For a recent project I had to manipulate a potentially large number of meshes. I chose to use THREE.InstancedBufferGeometry as it is very efficient ; it allows to draw the same mesh many times, with different attributes, in a single drawcall.

Working with instances is slightly different from using regular meshes. In a nutshell, you give the *blueprint *of the mesh you want to draw, adding attributes as you would with a THREE.Buffergeometry and set some special THREE.InstancedBufferAttribute that will affect each *instance* of the *blueprint.*

If you understand the concept of *blueprint* (the *actual* geometry), *instance* (the *placeholder* for a *blueprint*) and *InstancedBufferAttributes* (the *variables* applied to each *instance* of the *blueprint*), you’re good to go.

The big difference with *regular* meshes is that instead of setting the meshes’ translation/rotation/scale (**TRS** for short) directly on the mesh object, you have to either, manipulate all the instances’ BufferAttributes on the CPU then re-upload them to the GPU or perform procedural transforms directly on the vertex shader.

Anyhow, a *vertex shader* is involved to transform the *blueprint*. This may seem scary but it’s not, especially as brilliant people already did most of it :)

There is a limitation when using Instances ; in WebGL, you can’t pass more than 4 floats per *attribute*. This may not sound like much but it has a big impact on how you manipulate the meshes. You can’t pass a Matrix4 (4*4 floats) to transform an instance. This was a surprise for me, a Matrix4 is the way meshes’ store their transformations internally, it would be convenient to pass the elements of a matrix and use this *matrix InstancedAttribute* it to transform each instance of the *blueprint* but it is not technically feasible.

When life gives you lemons…

Therefore, the easiest way to transform an *instance* is to use 3 InstancedBufferAttributes to represent the TRS :

**translation**: a Vector3, equivalent to the*mesh.position***rotation**: a Vector4, equivalent to the*mesh.*(not the**quaternion***mesh.*!)**rotation****scale**: a Vector3, equivalent to the*mesh.scale*

here’s a method that instantiates **count** isosceles triangles and randomizes them:

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function getInstances( count ){ //creates an instancedBufferGeometry var geometry = new THREE.InstancedBufferGeometry(); //a vertex buffer for the 'blueprint' representing a single triangle var blueprint = []; for ( var i = 0; i < 3; i++){ var a = Math.PI / 180 * 120 * i; blueprint.push( Math.cos( a ), Math.sin( a ), 0 ); } //assign the positions as a 'regular' BufferAttribute var attribute = new THREE.BufferAttribute( new Float32Array( blueprint ), 3); geometry.addAttribute( 'position', attribute ); //and that's it for the 'blueprint' ; all instances will share these data //we can add more ; normals and uvs are very often used to shade the mesh. //now for the InstancedBufferAttributes, what makes each instance different. //we create some float buffers to store the properties of each instance var translation = new Float32Array( count * 3 ); var rotation = new Float32Array( count * 4 ); var scale = new Float32Array( count * 3 ); //and iterators for convenience :) var translationIterator = 0; var rotationIterator = 0; var scaleIterator = 0; //and a temp quaternion (rotations are represented by Quaternions, not Eulers) var q = new THREE.Quaternion(); //now let's feed some random values to transform the instances for ( i = 0; i < count; i++ ){ //a random position translation[ translationIterator++ ] = ( Math.random() - .5 ) * 1000; translation[ translationIterator++ ] = ( Math.random() - .5 ) * 1000; translation[ translationIterator++ ] = ( Math.random() - .5 ) * 1000; //a random rotation //randomize quaternion not sure if it's how you do it but it looks random q.set( ( Math.random() - .5 ) * 2, ( Math.random() - .5 ) * 2, ( Math.random() - .5 ) * 2, Math.random() * Math.PI ); q.normalize(); //assign to bufferAttribute rotation[ rotationIterator++ ] = q.x; rotation[ rotationIterator++ ] = q.y; rotation[ rotationIterator++ ] = q.z; rotation[ rotationIterator++ ] = q.w; //a random scale scale[ scaleIterator++ ] = 0.1 + ( Math.random() * 4 ); scale[ scaleIterator++ ] = 0.1 + ( Math.random() * 4 ); scale[ scaleIterator++ ] = 0.1 + ( Math.random() * 4 ); } //create the InstancedBufferAttributes from our float buffers geometry.addAttribute( 'translation', new THREE.InstancedBufferAttribute( translation, 3, 1 ) ); geometry.addAttribute( 'rotation', new THREE.InstancedBufferAttribute( rotation, 4, 1 ) ); geometry.addAttribute( 'scale', new THREE.InstancedBufferAttribute( scale, 3, 1 ) ); // create a material var material = new THREE.RawShaderMaterial( { vertexShader: vertexShader, fragmentShader: fragmentShader, side:THREE.DoubleSide } ); return new THREE.Mesh( geometry, material ); } |

