Develop Reference

Three.js - Scaling a plane to full screen

I am adding a plane to the scene like this:
// Camera
this.three.camera = new THREE.PerspectiveCamera(45, window.innerWidth/window.innerHeight, 0.1, 60);
// Plane
const planeGeometry = new THREE.PlaneBufferGeometry(1,1,this.options.planeSegments,this.options.planeSegments);
const planeMat = new THREE.ShaderMaterial( ... )
this.three.plane = new THREE.Mesh(planeGeometry,planeMat);
this.three.scene.add(this.three.plane);
Pretty basic. I am than trying to find out how I have to move the plane in the Z axis for it to fill the browser-viewport. For that,
// See attachment "solving for this" is closeZ
const closeZ = 0.5 / Math.tan((this.three.camera.fov/2.0) * Math.PI / 180.0);
this.uniforms.uZMax = new THREE.Uniform(this.three.camera.position.z - closeZ);
So now I know in my shader how much I can add to Z to make the plane fill the viewport. Vertex Shader looks like this:
uniform float uZMax;
void main() {
vec3 pos = (position.xy, uZMax);
gl_Position = projectionMatrix * modelViewMatrix * vec4( pos, 1 );
}
This actually zoom the plane to fill the viewport, but in Y-Axis, not in X-Axis.
I would like to discover why my math is referring to the Y-Axis and how I need to transform it, so the plane will fill the viewport width instead of it's height?
Edit:
I'm trying to achieve something like this https://tympanus.net/Tutorials/GridToFullscreenAnimations/index4.html - But in the given example they're just scaling the x- and y-pixels to fill the screen and therefore no actual 3d - and therefore again no lighting is going on.
I want to actually move the plane towards the camera using different z-values so I can calculate surface normals to then again calculate lighting in the fragment shader by how aligned the normal is with the light direction - like it's done in raymarching.

You can easily achieve such a fullscreen effect by using the following setup:
const camera = new THREE.OrthographicCamera( - 1, 1, 1, - 1, 0, 1 );
const geometry = new THREE.PlaneBufferGeometry( 2, 2 );
When creating a mesh with this geometry and a custom shader material, the orthographic camera will ensure the intended fullscreen effect. This approach is used in all post-processing example where the entire viewport has to be filled with a single quad.

I figured it out, and as suspected it has to do with the aspect ratio passed to the camera. For anyone looking for a solution after me, here is how it works:
I wrongly assumed that the field-of-value for the camera is the same in all directions. But the FOV is referring to the Y-Axis FOV, so we have to convert the camera-fov to the x-axis also:
function getXFOV() {
// Convert angle to radiant
const FOV = this.three.camera.fov;
let yFovRadiant = FOV * Math.PI/180;
// Calculate X-FOV Radiant
let xFovRadiant = 2 * Math.atan( Math.tan(yFovRadiant/2) * (window.innerWidth / window.innerHeight));
// Convert back to angle
let xFovAngle = xFovRadiant * 180/Math.PI;
return xFovAngle;
}
And then we simply use that angle in in the closeZ-calculation instead of the camera's fov. Now it snaps to the window-width.
const closeZ = 0.5 / Math.tan((this.getXFOV()) * Math.PI / 180.0);
this.uniforms.uZMax = new THREE.Uniform(this.three.camera.position.z - closeZ);

Drawing/Rendering 3D objects with epicycles and fourier transformations [Animation]

