrt(1.01 - b / l)*(PI / 0.25), PI)); |
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} |
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// Cylinder standing upright on the xz plane |
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float fCylinder(vec3 p, float r, float height) { |
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float d = length(p.xz) - r; |
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d = max(d, abs(p.y) - height); |
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return d; |
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} |
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// Capsule: A Cylinder with round caps on both sides |
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float fCapsule(vec3 p, float r, float c) { |
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return mix(length(p.xz) - r, length(vec3(p.x, abs(p.y) - c, p.z)) - r, step(c, abs(p.y))); |
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} |
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// Distance to line segment between <a> and <b>, used for fCapsule() version 2below |
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float fLineSegment(vec3 p, vec3 a, vec3 b) { |
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vec3 ab = b - a; |
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float t = saturate(dot(p - a, ab) / dot(ab, ab)); |
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return length((ab*t + a) - p); |
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} |
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// Capsule version 2: between two end points <a> and <b> with radius r |
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float fCapsule(vec3 p, vec3 a, vec3 b, float r) { |
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return fLineSegment(p, a, b) - r; |
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} |
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// Torus in the XZ-plane |
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float fTorus(vec3 p, float smallRadius, float largeRadius) { |
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return length(vec2(length(p.xz) - largeRadius, p.y)) - smallRadius; |
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} |
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// A circle line. Can also be used to make a torus by subtracting the smaller radius of the torus. |
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float fCircle(vec3 p, float r) { |
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float l = length(p.xz) - r; |
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return length(vec2(p.y, l)); |
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} |
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// A circular disc with no thickness (i.e. a cylinder with no height). |
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// Subtract some value to make a flat disc with rounded edge. |
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float fDisc(vec3 p, float r) { |
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float l = length(p.xz) - r; |
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return l < 0 ? abs(p.y) : length(vec2(p.y, l)); |
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} |
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// Hexagonal prism, circumcircle variant |
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float fHexagonCircumcircle(vec3 p, vec2 h) { |
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vec3 q = abs(p); |
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return max(q.y - h.y, max(q.x*sqrt(3)*0.5 + q.z*0.5, q.z) - h.x); |
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//this is mathematically equivalent to this line, but less efficient: |
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//return max(q.y - h.y, max(dot(vec2(cos(PI/3), sin(PI/3)), q.zx), q.z) - h.x); |
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} |
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// Hexagonal prism, incircle variant |
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float fHexagonIncircle(vec3 p, vec2 h) { |
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return fHexagonCircumcircle(p, vec2(h.x*sqrt(3)*0.5, h.y)); |
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} |
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// Cone with correct distances to tip and base circle. Y is up, 0 is in the middle of the base. |
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float fCone(vec3 p, float radius, float height) { |
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vec2 q = vec2(length(p.xz), p.y); |
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vec2 tip = q - vec2(0, height); |
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vec2 mantleDir = normalize(vec2(height, radius)); |
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float mantle = dot(tip, mantleDir); |
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float d = max(mantle, -q.y); |
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float projected = dot(tip, vec2(mantleDir.y, -mantleDir.x)); |
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// distance to tip |
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if ((q.y > height) && (projected < 0)) { |
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d = max(d, length(tip)); |
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} |
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// distance to base ring |
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if ((q.x > radius) && (projected > length(vec2(height, radius)))) { |
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d = max(d, length(q - vec2(radius, 0))); |
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} |
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return d; |
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} |
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// |
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// "Generalized Distance Functions" by Akleman and Chen. |
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// see the Paper at https://www.viz.tamu.edu/faculty/ergun/research/implicitmodeling/papers/sm99.pdf |
