further work section

docs/documentation.aux

@@ -24,25 +24,34 @@
 \citation{PixarPaper}
 \citation{PixarPaper}
 \citation{PixarPaper}
+\citation{MullerPBD}
 \citation{UmenhofferSimulation}
-\bibstyle{ACM-Reference-Format}
-\bibdata{references}
-\bibcite{PixarPaper}{{1}{2013}{{Iben et~al\mbox  {.}}}{{Iben, Meyer, Petrovic, Soares, Anderson, and Witkin}}}
-\bibcite{UmenhofferSimulation}{{2}{2016}{{Umenhoffer et~al\mbox  {.}}}{{Umenhoffer, Marschal, and Suti}}}
+\citation{MullerPBD}
+\citation{FTLHair}
+\citation{FTLHair}
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+\bibcite{MullerPBD}{{2}{2007}{{M\"{u}ller et~al\mbox  {.}}}{{M\"{u}ller, Heidelberger, Hennix, and Ratcliff}}}
+\bibcite{FTLHair}{{3}{2012}{{Müller et~al\mbox  {.}}}{{Müller, Kim, and Chentanez}}}
+\bibcite{UmenhofferSimulation}{{4}{2016}{{Umenhoffer et~al\mbox  {.}}}{{Umenhoffer, Marschal, and Suti}}}
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docs/documentation.bbl

@@ -2,7 +2,7 @@
 %%% Do NOT edit. File created by BibTeX with style
 %%% ACM-Reference-Format-Journals [18-Jan-2012].
 
-\begin{thebibliography}{2}
+\begin{thebibliography}{4}
 
 %%% ====================================================================
 %%% NOTE TO THE USER: you can override these defaults by providing
@@ -59,6 +59,38 @@
 \shownote{\url{http://graphics.pixar.com/library/CurlyHairB/paper.pdf}.}
 
 
+\bibitem[\protect\citeauthoryear{M\"{u}ller, Heidelberger, Hennix, and
+  Ratcliff}{M\"{u}ller et~al\mbox{.}}{2007}]%
+        {MullerPBD}
+\bibfield{author}{\bibinfo{person}{Matthias M\"{u}ller}, \bibinfo{person}{Bruno
+  Heidelberger}, \bibinfo{person}{Marcus Hennix}, {and} \bibinfo{person}{John
+  Ratcliff}.} \bibinfo{year}{2007}\natexlab{}.
+\newblock \showarticletitle{Position Based Dynamics}.
+\newblock \bibinfo{journal}{\emph{J. Vis. Comun. Image Represent.}}
+  \bibinfo{volume}{18}, \bibinfo{number}{2} (\bibinfo{date}{April}
+  \bibinfo{year}{2007}), \bibinfo{pages}{109–118}.
+\newblock
+\showISSN{1047-3203}
+\urldef\tempurl%
+\url{https://doi.org/10.1016/j.jvcir.2007.01.005}
+\showDOI{\tempurl}
+
+
+\bibitem[\protect\citeauthoryear{Müller, Kim, and Chentanez}{Müller
+  et~al\mbox{.}}{2012}]%
+        {FTLHair}
+\bibfield{author}{\bibinfo{person}{Matthias Müller}, \bibinfo{person}{Tae
+  Kim}, {and} \bibinfo{person}{Nuttapong Chentanez}.}
+  \bibinfo{year}{2012}\natexlab{}.
+\newblock \showarticletitle{Fast Simulation of Inextensible Hair and Fur}.
+\newblock \bibinfo{journal}{\emph{VRIPHYS 2012 - 9th Workshop on Virtual
+  Reality Interactions and Physical Simulations}}.
+\newblock
+\urldef\tempurl%
+\url{https://doi.org/10.2312/PE/vriphys/vriphys12/039-044}
+\showDOI{\tempurl}
+
+
 \bibitem[\protect\citeauthoryear{Umenhoffer, Marschal, and Suti}{Umenhoffer
   et~al\mbox{.}}{2016}]%
         {UmenhofferSimulation}

docs/documentation.blg

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docs/documentation.tex

@@ -151,17 +151,90 @@ The \citet{PixarPaper} paper also features great further readings in their
 citations, which gives a great glimpse into related previous works.
 
 The main characteristic of this approach is that a Mass Spring System deals with
-forces, and tries to stay true to the laws of physics. This will not be the case
+forces, and tries to stay true to the laws of physics. It accounts for internal 
+and external forces from which accelerations are computed based on Newton's 
+second law of motion. A time integration method is then used to update the
+velocities and finally the positions of the particles. This will not be the case
 with Position Based Dynamics.
 
 \subsection{Position Based Dynamics (PBD)}
-\citet{UmenhofferSimulation}
-Position Based Dynamics (PBD) 
 