First Note: They wont let me embed images until i have more reputation points (sorry), but all the links are images posted on imgur! :) thanks
I have replicated a method to animate any single path (1 closed path) using fourier transforms. This creates an animation of epicylces (rotating circles) which rotate around each other, and follow the imputed points, tracing the path as a continuous loop/function.
I would like to adopt this system to 3D. the two methods i can think of to achieve this is to use a Spherical Coordinate system (two complex planes) or 3 Epicycles --> one for each axis (x,y,z) with their individual parametric equations. This is probably the best way to start!!
2 Cycles, One for X and one for Y:
Picture: One Cycle --> Complex Numbers --> For X and Y
Fourier Transformation Background!!!:
• Eulers formula allows us to decompose each point in the complex plane into an angle (the argument to the exponential function) and an amplitude (Cn coefficients)
• In this sense, there is a connection to imaging each term in the infinite series above as representing a point on a circle with radius cn, offset by 2πnt/T radians
• The image below shows how a sum of complex numbers in terms of phases/amplitudes can be visualized as a set of concatenated cirlces in the complex plane. Each red line is a vector representing a term in the sequence of sums: cne2πi(nT)t
• Adding the summands corresponds to simply concatenating each of these red vectors in complex space:
Animated Rotating Circles:
Circles to Animated Drawings:
• If you have a line drawing in 2D (x-y) space, you can describe this path mathematically as a parametric function. (two separate single variable functions, both in terms of an auxiliary variable (T in this case):
• For example, below is a simple line drawing of a horse, and a parametric path through the black pixels in image, and that path then seperated into its X and Y components:
• At this point, we need to calculate the Fourier approximations of these two paths, and use coefficients from this approximation to determine the phase and amplitudes of the circles needed for the final visualization.
Python Code:
The python code used for this example can be found here on guithub
I have successful animated this process in 2D, but i would like to adopt this to 3D.
The Following Code Represents Animations in 2D --> something I already have working:
[Using JavaScript & P5.js library]
The Fourier Algorithm (fourier.js):
// a + bi
class Complex {
constructor(a, b) {
this.re = a;
this.im = b;
}
add(c) {
this.re += c.re;
this.im += c.im;
}
mult(c) {
const re = this.re * c.re - this.im * c.im;
const im = this.re * c.im + this.im * c.re;
return new Complex(re, im);
}
}
function dft(x) {
const X = [];
const Values = [];
const N = x.length;
for (let k = 0; k < N; k++) {
let sum = new Complex(0, 0);
for (let n = 0; n < N; n++) {
const phi = (TWO_PI * k * n) / N;
const c = new Complex(cos(phi), -sin(phi));
sum.add(x[n].mult(c));
}
sum.re = sum.re / N;
sum.im = sum.im / N;
let freq = k;
let amp = sqrt(sum.re * sum.re + sum.im * sum.im);
let phase = atan2(sum.im, sum.re);
X[k] = { re: sum.re, im: sum.im, freq, amp, phase };
Values[k] = {phase};
console.log(Values[k]);
}
return X;
}
The Sketch Function/ Animations (Sketch.js):
let x = [];
let fourierX;
let time = 0;
let path = [];
function setup() {
createCanvas(800, 600);
const skip = 1;
for (let i = 0; i < drawing.length; i += skip) {
const c = new Complex(drawing[i].x, drawing[i].y);
x.push(c);
}
fourierX = dft(x);
fourierX.sort((a, b) => b.amp - a.amp);
}
function epicycles(x, y, rotation, fourier) {
for (let i = 0; i < fourier.length; i++) {
let prevx = x;
let prevy = y;
let freq = fourier[i].freq;
let radius = fourier[i].amp;
let phase = fourier[i].phase;
x += radius * cos(freq * time + phase + rotation);
y += radius * sin(freq * time + phase + rotation);
stroke(255, 100);
noFill();
ellipse(prevx, prevy, radius * 2);
stroke(255);
line(prevx, prevy, x, y);
}
return createVector(x, y);
}
function draw() {
background(0);
let v = epicycles(width / 2, height / 2, 0, fourierX);
path.unshift(v);
beginShape();
noFill();
for (let i = 0; i < path.length; i++) {
vertex(path[i].x, path[i].y);
}
endShape();
const dt = TWO_PI / fourierX.length;
time += dt;
And Most Importantly! THE PATH / COORDINATES:
(this one is a triangle)
let drawing = [
{ y: -8.001009734 , x: -50 },
{ y: -7.680969345 , x: -49 },
{ y: -7.360928956 , x: -48 },
{ y: -7.040888566 , x: -47 },
{ y: -6.720848177 , x: -46 },
{ y: -6.400807788 , x: -45 },
{ y: -6.080767398 , x: -44 },
{ y: -5.760727009 , x: -43 },
{ y: -5.440686619 , x: -42 },
{ y: -5.12064623 , x: -41 },
{ y: -4.800605841 , x: -40 },
...
...
{ y: -8.001009734 , x: -47 },
{ y: -8.001009734 , x: -48 },
{ y: -8.001009734 , x: -49 },
];