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// |
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// This set of constants is used to construct a large variety of geometric primitives. |
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// Indices are shifted by 1 compared to the paper because we start counting at Zero. |
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// Some of those are slow whenever a driver decides to not unroll the loop, |
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// which seems to happen for fIcosahedron und fTruncatedIcosahedron on nvidia 350.12 at least. |
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// Specialized implementations can well be faster in all cases. |
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// |
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const vec3 GDFVectors[19] = vec3[]( |
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normalize(vec3(1, 0, 0)), |
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normalize(vec3(0, 1, 0)), |
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normalize(vec3(0, 0, 1)), |
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normalize(vec3(1, 1, 1 )), |
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normalize(vec3(-1, 1, 1)), |
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normalize(vec3(1, -1, 1)), |
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normalize(vec3(1, 1, -1)), |
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normalize(vec3(0, 1, PHI+1)), |
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normalize(vec3(0, -1, PHI+1)), |
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normalize(vec3(PHI+1, 0, 1)), |
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normalize(vec3(-PHI-1, 0, 1)), |
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normalize(vec3(1, PHI+1, 0)), |
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normalize(vec3(-1, PHI+1, 0)), |
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normalize(vec3(0, PHI, 1)), |
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normalize(vec3(0, -PHI, 1)), |
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normalize(vec3(1, 0, PHI)), |
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normalize(vec3(-1, 0, PHI)), |
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normalize(vec3(PHI, 1, 0)), |
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normalize(vec3(-PHI, 1, 0)) |
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); |
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// Version with variable exponent. |
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// This is slow and does not produce correct distances, but allows for bulging of objects. |
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float fGDF(vec3 p, float r, float e, int begin, int end) { |
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float d = 0; |
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for (int i = begin; i <= end; ++i) |
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d += pow(abs(dot(p, GDFVectors[i])), e); |
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return pow(d, 1/e) - r; |
|
|
|
} |
|
|
|
|
|
|
|
// Version with without exponent, creates objects with sharp edges and flat faces |
|
|
|
float 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, GDFVectors[i]))); |
|
|
|
return d - r; |
|
|
|
} |
|
|
|
|
|
|
|
// Primitives follow: |
|
|
|
|
|
|
|
float fOctahedron(vec3 p, float r, float e) { |
|
|
|
return fGDF(p, r, e, 3, 6); |
|
|
|
} |
|
|
|
|
|
|
|
float fDodecahedron(vec3 p, float r, float e) { |
|
|
|
return fGDF(p, r, e, 13, 18); |
|
|
|
} |
|
|
|
|
|
|
|
float fIcosahedron(vec3 p, float r, float e) { |
|
|
|
return fGDF(p, r, e, 3, 12); |
|
|
|
} |
|
|
|
|
|
|
|
float fTruncatedOctahedron(vec3 p, float r, float e) { |
|
|
|
return fGDF(p, r, e, 0, 6); |
|
|
|
} |
|
|
|
|
|
|
|
float fTruncatedIcosahedron(vec3 p, float r, float e) { |
|
|
|
return fGDF(p, r, e, 3, 18); |
|
|
|
} |
|
|
|
|
|
|
|
float fOctahedron(vec3 p, float r) { |
|
|
|
return fGDF(p, r, 3, 6); |
|
|
|
} |
|
|
|
|
|
|
|
float fDodecahedron(vec3 p, float r) { |
|
|
|
return fGDF(p, r, 13, 18); |
|
|
|
} |
|
|
|
|
|
|
|
float fIcosahedron(vec3 p, float r) { |
|
|
|
return fGDF(p, r, 3, 12); |
|
|
|
} |
|
|
|
|
|
|
|
float fTruncatedOctahedron(vec3 p, float r) { |
|
|
|
return fGDF(p, r, 0, 6); |
|
|
|
} |
|
|
|
|
|
|
|
float fTruncatedIcosahedron(vec3 p, float r) { |
|
|
|
return 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 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; |
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} |
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// produces a cylindical pipe that runs along the intersection. |
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// No objects remain, only the pipe. This is not a boolean operator. |
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float fOpPipe(float a, float b, float r) { |
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return length(vec2(a, b)) - r; |
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} |
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// first object gets a v-shaped engraving where it intersect the second |
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float fOpEngrave(float a, float b, float r) { |
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return max(a, (a + r - abs(b))*sqrt(0.5)); |
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} |
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// first object gets a capenter-style groove cut out |
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float fOpGroove(float a, float b, float ra, float rb) { |
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return max(a, min(a + ra, rb - abs(b))); |
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} |
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// first object gets a capenter-style tongue attached |
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float fOpTongue(float a, float b, float ra, float rb) { |
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return min(a, max(a - ra, abs(b) - rb)); |
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} |
gradient
8 years ago