Thanks to visit codestin.com
Credit goes to github.com

Skip to content

Switch to a 3d rotation trackball implementation with path independence #29244

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Closed
wants to merge 1 commit into from
Closed

Switch to a 3d rotation trackball implementation with path independence #29244

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
45 changes: 24 additions & 21 deletions doc/api/toolkits/mplot3d/view_angles.rst
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -57,34 +57,33 @@ To keep it this way, set ``mouserotationstyle: azel``.
This approach works fine for spherical coordinate plots, where the *z* axis is special;
however, it leads to a kind of 'gimbal lock' when looking down the *z* axis:
the plot reacts differently to mouse movement, dependent on the particular
orientation at hand. Also, 'roll' cannot be controlled.
orientation at hand. Also, the 'roll' axis about the viewing direction cannot
be controlled.

As an alternative, there are various mouse rotation styles where the mouse
manipulates a virtual 'trackball'. In its simplest form (``mouserotationstyle: trackball``),
the trackball rotates around an in-plane axis perpendicular to the mouse motion
(it is as if there is a plate laying on the trackball; the plate itself is fixed
(it is as if there is a flat plate laying on a trackball; the plate itself is fixed
in orientation, but you can drag the plate with the mouse, thus rotating the ball).
This is more natural to work with than the ``azel`` style; however,
the plot cannot be easily rotated around the viewing direction - one has to
move the mouse in circles with a handedness opposite to the desired rotation,
counterintuitively.
This is more natural to work with than the ``azel`` style; however, it is
difficult and unintuitive to control roll with it.

A different variety of trackball rotates along the shortest arc on the virtual
sphere (``mouserotationstyle: sphere``). Rotating around the viewing direction
is straightforward with it: grab the ball near its edge instead of near the center.
sphere (``mouserotationstyle: sphere``). Rotating roll is straightforward with it:
grab the ball near its edge instead of near the center.

Ken Shoemake's ARCBALL [Shoemake1992]_ is also available (``mouserotationstyle: Shoemake``);
it resembles the ``sphere`` style, but is free of hysteresis,
i.e., returning mouse to the original position
returns the figure to its original orientation; the rotation is independent
of the details of the path the mouse took, which could be desirable.
However, Shoemake's arcball rotates at twice the angular rate of the
mouse movement (it is quite noticeable, especially when adjusting roll),
and it lacks an obvious mechanical equivalent; arguably, the path-independent
rotation is not natural (however convenient), it could take some getting used to.
So it is a trade-off.

Henriksen et al. [Henriksen2002]_ provide an overview. In summary:
it resembles the ``sphere`` style, but has the benefit of being free of hysteresis,
such that returning the mouse to the original position returns the figure to its
original orientation. This path independence of the rotation has the nice property
of being able to 'undo' an errant rotation. However, Shoemake's arcball rotates at
twice the angular rate of the mouse movement (noticeable especially when adjusting
roll), and it lacks an obvious mechanical equivalent; arguably, the path-independent
rotation is not natural and it could take some getting used to.
So there is a trade-off.

Henriksen et al. [Henriksen2002]_ and Shambaugh [Shambaugh2024]_ provide
overviews. In summary:

.. list-table::
:width: 100%
Expand All @@ -106,7 +105,7 @@ Henriksen et al. [Henriksen2002]_ provide an overview. In summary:
- ❌
- ✓ [6]_
- ✔️
- ❌
- ✔️
- ✔️
* - sphere
- ❌
Expand All @@ -127,7 +126,7 @@ Henriksen et al. [Henriksen2002]_ provide an overview. In summary:
.. [3] Figure reacts the same way to mouse movements, regardless of orientation (no difference between 'poles' and 'equator')
.. [4] Returning mouse to original position returns figure to original orientation (rotation is independent of the details of the path the mouse took)
.. [5] The style has a corresponding natural implementation as a mechanical device
.. [6] While it is possible to control roll with the ``trackball`` style, this is not immediately obvious (it requires moving the mouse in large circles) and a bit counterintuitive (the resulting roll is in the opposite direction)
.. [6] While it is possible to control roll with the ``trackball`` style, this is not immediately obvious (it requires chaining multiple rotations together)

You can try out one of the various mouse rotation styles using:

Expand Down Expand Up @@ -202,4 +201,8 @@ The border is a circular arc, wrapped around the arcball sphere cylindrically
and Computer Graphics, Volume 10, Issue 2, March-April 2004, pp. 206-216,
https://doi.org/10.1109/TVCG.2004.1260772 `[full-text]`__;

.. [Shambaugh2024] Scott Shambaugh, "Virtual Trackballs: An Interactive
Taxonomy", 11 November 2024,
https://theshamblog.com/virtual-trackballs-a-taxonomy/

__ https://www.researchgate.net/publication/8329656_Virtual_Trackballs_Revisited#fullTextFileContent
15 changes: 12 additions & 3 deletions lib/mpl_toolkits/mplot3d/axes3d.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1364,7 +1364,12 @@ def clear(self):
def _button_press(self, event):
if event.inaxes == self:
self.button_pressed = event.button
self._sx, self._sy = event.xdata, event.ydata
self._sx0, self._sy0 = event.xdata, event.ydata
self._sx, self._sy = self._sx0, self._sy0
q0 = _Quaternion.from_cardan_angles(
*np.deg2rad((self.elev, self.azim, self.roll)))
self._q0 = q0

toolbar = self.get_figure(root=True).canvas.toolbar
if toolbar and toolbar._nav_stack() is None:
toolbar.push_current()
Expand Down Expand Up @@ -1566,6 +1571,7 @@ def _on_move(self, event):
return

dx, dy = x - self._sx, y - self._sy
dx0, dy0 = x - self._sx0, y - self._sy0
w = self._pseudo_w
h = self._pseudo_h

Expand All @@ -1589,19 +1595,22 @@ def _on_move(self, event):
*np.deg2rad((self.elev, self.azim, self.roll)))

if style == 'trackball':
k = np.array([0, -dy/h, dx/w])
# To avoid precession, we need to rotate relative to the
# original orientation, not the current orientation.
k = np.array([0, -dy0/h, dx0/w])
nk = np.linalg.norm(k)
th = nk / mpl.rcParams['axes3d.trackballsize']
dq = _Quaternion(np.cos(th), k*np.sin(th)/nk)
q = dq * self._q0
else: # 'sphere', 'arcball'
current_vec = self._arcball(self._sx/w, self._sy/h)
new_vec = self._arcball(x/w, y/h)
if style == 'sphere':
dq = _Quaternion.rotate_from_to(current_vec, new_vec)
else: # 'arcball'
dq = _Quaternion(0, new_vec) * _Quaternion(0, -current_vec)
q = dq * q

q = dq * q
elev, azim, roll = np.rad2deg(q.as_cardan_angles())

# update view
Expand Down
Loading