Describe algorithm in whitepaper

GodotXRIKRig/addons/godot-xr-ik-rig/scenes/PlayerIKRig.gd

@@ -11,8 +11,21 @@ onready var skel = $Character/Rig/Skeleton
 func _ready():
 	var idx_upperarm_l = skel.find_bone("upperarm.l")
 	var idx_lowerarm_l = skel.find_bone("lowerarm.l")
-	skel.set_bone_pose(idx_upperarm_l,Transform.IDENTITY.rotated(Vector3.FORWARD,PI/4))
-	skel.set_bone_pose(idx_lowerarm_l,Transform.IDENTITY.rotated(Vector3.FORWARD,PI/4))
+	var idx_upperarm_r = skel.find_bone("upperarm.r")
+	var idx_lowerarm_r = skel.find_bone("lowerarm.r")
+
+	var T_UpperArmDown = Transform.IDENTITY.rotated(Vector3.RIGHT,-PI/3)
+	var Tl_Elbow90 = Transform.IDENTITY.rotated(Vector3.BACK,-PI/2)
+	var Tr_Elbow90 = Transform.IDENTITY.rotated(Vector3.BACK,PI/2)
+
+	var T_ZminusPI4 = Transform.IDENTITY.rotated(Vector3.FORWARD,PI/4)
+	var T_ZplusPI4 = Transform.IDENTITY.rotated(Vector3.BACK,PI/4)
+	var T_YminusPI2 = Transform.IDENTITY.rotated(Vector3.UP,-PI/2)
+	skel.set_bone_pose(idx_upperarm_l,T_UpperArmDown)
+	skel.set_bone_pose(idx_upperarm_r,T_UpperArmDown)
+
+	skel.set_bone_pose(idx_lowerarm_l,Tl_Elbow90)
+	skel.set_bone_pose(idx_lowerarm_r,Tr_Elbow90)
 
 
 # Called every frame. 'delta' is the elapsed time since the previous frame.

GodotXRIKRig/docs/ik_arm.drawio.png.import

@@ -0,0 +1,30 @@
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GodotXRIKRig/docs/whitepaper.md

@@ -0,0 +1,37 @@
+# How the inverse kinematics is calculated
+
+
+
+The concept uses the following assumptions:
+  * The degrees-of-freedom are limited to 
+    * Shoulder joint with 3dof and restrictive joint limits
+    * The elbow with only 1dof
+    * The wrist with 3dof and restrictive joint limits
+  * for humans, within the reachable elbow positions, some areas are more likely to be used due to less muscle strain
+
+## Proposal 1 for am pose estimate
+
+Input:
+  * controller position
+  * shoulder position estimate
+
+Output:
+  * Elbow position
+  * Shoulder backslash (required to improve shoulder position estimate)
+
+### Step 1: Initial elbow position estimate
+
+We try to get a first good estimate using a very simple method: given 
+  * a vector *SpineShoulder*, going from the spine at approx. breast-hight to the shoulder position, and
+  * a vector *ShoulderWrist*, going from the shoulder to the wrist position, which can be easily inferred from the controller position,
+  * calculate the cross-product like this for the **right shoulder**:
+  ```var elbow_dir = SpineShoulder.cross(ShoulderWrist)```.
+
+### Step 2: Consider controller orientation
+
+
+### Step 3: Consider shoulder orientation
+
+
+### Step 4: Determine shoulder backslash for shoulder position estimation
+