[Bf-docboard-svn] bf-manual: [7341] trunk/blender_docs/manual: Added Advanced/Appendices with Rotation Modes chapter
Pep
noreply at blender.org
Fri Nov 6 14:40:57 CET 2020
Revision: 7341
https://developer.blender.org/rBM7341
Author: pepribal
Date: 2020-11-06 14:40:56 +0100 (Fri, 06 Nov 2020)
Log Message:
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Added Advanced/Appendices with Rotation Modes chapter
Modified Paths:
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trunk/blender_docs/manual/advanced/index.rst
trunk/blender_docs/manual/scene_layout/object/properties/transforms.rst
Added Paths:
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trunk/blender_docs/manual/advanced/appendices/
trunk/blender_docs/manual/advanced/appendices/index.rst
trunk/blender_docs/manual/advanced/appendices/rotations.rst
Added: trunk/blender_docs/manual/advanced/appendices/index.rst
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+
+############
+ Appendices
+############
+
+This chapter covers far more detailed explanations about some Blender tools (which may not be required for typical usage).
+
+.. toctree::
+ :maxdepth: 1
+
+ rotations.rst
+
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Added: trunk/blender_docs/manual/advanced/appendices/rotations.rst
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--- trunk/blender_docs/manual/advanced/appendices/rotations.rst (rev 0)
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+
+**************
+Rotation Modes
+**************
+
+Blender lets you define rotations in several ways. Each one of them has a series of advantages and drawbacks;
+there is no best rotation mode, as each one is suitable for specific cases.
+
+In all of these modes, positive angle values mean counter clockwise rotation direction,
+while negative values define clockwise rotation.
+
+Though you can rotate elements using the global or local transform orientations, these axes are not suitable
+to define rotations, as the effect of each of them cannot be isolated from the other two.
+
+Take, for instance, any 3 values for X, Y and Z rotation. Perform each one of these using global or local axes.
+Depending on the order in which you perform these, you will end up with different final orientations.
+So proper rotation coordinate systems are needed.
+
+Euler modes
+===========
+
+The axes system used for performing Euler rotations is the so called Euler gimbal.
+A gimbal is a particular set of 3 axes.
+The special thing about this is that the axes have a hierarchical relationship between them:
+one of the axes is at the top of the hierarchy, and has one of the other two axes as its immediate child;
+at the same time, this child axis is the parent of the remaining axis, the one at the very bottom of the hierarchy.
+
+Which axis is on top, which one in the middle and which at the bottom, depends on the particular Euler gimbal:
+there are 6 types of them, as there are 6 possible combinations: XYZ, XZY, YXZ, YZX, ZXY and ZYX Euler rotation modes.
+These modes are named using the letters of the axes in order, starting from the axis at the bottom of the hierarchy,
+and finishing with the one on top.
+
+The main problem of these systems comes when they lose their relative perpendicularity.
+And this happens when the axis in the middle rotates, causing the axis at the bottom to rotate with it.
+It keeps getting worse when this bottom axis approaches 90° (or equivalent angles).
+In that case, it will remain aligned with the axis on top of the hierarchy.
+In that very moment we have just lost one axis of rotation.
+This can cause very weird interpolations when animating. This particular loss of axis is known as the **gimbal lock**.
+
+.. hint::
+
+ The actual configuration of the gimbal axes can be seen in the 3D Viewport by enabling the *Rotate* object gizmo
+ and setting it to *Gimbal* (from the gizmos button in the header).
+ At the same time, rotation mode should be set to any of the Euler modes for the active object.
+
+ Now you can perform a rotation around the axis in the middle (e.g. in *XYZ Euler* mode that's the Y axis),
+ and see how easy it is to end up having a gimbal with just two axes.
+ In the specific case of the *XYZ Euler* mode with gimbal lock, a rotation around the X axis will have the same
+ effect as rotating around the Z axis, meaning, in practice, that no X axis rotations can be performed.
+
+One advantage of this mode is that animation curves are easy to understand and edit.
+However, special attention must be done when the middle axis approaches values close to 90° (or equivalent angles).
+
+Axis Angle mode
+===============
+
+This mode lets us define an axis (X, Y, Z) and a rotation angle (W) around that axis.
+
+If we define the rotation using interactive rotations (with the rotation gizmo), the values of X, Y and Z
+will not exceed 1.0 in absolute value, and W will be comprised between 0 and 180 degrees.
+
+If you wish to define rotations above 180º (e.g. to define multiple revolutions),
+you will need to edit the W value directly, but as soon as you perform an interactive rotation,
+that value will be adjusted again. Same thing goes for axis values.
+
+This system is suitable for elements revolving around a fixed axis, or to animate one of the elements at a time
+(either the axis or the angle).