For the vertex shader, you can do something like this (picked from the THREE examples):

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precision highp float; uniform mat4 modelViewMatrix; uniform mat4 projectionMatrix; uniform mat3 normalMatrix; //'blueprint' attribute attribute vec3 position; //instance attributes attribute vec3 translation; attribute vec4 rotation; attribute vec3 scale; // transforms the 'blueprint' geometry with instance attributes vec3 transform( inout vec3 position, vec3 T, vec4 R, vec3 S ) { //applies the scale position *= S; //computes the rotation where R is a (vec4) quaternion position += 2.0 * cross( R.xyz, cross( R.xyz, position ) + R.w * position ); //translates the transformed 'blueprint' position += T; //return the transformed position return position; } //re-use position for shading varying vec3 vPos; void main() { //collects the 'blueprint' coordinates vec3 pos = position; //transform it transform( pos, translation, rotation, scale ); //project to get the fragment position gl_Position = projectionMatrix * modelViewMatrix * vec4( pos, 1.0 ); //just to render something :) vPos = pos; } |

and the fragment uses the world position as the fragment color:

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precision highp float; varying vec3 vPos; void main() { gl_FragColor = vec4( normalize( vPos ), 1. ); } |

With the code above, the *instances *should be properly positioned, rotated and scaled and the mesh should look something like this:

so with this, you can already do a lot of funny stuff, anything that needs many objects to move individually. My project was to animate a wall of panels, much like how Portal levels build up. I ended up with this mesmerizing *ahem* demo:

Then I tried to assign *uvs* as *InstancedBufferAttributes *(related to each* instance)* rather than *BufferAttributes* (related to the *blueprint*).

Each *instance* now has it’s own uvs instead of using the *blueprint*‘s uvs.

You may wonder how the instances are animated, that’s quite simple ; you need two sets of positions (two meshes), then create a *target* attribute on the *blueprint *geometry (as it will be the same target for all the *instances*) and in the vertex shader, instead of writing:

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vec3 pos = position; |

you’d write :

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vec3 pos = mix( position, target, ratio ); |

where *ratio* is a value between 0 and 1. When the ratio is 0, the instance is in the original position, when the ratio is 1, it is in the target position, if ratio is between 0 and 1, the values are interpolated between the 2.

The ratio can be passed as an *InstancedBufferAttribute* so that each instance opens gradually and/or with a delay and of course, the ratio can be a noise function to get fancy animations.

It is also trivial to use a distribution object – the *translation* InstanceBufferAttributes are the vertices of the distribution mesh, the *rotation* can be computed with a *lookAt() –* which gives this kind of things:

Btw the background music was recorded randomly, it is “I bet you look good on the dancefloor” by the arctic monkeys :)

The next natural step for me was to try to *cover* a mesh with *instances* of triangles so that any mesh with a triangular basis would fit nicely and wrap the distribution mesh.

The source triangle should be scaled, skewed, rotated and translated so that a single matrix can transform it into any triangle in space. Little did I know that aligning a triangle to another triangle using a transform matrix requires a special type of transform called an *affine transform (*I couldn’t explain the difference between *homothetic* and *affine* really).

When life gives you affine transforms, run.