This answer is in response to: "Do you think [three.js] can replicate what i have in 2D but in 3D? with the rotating circles and stuff?"
Am not sure whether you're looking to learn 3D modeling from scratch (ie, creating your own library of vector routines, homogeneous coordinate transformations, rendering perspective, etc) or whether you're simply looking to produce a final product. In the case of the latter, three.js is a powerful graphics library built on webGL that in my estimation is simple enough for a beginner to dabble with, but has a lot of depth to produce very sophisticated 3D effects. (Peruse the examples at https://threejs.org/examples/ and you'll see for yourself.)
I happen to be working a three.js project of my own, and whipped up a quick example of epicyclic circles as a warm up exercise. This involved pulling pieces and parts from the following references...
https://threejs.org/docs/index.html#manual/en/introduction/Creating-a-scene
https://threejs.org/examples/#misc_controls_orbit
https://threejs.org/examples/#webgl_geometry_shapes (This three.js example is a great resource showing a variety of ways that a shape can be rendered.)
The result is a simple scene with one circle running around the other, permitting mouse controls to orbit around the scene, viewing it from different angles and distances.
<html>
<head>
<title>Epicyclic Circles</title>
<style>
body { margin: 0; }
canvas { width: 100%; height: 100% }
</style>
</head>
<body>
<script src="https://rawgit.com/mrdoob/three.js/dev/build/three.js"></script>
<script src="https://rawgit.com/mrdoob/three.js/dev/examples/js/controls/OrbitControls.js"></script>
<script>
// Set up the basic scene, camera, and lights.
var scene = new THREE.Scene();
scene.background = new THREE.Color( 0xf0f0f0 );
var camera = new THREE.PerspectiveCamera( 75, window.innerWidth/window.innerHeight, 0.1, 1000 );
scene.add(camera)
var light = new THREE.PointLight( 0xffffff, 0.8 );
camera.add( light );
camera.position.z = 50;
var renderer = new THREE.WebGLRenderer();
renderer.setSize( window.innerWidth, window.innerHeight );
document.body.appendChild( renderer.domElement );
// Add the orbit controls to permit viewing the scene from different angles via the mouse.
controls = new THREE.OrbitControls( camera, renderer.domElement );
controls.enableDamping = true; // an animation loop is required when either damping or auto-rotation are enabled
controls.dampingFactor = 0.25;
controls.screenSpacePanning = false;
controls.minDistance = 0;
controls.maxDistance = 500;
// Create center and epicyclic circles, extruding them to give them some depth.
var extrudeSettings = { depth: 2, bevelEnabled: true, bevelSegments: 2, steps: 2, bevelSize: .25, bevelThickness: .25 };
var arcShape1 = new THREE.Shape();
arcShape1.moveTo( 0, 0 );
arcShape1.absarc( 0, 0, 15, 0, Math.PI * 2, false );
var holePath1 = new THREE.Path();
holePath1.moveTo( 0, 10 );
holePath1.absarc( 0, 10, 2, 0, Math.PI * 2, true );
arcShape1.holes.push( holePath1 );
var geometry1 = new THREE.ExtrudeBufferGeometry( arcShape1, extrudeSettings );
var mesh1 = new THREE.Mesh( geometry1, new THREE.MeshPhongMaterial( { color: 0x804000 } ) );
scene.add( mesh1 );
var arcShape2 = new THREE.Shape();
arcShape2.moveTo( 0, 0 );
arcShape2.absarc( 0, 0, 15, 0, Math.PI * 2, false );
var holePath2 = new THREE.Path();
holePath2.moveTo( 0, 10 );
holePath2.absarc( 0, 10, 2, 0, Math.PI * 2, true );
arcShape2.holes.push( holePath2 );
var geometry2 = new THREE.ExtrudeGeometry( arcShape2, extrudeSettings );
var mesh2 = new THREE.Mesh( geometry2, new THREE.MeshPhongMaterial( { color: 0x00ff00 } ) );
scene.add( mesh2 );
// Define variables to hold the current epicyclic radius and current angle.
var mesh2AxisRadius = 30;
var mesh2AxisAngle = 0;
var animate = function () {
requestAnimationFrame( animate );
// During each animation frame, let's rotate the objects on their center axis,
// and also set the position of the epicyclic circle.
mesh1.rotation.z -= 0.02;
mesh2.rotation.z += 0.02;
mesh2AxisAngle += 0.01;
mesh2.position.set ( mesh2AxisRadius * Math.cos(mesh2AxisAngle), mesh2AxisRadius * Math.sin(mesh2AxisAngle), 0 );
renderer.render( scene, camera );
};
animate();
</script>
</body>
</html>
Note that I've used basic trigonometry within the animate function to position the epicyclic circle around the center circle, and fudged the rate of rotation for the circles (rather than doing the precise math), but there's probably a better "three.js"-way of doing this via matrices or built in functions. Given that you obviously have a strong math background, I don't think you'll have any issues with translating your 2D model of multi-epicyclic circles using basic trigonometry when porting to 3D.
Hope this helps in your decision making process on how to proceed with a 3D version of your program.

