From ed2485de45a9f3be26156e2e8d82be2b472ff358 Mon Sep 17 00:00:00 2001
From: bobarna <barnabas.borcsok@gmail.com>
Date: Wed, 9 Dec 2020 00:43:10 +0100
Subject: [PATCH] working on PBD section

---
 docs/documentation.aux |  43 +++--
 docs/documentation.bbl |  28 +++-
 docs/documentation.blg |  70 ++++----
 docs/documentation.log | 371 ++++++++++++++++++++++++++---------------
 docs/documentation.out |  25 ++-
 docs/documentation.pdf | Bin 437482 -> 476184 bytes
 docs/documentation.tex | 140 ++++++++++++----
 docs/references.bib    |   7 +
 8 files changed, 470 insertions(+), 214 deletions(-)

diff --git a/docs/documentation.aux b/docs/documentation.aux
index 914bbb8..0aaf0d2 100644
--- a/docs/documentation.aux
+++ b/docs/documentation.aux
@@ -19,11 +19,11 @@
 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The achieved visual look\relax }}{1}{figure.caption.1}\protected@file@percent }
 \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
 \newlabel{fig:teaser}{{1}{1}{The achieved visual look\relax }{figure.caption.1}{}}
+\providecommand \oddpage@label [2]{}
 \@writefile{toc}{\contentsline {section}{Abstract}{1}{section*.2}\protected@file@percent }
 \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent }
 \citation{PixarPaper}
 \citation{PixarPaper}
-\citation{PixarPaper}
 \citation{MullerPBD}
 \citation{UmenhofferSimulation}
 \citation{MullerPBD}
@@ -33,25 +33,42 @@
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Mass Spring System}{2}{subsection.2.1}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Position Based Dynamics (PBD)}{2}{subsection.2.2}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Follow-the-Leader (FTL)}{2}{subsection.2.3}\protected@file@percent }
-\@writefile{toc}{\contentsline {section}{\numberline {3}Results}{2}{section.3}\protected@file@percent }
-\@writefile{toc}{\contentsline {section}{\numberline {4}Conclusion}{2}{section.4}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {3}Simulation of a Single Hair Strand}{2}{section.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}A Particle}{2}{subsection.3.1}\protected@file@percent }
+\citation{PixarVolumetricHair}
+\citation{FTLHair}
+\citation{RappRealTime}
+\citation{UmenhofferSimulation}
 \bibstyle{ACM-Reference-Format}
 \bibdata{references}
 \bibcite{PixarPaper}{{1}{2013}{{Iben et~al\mbox  {.}}}{{Iben, Meyer, Petrovic, Soares, Anderson, and Witkin}}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces pseudo code for the PBD simulation\relax }}{3}{algocf.1}\protected@file@percent }
+\newlabel{alg:pseudoPBD}{{1}{3}{A Particle}{algocf.1}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Putting Hair on the Head}{3}{section.4}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {5}Results}{3}{section.5}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion}{3}{section.6}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {7}Future Work}{3}{section.7}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Hair-hair collisions}{3}{subsection.7.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Refinement and proper customizability of the propagation of hair strands on the head object.}{3}{subsection.7.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Better customizability}{3}{subsection.7.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}Halton sequence for randomizing hair positions}{3}{subsection.7.4}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.5}Rendering}{3}{subsection.7.5}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.6}Moving to the GPU}{3}{subsection.7.6}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{Acknowledgments}{3}{section*.8}\protected@file@percent }
 \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}}}
+\bibcite{PixarVolumetricHair}{{4}{2006}{{Petrovic et~al\mbox  {.}}}{{Petrovic, Henne, and Pixar}}}
+\bibcite{RappRealTime}{{5}{2014}{{Rapp}}{{Rapp}}}
+\bibcite{UmenhofferSimulation}{{6}{2016}{{Umenhoffer et~al\mbox  {.}}}{{Umenhoffer, Marschal, and Suti}}}
 \newlabel{tocindent-1}{0pt}
 \newlabel{tocindent0}{0pt}
 \newlabel{tocindent1}{6.95pt}
 \newlabel{tocindent2}{13.79999pt}
 \newlabel{tocindent3}{0pt}
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-\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}OBJ Reader}{3}{subsection.A.1}\protected@file@percent }
-\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Supported OBJ Data Types\relax }}{3}{table.caption.10}\protected@file@percent }
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-\newlabel{TotPages}{{3}{3}{}{page.3}{}}
+\@writefile{toc}{\contentsline {section}{References}{4}{section*.10}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {A}Supplementary development}{4}{appendix.A}\protected@file@percent }
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+\newlabel{tab:objdatatypes}{{1}{4}{Supported OBJ Data Types\relax }{table.caption.11}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Recording the simulation on-the-fly}{4}{subsection.A.2}\protected@file@percent }
+\newlabel{TotPages}{{4}{4}{}{page.4}{}}
diff --git a/docs/documentation.bbl b/docs/documentation.bbl
index ed7f9c6..63a24cf 100644
--- a/docs/documentation.bbl
+++ b/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}{4}
+\begin{thebibliography}{6}
 