After creating a source unit triangle (like the one used in the basic demo), my algorithm went as follows for each face of the mesh:

- find its center and compute its normal
- transform an Object3D so that it is positioned and oriented like the face
- use the inverse of the object’s matrix to transform the triangle’s vertices so that they lie on the ‘XY’ plane
- multiply the object’s transform matrix with the 2D affine transform (the one that aligns 2 triangles)
- use this matrix to transform the instance

steps 1 to 3 are really straight forward ; THREE has everything you need to do this, especially as, when using an old school THREE.Geometry, you can access the object’s faces’ list where every Face object holds the face normal. step 4 implied finding the affine transform… After 2 days of research (and headaches), I found this great JavaScript example and after some refactoring, I ended up with this glorious piece of code:

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var alignTriangles = function( exports ){ /** * find the transform matrix that aligns 3 source Vector3 to 3 destination Vector3 * @param src array of 3 source Vector3 * @param dst array of 3 destination Vector3 * @returns the return matrix {THREE.Matrix4} */ var object, center, normal, transform, rotation, inverse; function getTransform( src, dst, faceNormal ){ //init vars if need be if( object === undefined ){ object = new THREE.Object3D(); center = new THREE.Vector3(); normal = new THREE.Vector3(); transform = new THREE.Matrix4(); rotation = new THREE.Matrix4(); inverse = new THREE.Matrix4(); } //1 // computes the face center and copies the normal center.set( 0,0,0 ).add(dst[0]).add(dst[1]).add(dst[2]).multiplyScalar(1/3); normal.copy( faceNormal ); //2 // positions the generic object at the center object.position.copy( center ); //and make it point in the direction of the face object.lookAt( center.add( normal.multiplyScalar( 100 ) ) ); object.updateMatrixWorld(); //store this transform transform.copy( object.matrixWorld ); //3 // use the inverse of the object's matrix to transform the triangle's vertices inverse = inverse.getInverse(transform); var flat = []; dst.forEach(function( p ) { var v = p.clone().applyMatrix4(inverse); v.z = 0; flat.push(v); }); //4 // multiply the object's transform matrix with the 2D affine transform return transform.multiply( getTransformMatrix( rotation, src, flat ) ); } function adjugate(m) { return [ m[4] * m[8] - m[5] * m[7], m[2] * m[7] - m[1] * m[8], m[1] * m[5] - m[2] * m[4], m[5] * m[6] - m[3] * m[8], m[0] * m[8] - m[2] * m[6], m[2] * m[3] - m[0] * m[5], m[3] * m[7] - m[4] * m[6], m[1] * m[6] - m[0] * m[7], m[0] * m[4] - m[1] * m[3] ]; } function multiplyMatrices(a, b) { var c = new Float32Array(9); for (var i = 0; i < 3; ++i) { for (var j = 0; j < 3; ++j) { var cij = 0; for (var k = 0; k < 3; ++k) { cij += a[3 * i + k] * b[3 * k + j]; } c[3 * i + j] = cij; } } return c; } function getTransformMatrix( mat, source, dest ){ mat.identity(); var src = [ source[0].x, source[0].y, source[1].x, source[1].y, source[2].x, source[2].y]; var dst = [ dest[0].x, dest[0].y, dest[1].x, dest[1].y, dest[2].x, dest[2].y]; var t = multiplyMatrices( [dst[0], dst[2], dst[4], dst[1], dst[3], dst[5], 1, 1, 1], adjugate([src[0], src[2], src[4], src[1], src[3], src[5], 1, 1, 1]) ); mat.elements = [t[0], t[3], 0, t[6], t[1], t[4], 0, t[7], 0, 0, 1, 0, t[2], t[5], 0, t[8]]; return mat; } exports.getTransform = getTransform; return exports; }({}); |

and to use it:

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for( i = 0; i < faces.length; i++ ){ var f = faces[i]; var t = alignTriangles.getTransform( vs, [vertices[f.a],vertices[f.b],vertices[f.c]], f.normal ); } |

now* t *contains transform from our source triangle to the current face.

I thought it would work but nope! In fact, I obtained a completely valid Matrix4 **but**, as we need to *decompose* the Matrix4 into the *T,R & S *components to pass them as attributes to the GPU, I suspect some data, required for the affine transform, went missing. In other words, it *got schwifty* and the triangles wouldn’t fit.

After some further research, I found this StackOverflow thread explaining how to pass a Matrix4 as 4 vec4, then recompose it on the vertex shader. I followed the example and got it to work.

And there you have it: a fluffy Predator!

the HI-RES mesh is fairly big (250K faces, 8Mo) so it may turn your computer into a toaster.