The method that I would suggest is as follows. Start with a parametrized path v(t) = (v_x(t), v_y(t), v_z(t)). Consider the following projection onto the X-Y plane: v1(t) = (v_x(t)/2, v_y(t), 0). And the corresponding projection onto the X-Z plane: v2(t) = (v_x(t)/2, 0, v_z(t)).
When we add these projections together we get the original curve. But each projection is now a closed 2-D curve, and you have solutions for arbitrary closed 2-D curves. So solve each problem. And then interleave them to get a projection where your first circle goes in the X-Y plane, your second one in the X-Z plane, your third one in the X-Y plane, your fourth one in the X-Z plane ... and they sum up to your answer!

What is required to convert threejs perspective camera to orthographic

I have some code that converts a perspective camera to an orthographic camera. The problem is that when I make the conversion, the model becomes very tiny and hard to see.
I have calculated the zoom factor for the orthographic camera, based on the distance and the FOV. Are there any other properties that I need to set on the orthographic camera (e.g. clipping plane, etc..)?
I believe the position remains the same. I'm not sure what else I need to calculate.
fieldOfView = viewInfo.fov;
var getCameraPosition = function() {
return viewer._viewport._implementation.getCamera()._nativeCamera.position;
};
// Calculate the delta position between the camera and the object
var getPositionDelta = function(position1, position2) {
return {
x: position1.x - position2.x,
y: position1.y - position2.y,
z: position1.z - position2.z
}
};
var getDistance = function(positionDelta, cameraDirection) {
return dot(positionDelta, cameraDirection);
};
distance = getDistance(positionDelta, cameraDirection),
var depth = distance;
var viewportWidth = view.getDomRef().getBoundingClientRect().width;
var viewportHeight = view.getDomRef().getBoundingClientRect().height;
var aspect = viewportWidth / viewportHeight;
var height_ortho = depth * 2 * Math.atan( fieldOfView * (Math.PI/180) / 2 )
var width_ortho = height_ortho * aspect;
var near = viewInfo.near, far = viewInfo.far;
var newCamera = new THREE.OrthographicCamera(
width_ortho / -2, width_ortho / 2,
height_ortho / 2, height_ortho / -2,
near, far );
newCamera.position.copy( viewInfo.position );
var sCamera = new vk.threejs.OrthographicCamera(); //framework creatio of threejs cam
sCamera.setZoomFactor(orthoZoomFactor);
sCamera.setCameraRef(newCamera);
view.getViewport().setCamera(sCamera);
I also tried setting the same camera properties (e.g. clipping planes etc) of the perspective for the orthographic and I still had the same problem.
I guess I am missing some property or calculation required to put the object in the same position as when it was in perspective camera view.