 %%% ====================================================================
 %%% NOTE TO THE USER: you can override these defaults by providing
@@ -91,6 +91,32 @@
 \showDOI{\tempurl}
 
 
+\bibitem[\protect\citeauthoryear{Petrovic, Henne, and Pixar}{Petrovic
+  et~al\mbox{.}}{2006}]%
+        {PixarVolumetricHair}
+\bibfield{author}{\bibinfo{person}{L. Petrovic}, \bibinfo{person}{M. Henne},
+  {and} \bibinfo{person}{John~Anderson Pixar}.}
+  \bibinfo{year}{2006}\natexlab{}.
+\newblock \showarticletitle{Volumetric Methods for Simulation and Rendering of
+  Hair}.
+\newblock
+\urldef\tempurl%
+\url{https://graphics.pixar.com/library/Hair/paper.pdf}
+\showURL{%
+\tempurl}
+
+
+\bibitem[\protect\citeauthoryear{Rapp}{Rapp}{2014}]%
+        {RappRealTime}
+\bibfield{author}{\bibinfo{person}{M. Rapp}.} \bibinfo{year}{2014}\natexlab{}.
+\newblock \showarticletitle{Real-Time Hair Rendering}.
+\newblock
+\urldef\tempurl%
+\url{http://markusrapp.de/wordpress/wp-content/uploads/hair/MarkusRapp-MasterThesis-RealTimeHairRendering.pdf}
+\showURL{%
+\tempurl}
+
+
 \bibitem[\protect\citeauthoryear{Umenhoffer, Marschal, and Suti}{Umenhoffer
   et~al\mbox{.}}{2016}]%
         {UmenhofferSimulation}
diff --git a/docs/documentation.blg b/docs/documentation.blg
index d1cf04e..c9b4b63 100644
--- a/docs/documentation.blg
+++ b/docs/documentation.blg
@@ -13,49 +13,57 @@ Reallocated glb_str_end (elt_size=4) to 20 items from 10.
 Reallocated singl_function (elt_size=4) to 100 items from 50.
 Warning--empty booktitle in FTLHair
 Warning--no number and no volume in FTLHair
+Warning--empty booktitle in PixarVolumetricHair
+Warning--empty publisher in PixarVolumetricHair
+Warning--empty address in PixarVolumetricHair
+Warning--page numbers missing in both pages and numpages fields in PixarVolumetricHair
+Warning--empty booktitle in RappRealTime
+Warning--empty publisher in RappRealTime
+Warning--empty address in RappRealTime
+Warning--page numbers missing in both pages and numpages fields in RappRealTime
 Warning--empty booktitle in UmenhofferSimulation
 Warning--empty publisher in UmenhofferSimulation
 Warning--empty address in UmenhofferSimulation
 Warning--page numbers missing in both pages and numpages fields in UmenhofferSimulation
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diff --git a/docs/documentation.log b/docs/documentation.log
index e287b3a..14924fa 100644
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+\BOOKMARK [2][-]{subsection.7.5}{\376\377\0007\000.\0005\000\040\000R\000e\000n\000d\000e\000r\000i\000n\000g}{section.7}% 17
+\BOOKMARK [2][-]{subsection.7.6}{\376\377\0007\000.\0006\000\040\000M\000o\000v\000i\000n\000g\000\040\000t\000o\000\040\000t\000h\000e\000\040\000G\000P\000U}{section.7}% 18
+\BOOKMARK [1][-]{section*.8}{\376\377\000A\000c\000k\000n\000o\000w\000l\000e\000d\000g\000m\000e\000n\000t\000s}{}% 19
+\BOOKMARK [1][-]{section*.10}{\376\377\000R\000e\000f\000e\000r\000e\000n\000c\000e\000s}{}% 20
+\BOOKMARK [1][-]{appendix.A}{\376\377\000A\000\040\000S\000u\000p\000p\000l\000e\000m\000e\000n\000t\000a\000r\000y\000\040\000d\000e\000v\000e\000l\000o\000p\000m\000e\000n\000t}{}% 21
+\BOOKMARK [2][-]{subsection.A.1}{\376\377\000A\000.\0001\000\040\000O\000B\000J\000\040\000R\000e\000a\000d\000e\000r}{appendix.A}% 22
+\BOOKMARK [2][-]{subsection.A.2}{\376\377\000A\000.\0002\000\040\000R\000e\000c\000o\000r\000d\000i\000n\000g\000\040\000t\000h\000e\000\040\000s\000i\000m\000u\000l\000a\000t\000i\000o\000n\000\040\000o\000n\000-\000t\000h\000e\000-\000f\000l\000y}{appendix.A}% 23
diff --git a/docs/documentation.pdf b/docs/documentation.pdf
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diff --git a/docs/documentation.tex b/docs/documentation.tex
index 7e137e7..1077027 100644
--- a/docs/documentation.tex
+++ b/docs/documentation.tex
@@ -17,6 +17,8 @@
 \newcommand{\specialcell}[2][t]{%
   \begin{tabular}[#1]{@{}l@{}}#2\end{tabular}}
 