**UPDATE:** I’ve added a LO-RES setting (65k faces, 2Mo ) that should work better on regular computers, click to load:

On a side note, if your mesh disappears when you zoom in, it probably gets frustrum culled, try to disable culling on the Mesh:

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mesh.frustumCulled = false; |

another reason why it would disappear is if the geometry’s bounding sphere is too small, you can (hackily) fix this by doing so:

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geometry.computeBoundingSphere(); //recompute the bounding sphere geometry.boundingSphere.radius = 1000; // assign an arbitrarily large radius |

note that this will force the render of your mesh, use with caution :)

I can think of many silly use cases for this, instanced geometry (finally) allows control over hundreds of thousands of meshes, not particles, actual meshes! I put the files on GIT repo: https://github.com/nicoptere/FluffyPredator/

enjoy :)

tlecoz

Very interesting !

I ‘m in love with your glsl-function called “transform”

Until now, I used to do it like that (the rotation part) :

void rotateXYZAroundCenter(inout vec3 pos,in vec3 rotations){

vec3 s = sin(rotations);

vec3 c = cos(rotations);

// rotation around x

float xy = c.x * pos.y – s.x * pos.z;

float xz = s.x * pos.y + c.x * pos.z;

// rotation around y

float yz = c.y * xz – s.y * pos.x;

float yx = s.y * xz + c.y * pos.x;

// rotation around z

float zx = c.z * yx – s.z * xy;

float zy = s.z * yx + c.z * xy;

pos.x = zx ;

pos.y = zy ;

pos.z = yz ;

}

But your function is probably much more optimised.

Thanks !

nico

instanciation is quite powerful :)

I don’t know if this TRS transform is very different from your function (apart from the fact that it adds Translation and Scale :)) or if it is more efficient (it depends on whether or not the cross product is hardware accelerated) but it’s simpler to read and write.

the thing is that it needs a Quaternion instead of Euler rotations (XYZ) and that’s a touch more complex (for people like me at least ^^)

tlecoz

Hello

Every glsl-functions is optimized compared to those you write by yourself, thats why I said yours is probably more efficient.

I didnt had the time to go more into it but I will

Thank you again

Douglas

Hey!

I posted the same question on one of your youtube videos, but what method did you use to assign UV’s for each instanced mesh? :o

Best

/Douglas

nico

hey,

sorry I’m not much of a youtube person… :/

so for the uvs, you need to pass a scale and offset attribute to each instance ; the scale will ‘crop’ a portion of the texture – say you have a 4 * 3 grid, your scale will be 1/4 on the X axis and 1/3 on the Y axis – and the offset will tell which cell of the ‘grid’ you want to display – again with a 4 * 3 grid, to get the bottom right corner, the offset should be 3 * 1/4 = .75 / 2 * 1/3 = .66.

then in the vertex shader, you compute the uvs like so:

`vUv = uv * scale + offset;`

and you’ll probably need to flip the Y axis so adding a`vUv.y = 1. - vUv.y;`

could help.I haven’t tried the code but I hope it helps :)

Douglas

Alright! I’ll give it a go and get back to you with the results! :D

Douglas

And huge thanks for the reply!

Douglas

Heya!

I might have missed something, could you ellaborate on the formula you mentioned?

and also, should I pass the blueprint geometry’s UV’s, or should I, as you mentioned in the article, create an instanced bufferattribute and assign UV coordinates by hand?

If so, I tried doing that and it worked when I assigned the array as a buffer attribute, but when I used the same array as an instanced bufferattribute, my meshes are getting different colors that are similar to the image that I use as a texture!

nico

here:

https://codepen.io/nicoptere/pen/gGemyV?editors=1000

:)

Douglas

AHHHH! I had almost everything right in my implementation but hadn’t scaled the offsets! I’ll get back to you with the results! :D

Awesome Creative Coding – WP.DesaKami.ID

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John Zilka

Excellent article! I’m feeling rather stupid as I’m new to coding and three js, but do I understand correctly that this is the only way to place instances at the center of faces? I’ve worked out how to place instances on a surface but I’d like to place them at the center of each face. Currently, the techniques I’m using place an instance randomly meaning some faces get several, some get none. The goal is effectively a cube with one instance at the center of each of the 6 faces. Do I need to implement the code described in this article or is there an easier way? Thanks!

nico

hey, sorry for the very late reply.

if you want to place items on each face’s center, the easiest is to compute the center of each face on the CPU ( it’s the sum of the face’s 3 vertices XYZ divided by 3).

then use this to place the instances.