Let's assume you have a perspective view with a given vertical field of view angle fov_y (in degrees) and you know the size of the viewport width and height. Furthermore, you have the near and far plane. These are the values which you use to setup the THREE.PerspectiveCamera:
perspCamera = new THREE.PerspectiveCamera( fov_y, width / height, near, far );
Also, you know the position of the object and the position of the camera. An object doesn't have only a single position, but you have to choose a representative position for its depth.
First you have to calculate the depth of the object.
var v3_object = .... // THREE.Vector3 : positon of the object
var v3_camera = perspCamera.position;
var line_of_sight = new THREE.Vector3();
perspCamera.getWorldDirection( line_of_sight );
var v3_distance = v3_object.clone().sub( v3_camera );
depth = v3_distance.dot( line_of_sight );
Then you have to calculate the "size" of the rectangle which is projected to the viewport at the depth:
aspect = width / height;
height_ortho = depth * 2 * Math.atan( fov_y*(Math.PI/180) / 2 )
width_ortho = height_ortho * aspect;
With these values the THREE.OrthographicCamera can be setup like this:
var orthoCamera = new THREE.OrthographicCamera(
width_ortho / -2, width_ortho / 2,
height_ortho / 2, height_ortho / -2,
near, far );
orthoCamera.position.copy( perspCamera.position );
The positon and direction of the perspective camera can be committed to the orthographic camera like this:
orthoCamera.position.copy( perspCamera.position );
orthoCamera.quaternion.copy( perspCamera.quaternion );
See also stackoverflow question Three.js - Find the current LookAt of a camera?

smooth terrain from height map three js

I am currently trying to create some smooth terrain using the PlaneBufferGeometry of three.js from a height map I got from Google Images:
https://forums.unrealengine.com/filedata/fetch?id=1192062&d=1471726925
but the result is kinda choppy..
(Sorry, this is my first question and evidently I need 10 reputation to post images, otherwise I would.. but here's an even better thing: a live demo! left click + drag to rotate, scroll to zoom)
I want, like i said, a smooth terrain, so am I doing something wrong or is this just the result and i need to smoothen it afterwards somehow?
Also here is my code:
const IMAGE_SRC = 'terrain2.png';
const SIZE_AMPLIFIER = 5;
const HEIGHT_AMPLIFIER = 10;
var WIDTH;
var HEIGHT;
var container = jQuery('#wrapper');
var scene, camera, renderer, controls;
var data, plane;
image();
// init();
function image() {
var image = new Image();
image.src = IMAGE_SRC;
image.onload = function() {
WIDTH = image.width;
HEIGHT = image.height;
var canvas = document.createElement('canvas');
canvas.width = WIDTH;
canvas.height = HEIGHT;
var context = canvas.getContext('2d');
console.log('image loaded');
context.drawImage(image, 0, 0);
data = context.getImageData(0, 0, WIDTH, HEIGHT).data;
console.log(data);
init();
}
}
function init() {
// initialize camera
camera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, .1, 100000);
camera.position.set(0, 1000, 0);
// initialize scene
scene = new THREE.Scene();
// initialize directional light (sun)
var sun = new THREE.DirectionalLight(0xFFFFFF, 1.0);
sun.position.set(300, 400, 300);
sun.distance = 1000;
scene.add(sun);
var frame = new THREE.SpotLightHelper(sun);
scene.add(frame);
// initialize renderer
renderer = new THREE.WebGLRenderer();
renderer.setClearColor(0x000000);
renderer.setPixelRatio(window.devicePixelRatio);
renderer.setSize(window.innerWidth, window.innerHeight);
container.append(renderer.domElement);
// initialize controls
controls = new THREE.OrbitControls(camera, renderer.domElement);
controls.enableDamping = true;
controls.dampingFactor = .05;
controls.rotateSpeed = .1;
// initialize plane
plane = new THREE.PlaneBufferGeometry(WIDTH * SIZE_AMPLIFIER, HEIGHT * SIZE_AMPLIFIER, WIDTH - 1, HEIGHT - 1);
plane.castShadow = true;
plane.receiveShadow = true;
var vertices = plane.attributes.position.array;
// apply height map to vertices of plane
for(i=0, j=2; i < data.length; i += 4, j += 3) {
vertices[j] = data[i] * HEIGHT_AMPLIFIER;
}
var material = new THREE.MeshPhongMaterial({color: 0xFFFFFF, side: THREE.DoubleSide, shading: THREE.FlatShading});
var mesh = new THREE.Mesh(plane, material);
mesh.rotation.x = - Math.PI / 2;
mesh.matrixAutoUpdate = false;
mesh.updateMatrix();
plane.computeFaceNormals();
plane.computeVertexNormals();
scene.add(mesh);
animate();
}
function animate() {
requestAnimationFrame(animate);
renderer.render(scene, camera);
controls.update();
}

