Useful pc.Quat functions

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I’ve been using a couple of functions that I find particularly handy.

Often in my code I need to get just the element of rotation around the Y axis between two things, so I can adjust it. You can’t do this with .getEulerAngles().y because that will suddenly flip based on the rotation (the x, z elements would also flip). What you need is a stable twist around an axis that won’t suffer these effects - enter this.entity.getRotation().twist(pc.Vec3.UP) which returns the +/- angle around that axis.

Please note for performance reasons these expect UNIT vectors (.normalize() if not already unit length)

Want to get the signed angles between vectors? pc.Vec3.angle will return the +/- angle between two vectors. e.g.

var vector = new pc.Vec3().copy(enemy.getPosition()).sub(this.entity.getPosition()).normalize();
var angle = this.entity.forward.angle(vector)

*Clearly you should use working vectors rather than making one every time!

Want to work out the quaternion needed to rotate one vector to another? pc.Quat.fromToRotation will sort it out for you.

var vector = new pc.Vec3().copy(enemy.getPosition()).sub(this.entity.getPosition()).normalize();
var requiredRotation = new pc.Quat().fromToRotation(this.entity.forward, vector)

Also want to work out the rotation to look from something to something else without using pc.Entity.lookAt because maybe it’s not time to look that way yet?

pc.Quat.lookAt(from,to,[optional up]) is what you are after…

Here’s some script to drop into a file somewhere

!(function() {
var MAX_CACHE = 256

var quats = []
var vecs = []
var nextQuat = 0
var nextVec = 0

for (var i = 0; i < MAX_CACHE; i++) {
    vecs.push(new pc.Vec3)
    quats.push(new pc.Quat)
}

function Q(existing) {
    var q = quats[nextQuat++ & (MAX_CACHE-1)]
    if (existing != false) q.copy(existing || pc.Quat.IDENTITY)
    return q
}

function V(existing, y, z) {
    var v = vecs[nextVec++ & (MAX_CACHE-1)]
    if (y !== undefined && z !== undefined) {
        var d = v.data
        d[0] = existing
        d[1] = y
        d[2] = z
        return v
    }
    if (existing !== undefined) {
        var d1 = v.data
        var d2 = existing.data
        d1[0] = d2[0]
        d1[1] = d2[1]
        d1[2] = d2[2]
    }
    return v
}

pc.Vec3.temp = V
pc.Quat.temp = Q

function angleBetween(vector1, vector2, up) {
     up = up || pc.Vec3.UP
     return Math.atan2(V().cross(vector1, vector2).dot(up), vector1.dot(vector2)) * pc.math.RAD_TO_DEG
   }

pc.Vec3.prototype.angle = function(vector, up) { return angleBetween(this, vector, up); }

function orthogonal(v) {

    var x = Math.abs(v.x)
    var y = Math.abs(v.y)
    var z = Math.abs(v.z)
    var other = x < y
        ? ( x < z
            ? pc.Vec3.RIGHT
            : pc.Vec3.FORWARD )
        : ( y < z
            ? pc.Vec3.UP
            : pc.Vec3.FORWARD )
     return V().cross(v, other)
  }

function fromToRotation(v1, v2, q) {
    var kct = v1.dot(v2)
    q = q || Q()
    if (kct <= -0.999) {
        q.w = 0
        var v = orthogonal(v1).normalize()
        q.x = v.x
        q.y = v.y
        q.z = v.z
        return q
    }
    var half = V(v1).add(v2).scale(0.5)
    q.w = v1.dot(half)
    var cross = V().cross(v1, half)
    q.x = cross.x
    q.y = cross.y
    q.z = cross.z
    return q.normalize()
}

pc.Quat.prototype.fromToRotation = function(v1,v2) {
    return fromToRotation(v1, v2, this)
}

pc.Quat.prototype.twist = function(axis) {
    var orth = orthogonal(axis)
    var transformed = this.transformVector(orth, V())
    var flattened = V(transformed).sub(V(axis).scale(transformed.dot(axis))).normalize()
    var angle = Math.acos(orth.dot(flattened)) * pc.math.RAD_TO_DEG
    return V(this.x, this.y, this.z).dot(axis) > 0 ? -angle : angle
}

var m = new pc.Mat4

pc.Quat.prototype.lookAt = function(from, to, up) {
    m.setLookAt(from, to, up || pc.Vec3.UP)
    this.setFromMat4(m)
    return this
}

var oldMul = pc.Vec3.prototype.mul

pc.Vec3.prototype.mul = function(p0,p1,p2) {
    if(p0 instanceof pc.Quat) {
        return p0.transformVector(this, this)
    } else
        return oldMul.call(this, p0,p1,p2)
}
})();

Also adds an overload to transform a vector by a quaternion using .mul (rather like Unity).

You can also get a temporary Vec3 or Quat by calling pc.Vec3.temp(X,Y,Z) or pc.Vec3.temp(existing) and a quat with pc.Quat.temp(existing)

So using temporary working vectors and quaternions in a non async function might look like:

var vector = pc.Vec3.temp(enemy.getPosition()).sub(this.entity.getPosition()).normalize();
var requiredRotation = pc.Quat.temp().fromToRotation(this.entity.forward, vector)

This saves on garbage collection or allocating weirdly named temporary variables inside functions.

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