+\usepackage[]{algorithm2e}
+\usepackage{algorithmic}
 
 %% end of the preamble, start of the body of the document source.
 \begin{document}
@@ -141,22 +143,18 @@ movie Brave.
 This approach models the hair as a chain of particles with given mass, each
 connected via springs. This results in a mass-spring system, which is then
 modelled by considering well-known physics formula's such as Newton's second law
-of motion (``$F=m*a$'', and Hooke's Law, which states that the force ($F$)
-needed to extend or compress a spring by some distance ($x$) scales linearly with
+of motion $F=m*a$, and Hooke's Law, which states that the force $F$
+needed to extend or compress a spring by some distance $x$ scales linearly with
 respect to that distance. The paper by \citet{PixarPaper} created an elaborate
 system of springs, with additional core springs making the simulation stable
 and resulting in the desired look and feel.
 
-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. 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)}
 
 The paper by \citet{MullerPBD} presents an approach that omits the velocity as
@@ -182,7 +180,7 @@ 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
+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
@@ -205,7 +203,64 @@ 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{Simulation of a Single Hair Strand}
+
+\subsection{A Particle}
+
+We model an $S$ hair strand as a chain of $P$ particles and a set of $C$
+constraints. Each particle $p \in [1,\ldots,N]$ has three atributes: mass ($m_p$), position
+($\boldsymbol{x_p}$) and velocity ($\boldsymbol{v_p}$). 
+
+A constraint $c \in [1,\ldots,C]$ with cardinality $n_c$ is a function $C_c
+: \mathbb{R} ^{3n_c} \mapsto \mathbb{R}$. It operates on a set of indices $\{i_1,\ldots
+i_{n_c}\}, i_k \in [1,...,P]$. The constraint funtion also has a stiffnes
+parameter $k_c \in [0...1]$ and a type of either \emph{equality} or
+\emph{inequality}.
+
+Constraint $c$ with type \emph{equality} is satisfied if
+$C_c(\boldsymbol{x}_{p_1},\ldots, \boldsymbol{x}_{p_{n_j}})=0$. If its type is
+\emph{inequality}, then it is satisfied if $C_c(\boldsymbol{x}_{p_1}, \ldots,
+\boldsymbol{x}_{p_{n_c}}) \geq 0$. The stiffness parameter $k_c$ defines the
+strength of the constraint in a range from zero to one.
+
+Given these notations, the algorithm works in the following way:
+
+\begin{algorithm}
+    \caption{pseudo code for the PBD simulation}
+    \label{alg:pseudoPBD}
+    \begin{algorithmic}
+        \IF {$i \geq maxval$}
+            \STATE asd
+        \ENDIF
+    \end{algorithmic}
+\end{algorithm}
+
+\begin{verbatim}
+    class Particle {
+        vec3 pos;
+        vec3 tmp;
+        float w;
+        vec3 v;
+        vec3 color;
+    }
+\end{verbatim}
+
+\section{Putting Hair on the Head}
+
+
+
 \section{Results}
+The implementation is available at \url{git.sch.bme.hu/bobarna/brave-2}. The
+program is able to handle up to around 500 individual hair strands, each
+consisting of around 30 particles in real time. With the implemented OBJ reader,
+it is possible to achieve diverse visual results in no time. The 
+
+An example result shown in figure \TODO{include figure}, and can be seen in the
+supplementary videos \TODO{Google Drive (?) link with the videos}.
+
+An 8-minute-video was made to supplement this writing. It is accessible at
+\TODO{link to 8-minute video}
 
