diff --git a/nanover-server-py b/nanover-server-py index fe4995e..75478fb 160000 --- a/nanover-server-py +++ b/nanover-server-py @@ -1 +1 @@ -Subproject commit fe4995e8dcd71e5cb2b191b514aadb48b6d8c906 +Subproject commit 75478fbc1881e2e4a9122499872a2baed1b2ca51 diff --git a/source/concepts/applications.rst b/source/concepts/applications.rst index cfb6614..e3c2a66 100644 --- a/source/concepts/applications.rst +++ b/source/concepts/applications.rst @@ -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} ---- @@ -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. @@ -775,10 +775,10 @@ 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`. @@ -786,7 +786,7 @@ 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 \\ @@ -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