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2 changes: 1 addition & 1 deletion nanover-server-py
Submodule nanover-server-py updated 134 files
20 changes: 10 additions & 10 deletions source/concepts/applications.rst
Original file line number Diff line number Diff line change
Expand Up @@ -202,26 +202,26 @@ Then the position :math:`\mathbf{C}_p` of each user's suggested origin is:

.. math::

\begin{align}
\begin{aligned}
\mathbf{C}_p &= \begin{bmatrix}
r\cos{\theta_p}\\
0\\
r\sin{\theta_p}\\
\end{bmatrix}
\end{align}
\end{aligned}

And the rotation :math:`\mathbf{R}_p` is expressed as a quaternion, defined as:

.. math::

\begin{align}
\begin{aligned}
\mathbf{R}_p &= \begin{bmatrix}
0\\
\sin{\frac{1}{2} \big(-\theta_p - \frac{2\pi}{N}\big)}\\
0\\
\cos{\frac{1}{2} \big(-\theta_p - \frac{2\pi}{N}\big)}\\
\end{bmatrix}
\end{align}
\end{aligned}

----

Expand Down Expand Up @@ -763,10 +763,10 @@ The Gaussian force is defined by:

.. math::

\begin{align}
\begin{aligned}
\mathbf{F}_{\text{COM}}^{\text{Gaussian}} &= -\frac{\mathbf{d}}{\sigma^2}\exp{-\frac{| \mathbf{d} | ^2}{2\sigma^2}} \\
E_{\text{COM}}^{\text{Gaussian}} &= - \exp{-\frac{| \mathbf{d} |^2}{2\sigma^2}}
\end{align}
\end{aligned}

with :math:`\sigma = 1`. With this force, the user interaction is stronger when
applied close to the particles.
Expand All @@ -775,18 +775,18 @@ The harmonic force is defined by:

.. math::

\begin{align}
\begin{aligned}
\mathbf{F}_{\text{COM}}^{\text{Harmonic}} &= -k \mathbf{d} \\
E_{\text{COM}}^{\text{Harmonic}} &= \frac{1}{2}k| \mathbf{d} |^2
\end{align}
\end{aligned}

with :math:`k = 2`.

The constant force is defined by:

.. math::

\begin{align}
\begin{aligned}
\mathbf{F}_{\text{COM}}^{\text{Constant}} &=
\begin{cases}
(0, 0, 0),& \text{if } | \mathbf{d} | = 0 \\
Expand All @@ -797,7 +797,7 @@ The constant force is defined by:
0,& \text{if } | \mathbf{d} | = 0 \\
1,& \text{otherwise}
\end{cases}
\end{align}
\end{aligned}

The direction of the constant force is undefined when the origin of the
interaction and the center of mass of the selection overlap, so the force is
Expand Down
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