The result is jagged because the height map has low color depth. I took the liberty of coloring a portion of the height map (Paint bucket in Photoshop, 0 tolerance, non-continuous) so you can see for yourself how large are the areas which have the same color value, i.e. the same height.
The areas of the same color will create a plateau in your terrain. That's why you have plateaus and sharp steps in your terrain.
What you can do is either smooth out the Z values of the geometry or use a height map which utilizes 16bits or event 32bits for height information. The current height map only uses 8bits, i.e. 256 values.

One thing you could do to smooth things out a bit is to sample more than just a single pixel from the heightmap. Right now, the vertex indices directly correspond to the pixel position in the data-array. And you just update the z-value from the image.
for(i=0, j=2; i < data.length; i += 4, j += 3) {
vertices[j] = data[i] * HEIGHT_AMPLIFIER;
}
Instead you could do things like this:
get multiple samples with certain offsets along the x/y axes
compute an (weighted) average value from the samples
That way you would get some smoothing at the borders of the same-height areas.
The second option is to use something like a blur-kernel (gaussian blur is horribly expensive, but maybe something like a fast box-blur would work for you).
As you are very limited in resolution due to just using a single byte, you should convert that image to float32 first:
const highResData = new Float32Array(data.length / 4);
for (let i = 0; i < highResData.length; i++) {
highResData[i] = data[4 * i] / 255;
}
Now the data is in a format that allows for far higher numeric resolution, so we can smooth that now. You could either adjust something like the StackBlur for the float32 use-case, use ndarrays and ndarray-gaussian-filter or implement something simple yourself. The basic idea is to find an average value for all the values in those uniformly colored plateaus.
Hope that helps, good luck :)

How can I change this Three.js ConvexGeometry to a non-convex geometry?

