Notes:Inverse kinematics - Revision history

Frankiezafe: /* References */

2018-08-15T13:12:21Z

‎References

Frankiezafe: /* Selecting a point on the circle */

2018-04-23T08:14:41Z

‎Selecting a point on the circle

Frankiezafe: /* Projection of initial orientation */

2018-04-23T08:13:50Z

‎Projection of initial orientation

Frankiezafe: /* Projection of initial orientation */

2018-04-23T08:09:27Z

‎Projection of initial orientation

Frankiezafe: /* Selecting a point on the circle */

2018-04-23T07:57:31Z

‎Selecting a point on the circle

Frankiezafe: /* Bone's rotation */

2018-04-23T07:56:36Z

‎Bone's rotation

Frankiezafe: /* Selecting a point on the circle */

2018-04-23T07:55:23Z

‎Selecting a point on the circle

Frankiezafe: /* Selecting a point on the circle */

2018-04-23T07:54:41Z

‎Selecting a point on the circle

Frankiezafe: /* Selecting a point on the circle */

2018-04-23T07:50:14Z

‎Selecting a point on the circle

Frankiezafe: /* Bone's rotation */

2018-04-23T07:48:40Z

‎Bone's rotation

@@ Line 100: / Line 100: @@
 [[category:avatar]]
 [[category:threejs]]
-[[category:3d]]
+[[category:3D]]
 [[category:animation]]

@@ Line 64: / Line 64: @@
 </video></html>
-Computation of inverse kinematics of left and right legs.
+Computation of inverse kinematics on left and right legs.
 This method is not too bad, but only works if the orientation of the higher bone in the hierarchy is close to the world's orientation. Once this bone is not aligned anymore, the procedure fails to output valid results: the leg is twisted when the avatar is lying on the floor, for instance, and the arm kinetics are simply wrong.

@@ Line 70: / Line 70: @@
 == Projection of initial orientation ==
-The first version of the algorithm is not tacking into account the initial orientation of the origin bones (higher one in the hierarchy). The problem is solved in world space, independently of the orientation of the limb before the computation of the IK.
+The first version of the algorithm is not taking into account the initial orientation of the origin bones (higher one in the hierarchy). The problem is solved in world space, independently of the orientation of the limb before the computation of the IK.
 To solve this, we need a bit more complex projection of axis.
-Here above, we have compute:
+Here above, we have computed:
 # the radius of the circle;
@@ Line 81: / Line 81: @@
 # and the '''offset''' vector bringing us form the center to a specific point on its perimeter.
-The 3 first point are valid, but the last one is based on a world axis! We can based a final steps one the orientation of the plane, as it's give us 3 valid axis. 2 of them are coplanars, X and Y unit axis, and Z is representing the normal of the circle's plane. This last one is the only valid one (there's only one normal to a plane), X and Y have to be aligned with the origin ones.
+The 3 first point are valid, but the last one is based on world axis! We can based a fourth steps on the orientation of the plane, as it's give us 3 valid axis. 2 of them are coplanars to the circle's plane, X and Y unit axis, and Z is representing the normal<ref>Definition of normal vector on [http://mathworld.wolfram.com/NormalVector.html wolfram]</ref>. This last one is the only valid one (there's only one normal to a plane), X and Y must be re-aligned with the origin ones, without leaving the plane.
 To achieve this, we have to project one relevant axis onto the circle's plane.

@@ Line 70: / Line 70: @@
 == Projection of initial orientation ==
-Solving the rotation of the bones is trickier than it seems. This is due to the fact that the circle of sphere's intersection gives an infinity of valid positions. It is easy for a human to point the right position on this circle (the knee / elbow should be there). The second step of the algorithm has been to identify a good procedure to find a plausible point.
+The first version of the algorithm is not tacking into account the initial orientation of the origin bones (higher one in the hierarchy). The problem is solved in world space, independently of the orientation of the limb before the computation of the IK.
 == References ==

← Older revision		Revision as of 07:57, 23 April 2018
Line 58:		Line 58:

	[[File:Threejs-ik-end of the day.png\|400px]]		[[File:Threejs-ik-end of the day.png\|400px]]
		+
		+	<html><video width="400" height="400" controls>
		+	<source src="https://frankiezafe.org/images/b/b0/Ik_cropped0001-0629.ogv" type="video/mp4">
		+	Your browser does not support the video tag.
		+	</video></html>
		+
		+	Computation of inverse kinematics of left and right legs.

	This method is not too bad, but only works if the orientation of the higher bone in the hierarchy is close to the world's orientation. Once this bone is not aligned anymore, the procedure fails to output valid results: the leg is twisted when the avatar is lying on the floor, for instance, and the arm kinetics are simply wrong.		This method is not too bad, but only works if the orientation of the higher bone in the hierarchy is close to the world's orientation. Once this bone is not aligned anymore, the procedure fails to output valid results: the leg is twisted when the avatar is lying on the floor, for instance, and the arm kinetics are simply wrong.

@@ Line 61: / Line 61: @@
 This method is not too bad, but only works if the orientation of the higher bone in the hierarchy is close to the world's orientation. Once this bone is not aligned anymore, the procedure fails to output valid results: the leg is twisted when the avatar is lying on the floor, for instance, and the arm kinetics are simply wrong.
-== Bone's rotation ==
+== Projection of initial orientation ==
-−
-<html><video width="400" height="400" controls>
-  <source src="https://frankiezafe.org/images/b/b0/Ik_cropped0001-0629.ogv" type="video/mp4">
-  Your browser does not support the video tag.
-</video></html>
 Solving the rotation of the bones is trickier than it seems. This is due to the fact that the circle of sphere's intersection gives an infinity of valid positions. It is easy for a human to point the right position on this circle (the knee / elbow should be there). The second step of the algorithm has been to identify a good procedure to find a plausible point.

@@ Line 59: / Line 59: @@
 [[File:Threejs-ik-end of the day.png|400px]]
-This method is not too bad, but only works if the orientation of the higher bone in the hierarchy is close to the world's orientation. Once this bone is not aligned anymore, the procedure fails to output valid results: the leg is completely twisted when the avatar is lying on the floor, for instance, and the arm kinetics are completly wrong.
+This method is not too bad, but only works if the orientation of the higher bone in the hierarchy is close to the world's orientation. Once this bone is not aligned anymore, the procedure fails to output valid results: the leg is twisted when the avatar is lying on the floor, for instance, and the arm kinetics are simply wrong.
 == Bone's rotation ==