 \section{Conclusion}
 After investigating and trying out multiple methods to simulate hair, we arrived
@@ -213,34 +268,60 @@ 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.
+surpassed when adding around a thousand strands each with more than 30
+particles.
 
-\section{Further Work}
+\section{Future 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.
 
-\begin{itemize}
-    \item Hair-hair collisions
-        \begin{itemize} 
-            \item As it is computationally extensive to simulate each particle
-                colliding with all of the other particles, a particle density
-                field could be used. One such method of grouping hair particles
-                and their corresponding velocities into a 3D voxel grid is
-                outlined in the \cite{PixarVolumetricHair} paper, which was also
-                utilized in the \citet{FTLHair} paper for handling hair-hair
-                collisions.
-        \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}
+\subsection{Hair-hair collisions}
+As it is computationally extensive to simulate each particle colliding with all
+of the other particles, a particle density field could be used. One such method
+of grouping hair particles and their corresponding velocities into a 3D voxel
+grid is outlined in the \citet{PixarVolumetricHair} paper, which was also
+utilized in the \citet{FTLHair} paper for handling hair-hair collisions.
+
+\subsection{Refinement and proper customizability of the propagation of hair
+strands on the head object.} 
+A drawable texture map is considered for the ability to tell the simulation
+where to put the hair strands on the surface of the head.
+
+\subsection{Better customizability}
+In the current implementation there is no way to properly customize the look and
+feel of the hair without accessing the source code. A possible improvement could
+be to read material and texture data for the hair from the OBJ file. Another
+huge improvement could be to set the constraints in real time, giving the user
+much better control of the hair. Other properties, such as length of the hair
+segments and color of the hair could be set as well.
+
+\subsection{Halton sequence for randomizing hair positions}
+In the current implementation, a standard C++ random number generator is
+utilized. Utilizing a low-discrepancy number sequence for randomizing hair
+strand positions would be an improvement.
+
+\subsection{Rendering}
+This semester left no time to try out different methods for rendering and
+visualizing the hair. The current implementation connects the individual
+particles with GL\_LINES, resulting in a sub-optimal visual experience. Offline
+(e.g. ray-tracing) methods could utilize the current simulation method. 
+The paper by \citet{RappRealTime} discusses the real-time aspect of hair
+rendering in great detail, supplemented with a broad discussion on different
+parts of the (OpenGL) rendering pipeline that could be utilized.
+
+\subsection{Moving to the GPU}
+The current implementation runs solely on the CPU. A big leap forward would be
+the utilization of the GPU. Compute shaders for computations are considered. The
+paper by \citet{UmenhofferSimulation} discusses a parametrization of the
+different constraint solves, although as they work on the same dataset, some
+computation problems are present during the parellelization of the
+problem.
+
+Tesselation and geometry shaders could be utilized for the rendering and display
+of the particles, resulting in a far better image with the same simulation
+method and properties.
 
 %%
 %% The acknowledgments section is defined using the "acks" environment
@@ -345,7 +426,6 @@ all the rendered frames. This script uses the free and open-sorce ffmpeg command
 line utility\footnote{\url{https://ffmpeg.org/}}
 
 
-
 \end{document}
 \endinput
 %%
diff --git a/docs/references.bib b/docs/references.bib
index 1a7a180..120581b 100644
--- a/docs/references.bib
+++ b/docs/references.bib
@@ -63,3 +63,10 @@ url = {https://matthias-research.github.io/pages/publications/FTLHairFur.pdf}
   url = {https://graphics.pixar.com/library/Hair/paper.pdf}
 
 }
+
+@inproceedings{RappRealTime,
+  title={Real-Time Hair Rendering},
+  author={M. Rapp},
+  year={2014},
+  url={http://markusrapp.de/wordpress/wp-content/uploads/hair/MarkusRapp-MasterThesis-RealTimeHairRendering.pdf}
+}
-- 
GitLab