I'm worked with Three.JS before, but not on meshes. I think I am approaching my problem the right way, but I'm not sure.
The Goal
I'm trying to make a 3D blobby object that has specific verticies. The direction of the verticies are fixed, but their radius from center varies. You can imagine it sort of like an audio equalizer, except radial and in 3D.
I'm open to scrapping this approach and taking a totally different one if there's some easier way to do this.
Current Progress
I took this example and cleaned/modified it to my needs. Here's the HTML and JavaScript:
HTML (disco-ball.html)
<!DOCTYPE html>
<html>
<head>
<title>Disco Ball</title>
<script type="text/javascript" src="../libs/three.js"></script>
<script type="text/javascript" src="../libs/stats.js"></script>
<script type="text/javascript" src="../libs/ConvexGeometry.js"></script>
<script type="text/javascript" src="../libs/dat.gui.js"></script>
<style type='text/css'>
/* set margin to 0 and overflow to hidden, to go fullscreen */
body { margin: 0; overflow: hidden; }
</style>
</head>
<body>
<div id="Stats-output"></div>
<div id="WebGL-output"></div>
<script type="text/javascript" src="01-app.js"></script>
</body>
</html>
And the JavaScript (01-app.js):
window.onload = init;
const PARAMS = {
SHOW_SURFACE : true,
SHOW_POINTS : true,
SHOW_WIREFRAME : true,
SHOW_STATS : true
};
// once everything is loaded, we run our Three.js stuff.
function init() {
var renderParams = {
webGLRenderer : createWebGLRenderer(),
step : 0,
rotationSpeed : 0.007,
scene : new THREE.Scene(),
camera : createCamera(),
};
// Create the actual points.
var points = getPoints(
100, // Number of points (approximate)
10, // Unweighted radius
// Radius weights for a few points. This is a multiplier.
[2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2]
);
if (PARAMS.SHOW_STATS) {
renderParams.stats = initStats();
}
if (PARAMS.SHOW_SURFACE) {
renderParams.surface = getHullMesh(points);
renderParams.scene.add(renderParams.surface);
}
if (PARAMS.SHOW_POINTS) {
renderParams.sphereGroup = getSphereGroup(points);
renderParams.scene.add(sphereGroup);
}
render(renderParams);
}
function render(params) {
if (params.stats) {
params.stats.update();
}
if (params.sphereGroup) {
params.sphereGroup.rotation.y = params.step;
}
params.step += params.rotationSpeed;
if (params.surface) {
params.surface.rotation.y = params.step;
}
// render using requestAnimationFrame
requestAnimationFrame(function () {render(params)});
params.webGLRenderer.render(params.scene, params.camera);
}
// ******************************************************************
// Helper functions
// ******************************************************************
function getPoints (count, baseRadius, weightMap) {
// Because this is deterministic, we can pass in a weight map to adjust
// the radii.
var points = distributePoints(count,baseRadius,weightMap);
points.forEach((d,i) => {
points[i] = new THREE.Vector3(d[0],d[1],d[2]);
});
return points;
}
// A deterministic function for (approximately) evenly distributing n points
// over a sphere.
function distributePoints (count, radius, weightMap) {
// I'm not sure why I need this...
count *= 100;
var points = [];
var area = 4 * Math.PI * Math.pow(radius,2) / count;
var dist = Math.sqrt(area);
var Mtheta = Math.round(Math.PI / dist);
var distTheta = Math.PI / Mtheta
var distPhi = area / distTheta;
for (var m = 0; m < Mtheta; m++) {
let theta = (Math.PI * (m + 0.5)) / Mtheta;
let Mphi = Math.round((2 * Math.PI * Math.sin(theta)) / distPhi);
for (var n = 0; n < Mphi; n++) {
let phi = ((2 * Math.PI * n) / Mphi);
// Use the default radius, times any multiplier passed in through the
// weightMap. If no multiplier is present, use 1 to leave it
// unchanged.
points.push(createPoint(radius * (weightMap[points.length] || 1),theta,phi));
}
}
return points;
}
function createPoint (radius, theta, phi) {
var x = radius * Math.sin(theta) * Math.cos(phi);
var y = radius * Math.sin(theta) * Math.sin(phi);
var z = radius * Math.cos(theta);
return [Math.round(x), Math.round(y), Math.round(z)];
}
function createWebGLRenderer () {
// create a render and set the size
var webGLRenderer = new THREE.WebGLRenderer();
webGLRenderer.setClearColor(new THREE.Color(0xEEEEEE, 1.0));
webGLRenderer.setSize(window.innerWidth, window.innerHeight);
webGLRenderer.shadowMapEnabled = true;
// add the output of the renderer to the html element
document.getElementById("WebGL-output").appendChild(webGLRenderer.domElement);
return webGLRenderer;
}
function createCamera () {
// create a camera, which defines where we're looking at.
var camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 0.1, 1000);
// position and point the camera to the center of the scene
camera.position.x = -30;
camera.position.y = 40;
camera.position.z = 50;
camera.lookAt(new THREE.Vector3(0, 0, 0));
return camera;
}
function getSphereGroup (points) {
sphereGroup = new THREE.Object3D();
var material = new THREE.MeshBasicMaterial({color: 0xFF0000, transparent: false});
points.forEach(function (point) {
var spGeom = new THREE.SphereGeometry(0.2);
var spMesh = new THREE.Mesh(spGeom, material);
spMesh.position.copy(point);
sphereGroup.add(spMesh);
});
return sphereGroup;
}
function getHullMesh (points) {
// use the same points to create a convexgeometry
var surfaceGeometry = new THREE.ConvexGeometry(points);
var surface = createMesh(surfaceGeometry);
return surface;
}
function createMesh(geom) {
// assign two materials
var meshMaterial = new THREE.MeshBasicMaterial({color: 0x666666, transparent: true, opacity: 0.25});
meshMaterial.side = THREE.DoubleSide;
var wireFrameMat = new THREE.MeshBasicMaterial({color: 0x0000ff});
wireFrameMat.wireframe = PARAMS.SHOW_WIREFRAME;
// create a multimaterial
var mesh = THREE.SceneUtils.createMultiMaterialObject(geom, [meshMaterial, wireFrameMat]);
return mesh;
}
function initStats() {
var stats = new Stats();
stats.setMode(0); // 0: fps, 1: ms
// Align top-left
stats.domElement.style.position = 'absolute';
stats.domElement.style.left = '0px';
stats.domElement.style.top = '0px';
document.getElementById("Stats-output").appendChild(stats.domElement);
return stats;
}
What I'm Missing
You can see that there are two points on the "ball" for which I've doubled the radius (big spikes). Of course, since I'm using a ConvexGeometry, the shape is convex... so a number of the points are hidden. What kind of ... non-convex geometry can I use to make those points no longer be hidden?
I would like to subdivide the mesh a bit so it's not simply vertex-to-vertex, but a bit smoother. How can I do that (the spikes less spikey and more blobby)?
I'd like to modify the mesh so different points spike different amounts every few seconds (I have some data arrays that describe how much). How do I modify the geometry after its been made? Ideally with some kind of tweening, but I can do without of that's extremely hard =)
Thanks!

