Signed angle between fingers and palm

[henryjoe]

I want to control a servo with the angle between pointable.direction and palm normal.
This doesn't work:

  var angleIndex = Math.acos(Leap.vec3.dot(hand.palmNormal, index.direction));

because I get an unsigned angle, which goes from positive to zero when finger and palm normal are parallel, but starts to increase in the positive when the finger gets closer to the palm.

Any suggestion on how to compute the sign?
Is there a better way than using pointable.direction and hand.palmNormal?

I believe that what had been said in older posts on the intrinsic problems of getting the signed angle between vectors doesn't apply to palm and fingers, but I may be wrong...

henry

[Joe_Ward]

You should be able to use the cross product here. The angle returned follows the right hand rule so as the index finger moves from pointing straight out, down toward the normal, the (index.direction ⊗ palmNormal) vector will point toward the pinky. Once the index passes the normal, (index.direction ⊗ palmNormal) will flip and point towards the thumb.

You can take the dot product of (index,direction ⊗ palmNormal) and (hand.direction ⊗ hand.palmNormal) to determine which way the vector is pointing. If the value is positive, then the two cross product vectors are pointing the same way; if negative, they are pointing in opposite directions.

[Joe_Ward]

Here's an example I wrote in Java that computes the angle between the metacarpal bone and the distal phalanx. The zero angle is straight ahead. Negative angles (0 to -180) are down towards the palm. If you bend you fingers upward or go past -180, you get to positive numbers again.

You can use the palm normal instead of the metacarpal direction, of course.

float fingerCurl(Finger finger){
  //Angle between metacarpal and distal phalange bones
  Vector metacarpalDirection = finger.bone(Bone.Type.TYPE_INTERMEDIATE).basis().getZBasis().opposite();
  Vector distalPhalangeDirection = finger.bone(Bone.Type.TYPE_DISTAL).basis().getZBasis().opposite(); 
  float rawangle = metacarpalDirection.angleTo(distalPhalangeDirection) * 180/PI;

  //Find sign
  Vector crossBones = metacarpalDirection.cross(distalPhalangeDirection);
  Vector boneXBasis = finger.bone(Bone.Type.TYPE_METACARPAL).basis().getXBasis();
  if(finger.hand().isLeft()) boneXBasis = boneXBasis.opposite(); //Left hand uses a left-hand basis
  int sign = (crossBones.dot(boneXBasis) >= 0) ? 1 : -1;
  return sign * rawangle;  
}

The Java and JavaScript APIs are a bit different, but it shouldn't be too hard to translate.

[henryjoe]

Thaks Joe, the dot of the two cross, and the introduction of hand.direction fixed the problem.
For those who need, follows a quick and suboptimal test code (note: Vector.js taken from https://github.com/deckar01/LeapJS, but the vector lib included in LM is equivalent):

var fings = [0,0,0,0,0];
function leapFrame(frame){
  var hand = frame.hands[0];
  var pointables = frame.pointables;
  if (hand && pointables.length > 0 && hand.confidence > .5) {
    for (var f in pointables) {
      var i = pointables[f].type;
      fings[i] = pointables[f];

      var b = new Vector(fings[i].direction);
      var pn = new Vector(hand.palmNormal);
      var hd = new Vector(hand.direction);
      var angle = pn.angleTo(b);

      var dotcross = (b.cross(pn)).dot(hd.cross(pn));
      var signed = angle * (dotcross>=0 ?1 :-1);

      if (i == 0) { // thumb
        var thumbAngleV = hd.angleTo(b);
        var thumbAngleH = pn.angleTo(b);
        console.log('thumb V-H: " + thumbAngleV + '-' + thumbAngleH );
      } else {
        console.log('finger ' + i + ': ' + signed);
      }
    }    
  }
}

[edwon]

Anybody have a version of this for C# in Unity? I'm trying to get an accurate "finger curl" measurement for each finger.

Tried converting the java to C# but I'm tripping up on the .opposite endings. Are they just flipping the sign?

[edwon]

Actually I'd really prefer just a per finger 0-1 curl variable from the api, that would be super helpful. But some code I can put into a function would be super useful as well.

[Joe_Ward]

Tried converting the java to C# but I'm tripping up on the .opposite endings. Are they just flipping the sign?

Yes. Java doesn't support operator overloading, so a function is required to negate the vector. In C# you can just use the "-" operator:

Vector thisWay = new Vector(1, 1, 1);
Vector thatWay = -thisWay; // (-1, -1, -1)

[edwon]

Ok cool, I ended up implementing a different solution by getting the distance of the tip of the finger from the palm plane. It actually works pretty well for triggering things by just moving one finger a bit. This is the code for anyone who might find it useful.

    // CHECK IF PRESSING
    // calculate distance to palm

    float distanceFromPalmNormal = LeapUtil.DistanceFromPalmNormal(b3PosWorld,hand,uiControl.handController);

    if (distanceFromPalmNormal > maxDistance)
    {
      pressing = true;
    } else {
      pressing = false;
    }

public static float DistanceFromPalmNormal(Vector3 position, Hand hand, HandController handController)
{
	// get palm position and normal
	Leap.Vector palmNorm = hand.PalmNormal;

    // note LeapUtil.LeapToWorld functions are just using ToUnity or ToUnityScaled per the documentation

	Vector3 palmNormWorld = LeapUtil.LeapToWorldRot(palmNorm, handController);
	Leap.Vector palmPos = hand.PalmPosition;
	Vector3 palmPosWorld = LeapUtil.LeapToWorldPos(palmPos, handController);

	// project to figure out the distance along the normal
	Vector3 vector = position - palmPosWorld;
	Vector3 projection = Vector3.Project(vector, palmNormWorld);
	float distance = projection.sqrMagnitude;
}

[mryosoo]

Hi everyone, can someone translate this code in python? i am having trouble with the syntax and declarations. Any help will be appreciated.

[Joe_Ward]

Line-by-line, Python to C# translation is primarily a matter of removing the type declarations and changing the member capitalization. However, the code above is from a Unity project and uses functions that are defined in scripts included only in the Unity assets, not the SDK. Thus you would also need to translate the LeapUtil functions in addition to the code above.

[mryosoo]

oh, i see. I will try to do what i can and do some experiments. Anyway thanks for the answering.

[farami]

hi can anyone share the code how to get the angle of finger between fingers and palm? thank you