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Rotation axis #198

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Rotation axis #198

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5f9c18c
Add note to THREEJS bones example
pehrlich Nov 14, 2014
17631ed
Correct rotationAxis for frame and hand, fixes #191
pehrlich Nov 14, 2014
193ab5a
Use atan2 in rotationAngle methods
pehrlich Nov 14, 2014
d102e89
Update frame.js
Nov 17, 2014
7e41cd0
Fix hand rotationAngle
Nov 17, 2014
afbf56c
Fix hand rotationAngle
Nov 17, 2014
c332680
Remove errant plus signs; build.
pehrlich Nov 17, 2014
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3 changes: 3 additions & 0 deletions examples/threejs-bones.html
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Original file line number Diff line number Diff line change
Expand Up @@ -18,6 +18,9 @@
</body>

<script>
// note: before implementing based off of this, you can instead grab the boneHand plugin
// here: js.leapmotion.com

var colors = [0xff0000, 0x00ff00, 0x0000ff];
var baseBoneRotation = (new THREE.Quaternion).setFromEuler(
new THREE.Euler(Math.PI / 2, 0, 0)
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70 changes: 53 additions & 17 deletions leap-0.6.3.js
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Original file line number Diff line number Diff line change
Expand Up @@ -1836,14 +1836,25 @@ Frame.prototype.hand = function(id) {
Frame.prototype.rotationAngle = function(sinceFrame, axis) {
if (!this.valid || !sinceFrame.valid) return 0.0;

// A derivation of the following can be found here:
// http://en.wikipedia.org/wiki/Axis–angle_representation
var rot = this.rotationMatrix(sinceFrame);
var cs = (rot[0] + rot[4] + rot[8] - 1.0)*0.5;
var angle = Math.acos(cs);

var axis = [
rot[7] - rot[5],
rot[2] - rot[6],
rot[3] - rot[1]
];

var sin = Leap.vec3.len(axis);
var cos = (rot[0] + rot[4] + rot[8] - 1.0) * 0.5;

var angle;
angle = Math.atan2(sin,cos);
angle = isNaN(angle) ? 0.0 : angle;

if (axis !== undefined) {
var rotAxis = this.rotationAxis(sinceFrame);
angle *= vec3.dot(rotAxis, vec3.normalize(vec3.create(), axis));
angle *= vec3.dot(sin, vec3.normalize(vec3.create(), axis));
}

return angle;
Expand All @@ -1854,6 +1865,9 @@ Frame.prototype.rotationAngle = function(sinceFrame, axis) {
* the current frame and the specified frame.
*
* The returned direction vector is normalized.
*
* In the case of a complete reversal of direction (180 deg / PI rad)
* this method will return an undefined axis.
*
* The Leap derives frame rotation from the relative change in position and
* orientation of all objects detected in the field of view.
Expand All @@ -1869,10 +1883,14 @@ Frame.prototype.rotationAngle = function(sinceFrame, axis) {
*/
Frame.prototype.rotationAxis = function(sinceFrame) {
if (!this.valid || !sinceFrame.valid) return vec3.create();

var rotation = Leap.mat3.create();
Leap.mat3.multiply(rotation, this._rotation, sinceFrame._rotation);

return vec3.normalize(vec3.create(), [
this._rotation[7] - sinceFrame._rotation[5],
this._rotation[2] - sinceFrame._rotation[6],
this._rotation[3] - sinceFrame._rotation[1]
rotation[7] - rotation[5],
rotation[2] - rotation[6],
rotation[3] - rotation[1]
]);
}

Expand Down Expand Up @@ -2754,15 +2772,29 @@ Hand.prototype.rotationAngle = function(sinceFrame, axis) {
var sinceHand = sinceFrame.hand(this.id);
if(!sinceHand.valid) return 0.0;
var rot = this.rotationMatrix(sinceFrame);
var cs = (rot[0] + rot[4] + rot[8] - 1.0)*0.5
var angle = Math.acos(cs);
angle = isNaN(angle) ? 0.0 : angle;

var axis = [
rot[7] - rot[5],
rot[2] - rot[6],
rot[3] - rot[1]
];

var sin = Leap.vec3.len(axis);
var cos = (rot[0] + rot[4] + rot[8] - 1.0) * 0.5;

var angle;
if (-1e-7 < sin && sin < 1e-7) { // small values of sin
angle = 0;
} else {
angle = Math.atan2(sin,cos);
angle = isNaN(angle) ? 0.0 : angle;
}

if (axis !== undefined) {
var rotAxis = this.rotationAxis(sinceFrame);
angle *= vec3.dot(rotAxis, vec3.normalize(vec3.create(), axis));
angle *= vec3.dot(sin, vec3.normalize(vec3.create(), axis));
}
return angle;
}
};

/**
* The axis of rotation derived from the change in orientation of this hand, and
Expand All @@ -2783,12 +2815,16 @@ Hand.prototype.rotationAxis = function(sinceFrame) {
if (!this.valid || !sinceFrame.valid) return vec3.create();
var sinceHand = sinceFrame.hand(this.id);
if (!sinceHand.valid) return vec3.create();

var rotation = Leap.mat3.create();
Leap.mat3.multiply(rotation, this._rotation, sinceHand._rotation);

return vec3.normalize(vec3.create(), [
this._rotation[7] - sinceHand._rotation[5],
this._rotation[2] - sinceHand._rotation[6],
this._rotation[3] - sinceHand._rotation[1]
rotation[7] - rotation[5],
rotation[2] - rotation[6],
rotation[3] - rotation[1]
]);
}
};