Smooth and animate a mesh.
Three provides a huge range of options. These are just suggestions, your best bet is to read the Three documentation start point and find what suits you.
A mesh is just a set of 3D points and an array of indexes describing each triangle. Once you have built the mesh you only need to update the verts and let Three update the shader attributes, and the mesh normals
Your questions
Q1. Use Three.Geometry for the mesh.
Q2. As you are building the mesh you can use the curve helpers eg Three.CubicBezierCurve3 or Three.QuadraticBezierCurve3 or maybe your best option Three.SplineCurve
Another option is to use a modifier and create the simple mesh and then let Three subdivide the mesh for you. eg three example webgl modifier subdivision
Though not the fastest solution, if the vert count is low it will do this each frame without any loss of frame rate.
Q3. Using Three.Geometry you can can set the mesh morph targets, an array of vertices.
Another option is to use a modifier, eg three example webgl modifier subdivision
Or you can modify the vertices directly each frame.
for ( var i = 0, l = geometry.vertices.length; i < l; i ++ ) {
geometry.vertices[ i ].x = ?;
geometry.vertices[ i ].y = ?;
geometry.vertices[ i ].z = ?;
}
mesh.geometry.verticesNeedUpdate = true;
How you do it?
There are a zillion other ways to do this. Which is the best will depend on the load and amount of complexity you want to create. Spend some time and read the doc's, and experiment.
What I would do! maybe?
I am not too sure what you are trying to achieve but the following is a way of getting some life into the animation rather than the overdone curves that seem so ubiquitous these days.
So if the vert count is not too high I would use a Three.BufferGeometry and modify the verts each frame. Rather than use curves I would weight subdivision verts to follow a polynomial curve f(x) = x^2/(x^2 + (1-x)^2) where x is the normalized distance between two control verts (note don't use x=0.5 rather subdivide the mesh in > 2 times)
EG the two control points and two smoothing verts
// two control points
const p1 = {x,y,z};
const p2 = {x,y,z};
// two weighted points
// dx,dy,dz are deltas
// w is the weighted position s-curve
// wa, and wd are acceleration and drag coefficients. Try to keep their sum < 1
const pw1 = {x, y, z, dx, dy, dz, w : 1/3, wa : 0.1,wd : 0.7};
const pw2 = {x, y, z, dx, dy, dz, w : 2/3, wa : 0.1,wd : 0.7};
// Compute w
pw1.w = Math.pow(pw1.w,2) / ( Math.pow(pw1.w,2) + Math.pow(1 - pw1.w,2));
pw2.w = Math.pow(pw2.w,2) / ( Math.pow(pw2.w,2) + Math.pow(1 - pw2.w,2));
Then for each weighted point you can find the new delta and update the position
// do for x,y,z
x = (p2.x - p1.x); // these points are updated every frame
// get the new pw1 vert target position
x = p1.x + x * w;
// get new delta
pw1.dx += (x - pw1.x) * pw1.wa; // set delta
pw1.dx *= pw1.wd;
// set new position
pw1.x += pw1.dx;
Do for all weighted points then set geometry.vertices
The wa,wd coefficients will change the behaviour of the smoothing, you will have to play with these values to suit your own taste. Must be 0 <= (wa,wd) < 1 and the sum should be wa + wd < 1. High sumed values will result in oscillations, too high and the oscillations will be uncontrolled.