From 781cb0eef7c65a2a45dfd3b8e5eed7c932cd9751 Mon Sep 17 00:00:00 2001
From: rockfool <rockfool10@gmail.com>
Date: Mon, 16 Sep 2019 13:46:51 -0400
Subject: [PATCH] documentation issues fixed

---
 docs/source/methods/geometry.rst | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/docs/source/methods/geometry.rst b/docs/source/methods/geometry.rst
index d0d556f17..ca45e035d 100644
--- a/docs/source/methods/geometry.rst
+++ b/docs/source/methods/geometry.rst
@@ -920,11 +920,11 @@ as follows,
 .. math::
     : label: white-reflection-pdf
     
-    f(\mu, \phi) = frac{\miu}{\pi} d\miu d\phi = 2\mu d\mu frac{d\phi}{2\pi}
+    f(\mu, \phi) = frac{\mu}{\pi} d\mu d\phi = 2\mu d\mu frac{d\phi}{2\pi}
     \mu \in [0, 1]
     \phi \in [0, 2\pi]
 
-where :math:`{mu = cos(\theta)}` is the cosine of the polar angle between reflected direction 
+where :math:`{\mu = cos(\theta)}` is the cosine of the polar angle between reflected direction 
 and the normal to the surface; and :math: `{\theta}` is the azimuthal angle. 
 Thus, the cosine of the polar angle can extracted like this,
 .. math::
@@ -933,29 +933,29 @@ Thus, the cosine of the polar angle can extracted like this,
    f(\mu)d\mu = 2\mu d\mu
 
 
-and the azimuthal angle is uniform in the range of 2*PI, 
+and the azimuthal angle is uniform, 
 .. math:: 
     : label: white-reflection-unifrm
     
     f(\phi) = frac{d\phi}{2\pi} 
 
-Then, the cosine can be obtained by analytical inversion of cumulative density distribution (cdf)
+Then, the cosine can be sampled by analytical inversion of cumulative density distribution (cdf)
 like this, 
 .. math::
     : label: white-reflection-sqrt-prn
     
-    \mu = \sqrt{\eta_(1)} 
+    \mu = sqrt{\eta_(1)} 
     \phi = 2\pi \eta_(2) 
 
-where :math: `{\eta}` is the uniform random number, simply computed from random number generator. 
+where :math: `{\eta}` is the uniform random number, simply computed by random number generator. 
 Eventually, the final reflected direction vector can be computed via the rotation of normal to 
 the surface like this,
 .. math::
     : label: white-reflection-rotation
 
-    u^' = u \mu + frac{uw \sqrt{1-\mu^2} cos(\phi) - v \sqrt{1-\mu^2}sin(\phi)}{\sqrt{1-w^2}}
-    v^' = v \mu + frac{vw \sqrt{1-\mu^2} cos(phi) + u \sqrt{1-\mu^2} sin(phi)}{\sqrt{1-w^2}}
-    w^' = w \mu - \sqrt{1-w^2} \sqrt{1-\mu^2} cos(\phi)
+    u^' = u \mu + frac{uw sqrt{1-\mu^2} cos(\phi) - v sqrt{1-\mu^2}sin(\phi)}{sqrt{1-w^2}}
+    v^' = v \mu + frac{vw sqrt{1-\mu^2} cos(phi) + u sqrt{1-\mu^2} sin(phi)}{sqrt{1-w^2}}
+    w^' = w \mu - sqrt{1-w^2} sqrt{1-\mu^2} cos(\phi)
 
 The white reflection boundary can apply to any kind of surface, as long as the normal to the surface
 is known as mentioned above in :ref:`reflection`.