/**
* The transform matrix expressing the rotation derived from the change in
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6 changes: 3 additions & 3 deletions leap-0.6.3.min.js
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32 changes: 25 additions & 7 deletions lib/frame.js
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Original file line number Diff line number Diff line change
Expand Up @@ -318,14 +318,25 @@ Frame.prototype.hand = function(id) {
Frame.prototype.rotationAngle = function(sinceFrame, axis) {
if (!this.valid || !sinceFrame.valid) return 0.0;

// A derivation of the following can be found here:
// http://en.wikipedia.org/wiki/Axis–angle_representation
var rot = this.rotationMatrix(sinceFrame);
var cs = (rot[0] + rot[4] + rot[8] - 1.0)*0.5;
var angle = Math.acos(cs);

var axis = [
rot[7] - rot[5],
rot[2] - rot[6],
rot[3] - rot[1]
];

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A reasonably clear derivation can be found here: http://en.wikipedia.org/wiki/Axis–angle_representation#Exponential_map_from_so.283.29_to_SO.283.29

Also see the log map section.

var sin = Leap.vec3.len(axis);
var cos = (rot[0] + rot[4] + rot[8] - 1.0) * 0.5;

var angle;
angle = Math.atan2(sin,cos);
angle = isNaN(angle) ? 0.0 : angle;

if (axis !== undefined) {
var rotAxis = this.rotationAxis(sinceFrame);
angle *= vec3.dot(rotAxis, vec3.normalize(vec3.create(), axis));
angle *= vec3.dot(sin, vec3.normalize(vec3.create(), axis));
}

return angle;
Expand All @@ -336,6 +347,9 @@ Frame.prototype.rotationAngle = function(sinceFrame, axis) {
* the current frame and the specified frame.
*
* The returned direction vector is normalized.
*
* In the case of a complete reversal of direction (180 deg / PI rad)
* this method will return an undefined axis.
*
* The Leap derives frame rotation from the relative change in position and
* orientation of all objects detected in the field of view.
Expand All @@ -351,10 +365,14 @@ Frame.prototype.rotationAngle = function(sinceFrame, axis) {
*/
Frame.prototype.rotationAxis = function(sinceFrame) {
if (!this.valid || !sinceFrame.valid) return vec3.create();

var rotation = Leap.mat3.create();
Leap.mat3.multiply(rotation, this._rotation, sinceFrame._rotation);

return vec3.normalize(vec3.create(), [
this._rotation[7] - sinceFrame._rotation[5],
this._rotation[2] - sinceFrame._rotation[6],
this._rotation[3] - sinceFrame._rotation[1]
rotation[7] - rotation[5],
rotation[2] - rotation[6],
rotation[3] - rotation[1]
]);
}

Expand Down
38 changes: 28 additions & 10 deletions lib/hand.js
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Original file line number Diff line number Diff line change
Expand Up @@ -246,15 +246,29 @@ Hand.prototype.rotationAngle = function(sinceFrame, axis) {
var sinceHand = sinceFrame.hand(this.id);
if(!sinceHand.valid) return 0.0;
var rot = this.rotationMatrix(sinceFrame);
var cs = (rot[0] + rot[4] + rot[8] - 1.0)*0.5
var angle = Math.acos(cs);
angle = isNaN(angle) ? 0.0 : angle;

var axis = [
rot[7] - rot[5],
rot[2] - rot[6],
rot[3] - rot[1]
];

var sin = Leap.vec3.len(axis);
var cos = (rot[0] + rot[4] + rot[8] - 1.0) * 0.5;

var angle;
if (-1e-7 < sin && sin < 1e-7) { // small values of sin
angle = 0;
} else {
angle = Math.atan2(sin,cos);
angle = isNaN(angle) ? 0.0 : angle;
}

if (axis !== undefined) {
var rotAxis = this.rotationAxis(sinceFrame);
angle *= vec3.dot(rotAxis, vec3.normalize(vec3.create(), axis));
angle *= vec3.dot(sin, vec3.normalize(vec3.create(), axis));
}
return angle;
}
};

/**
* The axis of rotation derived from the change in orientation of this hand, and
Expand All @@ -275,12 +289,16 @@ Hand.prototype.rotationAxis = function(sinceFrame) {
if (!this.valid || !sinceFrame.valid) return vec3.create();
var sinceHand = sinceFrame.hand(this.id);
if (!sinceHand.valid) return vec3.create();

var rotation = Leap.mat3.create();
Leap.mat3.multiply(rotation, this._rotation, sinceHand._rotation);

return vec3.normalize(vec3.create(), [
this._rotation[7] - sinceHand._rotation[5],
this._rotation[2] - sinceHand._rotation[6],
this._rotation[3] - sinceHand._rotation[1]
rotation[7] - rotation[5],
rotation[2] - rotation[6],
rotation[3] - rotation[1]
]);
}
};

/**
* The transform matrix expressing the rotation derived from the change in
Expand Down