+The paper by \citet{MullerPBD} presents an approach that omits the velocity as
+well as the force layer of the then-present popular approaches for simulation
+methods of dynamic systems in computer graphics.
+
+Position Based Dynamics (PBD) -- as its name suggests -- works with the position
+of particles. A big advantage of such a system lies in its controllability, and
+the easy reducability of overshooting problems present in force based systems.
+Another favorable aspect is that PBD methods are generally easier with the maths
+and somewhat easier to implement in terms of the needed mathematical and
+physical background needed to grasp its inner workings. In addition, -- as it
+works directly with the position of particles -- collision constraints can be
+handled easily and penetrations can be resolved completely by projecting points
+onto the penetrated surface. Although such measures can only be applied on the
+expanse of physical accuracy, position based dynamics being only a ``good
+enough'' approximation of how objects behave in real life.
+
+Chapter 2 of the paper by \citet{UmenhofferSimulation} builds on the
+\citet{MullerPBD} paper and gives a concise overview of the position based
+dynamics method, and goes on to show the type of constraints that can be applied
+to control to behaviour of such a system -- which is present in both papers.
+
+
+\subsection{Follow-the-Leader (FTL)}
+The Dynamic Follow-The-Leader (FTL) method outlined in \citet{FTLHair} focuses
+on the fast simulation of hair and fur on animated characters. The sheer number
+of computation needed for simulating thousands of hair strands, each consisting
+of numerous particles presents a big challenge. Also, as each strand is
+inextensible, it is not trivial to come up with an algorithm that does its job
+in feasible time. 
+
+As it will be covered later in this article, the already introduced PBD method
+needs multiple iterations per frame in order to keep the system from stretching
+and becoming unstable. The FTL method by \citet{FTLHair} presents a method that
+takes only a single iteration through the particles of each hair strand per
+frame to achieve the desired results.
+
+As this sounds fascinating, and cuts the computation time needed substantially,
+in the early stages of my project, I implemented the FTL method alongside PBD.
+It \textit{works}, and is fast, although due to the iteration count being one,
+when greater forces are being applied to the system, a substantial amount of
+stretching was introduced to the system. As it seemed in comparison that the
+``basic'' PBD method yielded the same -- or even more accurate -- results, and
+it was feasible to allow myself to use multiple iterations per frame, I did
+not further investigate if there could have been improvements made to my
+implementation to eliminate the stretching in the presence of greater forces.
+
+\section{Results}
+
+\section{Conclusion}
+After investigating and trying out multiple methods to simulate hair, we arrived
+at the Position Based Dynamics (PBD) method. An overview of the PBD method, and
+an introduction to the constraint types used in our implementation was given.
+An implementation was made in C++ and OpenGL, which easily simulates the hair
+strands in real time, although the limit of the real-time nature can easily be
+surpassed when adding thousands of strands with hundreds of particles.
+
+\section{Further Work}
+As this was part only of a semester-long Project Laboratory course, a great deal
+of time was dedicated in the early stages of the project to investigate and
+explore the subject area. This left only a sub-optimal time for implementing all
+desired aspects of the simulation.
 
-\subsection{Follow the Leader (FTL)}
-The Dynamic Follow-The-Leader method outlined in \TODO{reference article}
-
+\begin{itemize}
+    \item Hair-hair collisions
+        \begin{itemize}
+    \item 
+\end{itemize}
+    \item Refinement and proper customizability of the propagation of hair
+        strands on the Head Object. 
+        \begin{itemize}
+                \item A drawable texture map is considered for the ability to
+                    tell the simulation where to put the hair strands on the
+                    surface of the hair.
+        \end{itemize}
+    \item 
+\end{itemize}
 
 %%
 %% The acknowledgments section is defined using the "acks" environment

docs/references.bib

@@ -23,3 +23,43 @@ keywords = {mass-spring models, hair simulation},
 location = {Anaheim, California},
 series = {SCA '13}
 }
+
+@article{MullerPBD,
+author = {M\"{u}ller, Matthias and Heidelberger, Bruno and Hennix, Marcus and Ratcliff, John},
+title = {Position Based Dynamics},
+year = {2007},
+issue_date = {April, 2007},
+publisher = {Academic Press, Inc.},
+address = {USA},
+volume = {18},
+number = {2},
+issn = {1047-3203},
+url = {https://doi.org/10.1016/j.jvcir.2007.01.005},
+doi = {10.1016/j.jvcir.2007.01.005},
+abstract = {The most popular approaches for the simulation of dynamic systems in computer graphics are force based. Internal and external forces are accumulated from which accelerations are computed based on Newton's second law of motion. A time integration method is then used to update the velocities and finally the positions of the object. A few simulation methods (most rigid body simulators) use impulse based dynamics and directly manipulate velocities. In this paper we present an approach which omits the velocity layer as well and immediately works on the positions. The main advantage of a position based approach is its controllability. Overshooting problems of explicit integration schemes in force based systems can be avoided. In addition, collision constraints can be handled easily and penetrations can be resolved completely by projecting points to valid locations. We have used the approach to build a real time cloth simulator which is part of a physics software library for games. This application demonstrates the strengths and benefits of the method.},
+journal = {J. Vis. Comun. Image Represent.},
+month = apr,
+pages = {109–118},
+numpages = {10},
+keywords = {Physically based simulation, Cloth simulation, Integration schemes, Game physics}
+}
+
+@inproceedings{FTLHair,
+author = {Müller, Matthias and Kim, Tae and Chentanez, Nuttapong},
+year = {2012},
+month = {12},
+pages = {},
+title = {Fast Simulation of Inextensible Hair and Fur},
+journal = {VRIPHYS 2012 - 9th Workshop on Virtual Reality Interactions and
+    Physical Simulations},
+doi = {10.2312/PE/vriphys/vriphys12/039-044},
+url = {https://matthias-research.github.io/pages/publications/FTLHairFur.pdf}
+}
+
+@inproceedings{PixarVolumetricHair,
+  title={Volumetric Methods for Simulation and Rendering of Hair},
+  author={L. Petrovic and M. Henne and John Anderson Pixar},
+  year={2006},
+  url = {https://graphics.pixar.com/library/Hair/paper.pdf}
+
+}