+The problem might come when animating (interpolating) both components at the same time: axis and angle.
+The resulting effect might not be as expected.
+
+The *Gimbal* gizmo in this rotation mode shows a set of three orthogonal axes in which the Z axis goes
+along the defined rotation axis, i.e. it points towards the direction defined by the (X, Y, Z) point.
+
+The axis-angle system is free from gimbal lock, but animation curves in this mode are not intuitive at all
+when animating axis and angle at the same time, in which case they are difficult to understand and edit.
+
+Quaternion mode
+===============
+
+In this mode, rotations are also defined by 4 values (X, Y, Z and W). X, Y and Z also define an axis, and W an angle,
+but it does it quite differently from axis-angle. The important thing here is the relation between all four values.
+
+To describe it in an intuitive way, let's take the effect of the X coordinate: what it does is to rotate the element
+around the X axis up to 180 degrees. The same goes for Y and Z. The effect of W is to avoid those rotations and leave
+the element with zero rotation. The final orientation is a combination of these four effects.
+
+As the relation between components is what defines the final orientation, multiplying or dividing all four numbers
+by a constant value will yield the very same rotation.
+
+This mode is ideal for interpolating between **any** pair of orientations. It doesn't suffer from gimbal lock or any
+interpolation undesired effect. The only drawback is that you cannot interpolate between two orientations that are at
+a distance grater than than 180°, as the animation will take the shortest path between them.
+Thus to animate a revolving element you must set up many intermediate keyframes, 180º from each other at most.
+
+The *Gimbal* gizmo in this mode is equivalent to the *Local* one, and doesn't have any special meaning.
+
+The animation curves in this mode are not intuitive, so they are also difficult to understand and edit.
+
+More about quaternions
+----------------------
+
+This section is not really useful for 3D artists, but it can be suitable for the curious or the scientist.
+
+Quaternions are a number system extending the complex numbers. They represent a 4 component vector, whose
+components are called, in Blender, X, Y, Z and W.
+
+When rotating interactively in quaternion mode, the so called norm (length) of the quaternion will remain constant.
+
+.. note::
+
+ The norm of a quaternion q is defined mathematically as:
+
+ :math:`\lvert q \rvert = \sqrt{X^2 + Y^2 + Z^2 + W^2}`
+
+However, if one of the quaternion components is locked during the interactive transformation using the proper
+lock button, the norm will not remain unchanged, as that blocked component will not be able to adjust itself to
+keep the unit norm.
+
+.. hint::
+
+ Interactive rotations with the gizmo don't change the norm of the current quaternion.
+
+ Editing a single XYZW component individually you can change the norm.
+
+ To make the norm 1.0 again you can switch to any rotation mode and back again into quaternion.
+
+The rotation components of a quaternion keep a tight relation with those of axis-angle. To find a correspondence,
+first of all we must deal with the normalized version of the quaternion, that is, one whose norm equals 1.0.
+To normalize a quaternion, just divide each one of its components by its norm.
+As we have seen before, dividing all four values by the same number gives the same orientation.
+
+Once we have calculated the components of the normalized quaternion, the relation with the axis-angle components
+is as follows:
+
+* X, Y and Z mean exactly the same as in axis-angle: they just define an axis around which the rotation takes place.
+* W can be used to retrieve the actual rotation around the defined angle. The following formula applies:
+ :math:`W = \cos(\frac{a}{2})`, where *a* is actually the rotation angle we are looking for.
+
+Other considerations
+====================
+
+In axis-angle and quaternion modes we can lock rotations in interactive modes in a per component basis,
+instead of doing it by axis. To do so we can activate this locking ability using the lock buttons next to the
+corresponding *Rotation* transform buttons.
+
+Regarding rotation animations, all keyframes must be defined in the same rotation mode, which must be the
+selected rotation mode for the object throughout the entire animation.
Property changes on: trunk/blender_docs/manual/advanced/appendices/rotations.rst
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Added: svn:eol-style
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Modified: trunk/blender_docs/manual/advanced/index.rst
===================================================================
--- trunk/blender_docs/manual/advanced/index.rst 2020-11-06 10:12:26 UTC (rev 7340)
+++ trunk/blender_docs/manual/advanced/index.rst 2020-11-06 13:40:56 UTC (rev 7341)
@@ -16,3 +16,4 @@
limits.rst
operators.rst
blender_directory_layout.rst
+ appendices/index.rst
Modified: trunk/blender_docs/manual/scene_layout/object/properties/transforms.rst
===================================================================
--- trunk/blender_docs/manual/scene_layout/object/properties/transforms.rst 2020-11-06 10:12:26 UTC (rev 7340)
@@ Diff output truncated at 10240 characters. @@
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