spellcheck

docs/documentation.tex

@@ -132,12 +132,12 @@ graphics, it came naturally to choose a subject in this area. As I had little
  hands-on experience in this field, a long time had to be dedicated
 to research and trying out different simulation methods.
 
-The first of this paper reflects this, giving an overview of considered methods,
-and other possible routes that could have been taken to implement hair
+The first part of this paper reflects this, giving an overview of considered
+methods, and other possible routes that could have been taken to implement hair
 simulation.
 
 
-The implementation and all of the code mentioned is avaiable at
+The implementation and all of the code mentioned is available at
 \url{http://git.sch.bme.hu/bobarna/brave-2}.
 
 \section{Overview of considered methods}
@@ -154,7 +154,7 @@ 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
+modeled 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
 respect to that distance. The paper by \citet{PixarPaper} created an elaborate
@@ -192,7 +192,7 @@ 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 by \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
@@ -221,12 +221,12 @@ implementation to eliminate the stretching in the presence of greater forces.
 \subsection{Algorithm Overview}
 \label{section:algorithmOverview}
 We model an $S$ hair strand as a chain of $N$ particles and a set of $M$
-constraints. Each particle $p \in [1,\ldots,N]$ has three atributes: mass ($m_p$), position
+constraints. Each particle $p \in [1,\ldots,N]$ has three attributes: mass ($m_p$), position
 ($\boldsymbol{x_p}$) and velocity ($\boldsymbol{v_p}$). 
 
 A constraint $c \in [1,\ldots,M]$ with cardinality $n_c$ is a function $C_c
 : \mathbb{R} ^{3n_c} \mapsto \mathbb{R}$. It operates on a set of indices $\{i_1,\ldots
-i_{n_c}\}, i_k \in [1,...,N]$. The constraint funtion also has a stiffnes
+i_{n_c}\}, i_k \in [1,...,N]$. The constraint function also has a stiffness
 parameter $k_c \in [0...1]$ and a type of either \emph{equality} or
 \emph{inequality}.
 
@@ -301,7 +301,7 @@ Euler integration step. In line \lineRefSingle{16} the iterative solver manipula
 these temporary position estimates such that they satisfy the constraints. It
 does this by repeatedly projecting each constraint in an iterative manner to
 similar to that of a Gauss-Seidel
-\footnote{url{https://en.wikipedia.org/wiki/Gauss\%E2\%80\%93Seidel\_method}}
+\footnote{\url{https://en.wikipedia.org/wiki/Gauss\%E2\%80\%93Seidel\_method}}
 solver \emph{(see section \ref{sec:solver})}. Once the solver finishes with the
 iterations, in lines \lineRef{19}{20} each particle is moved to the calculated
 (once temporary) positions, and the velocity of each particle is updated
@@ -313,7 +313,7 @@ Velocities are manipulated in lines \lineRefSingle{6}, \lineRefSingle{8} and
 Line \lineRefSingle{6} allows to account for external forces
 in the simulation if some of the forces cannot be converted to positional
 constraints. \emph{(For example the pulling force between subsequent particles
-are modelled as distance constraints instead of external forces, and so are the
+are modeled as distance constraints instead of external forces, and so are the
 forces generated by the particles colliding with other objects.)} We use it to
 add gravity, and to generate wind effects for demonstration purposes. If only
 the gravitational force is present, then the line becomes $\b{p_v} \gets \b{p_v}
@@ -327,10 +327,10 @@ between $98\%$ to $99.9\%$ seemed to be a good enough solution.
 
 The initial constraints $C_1, \ldots, C_M$ are fixed throughout the simulation.
 In addition to these initial constraints, line \lineRefSingle{13} generates additional
-$M_{coll}$ collisition constrants. These change from time step to time step. The
+$M_{coll}$ collision constraints. These change from time step to time step. The
 projection step in line \lineRefSingle{16} considers both the fixed and the
 collision constraints. Our implementation does not yet utilize this opportunity
-to dynamicaly generate collision constraints. This is one of the possible future
+to dynamically generate collision constraints. This is one of the possible future
 works outlined in the subsection \nameref{subsec:future_work_collision}.
 
 \subsection{The Solver}
@@ -351,7 +351,7 @@ method: we repeatedly iterate through all the constraints and project the
 particles to valid locations with respect to the given constraint alone.
 Modifications to point locations immediately get visible to the process. This
 speeds up convergence significantly, because pressure waves can propagate
-throught the chain of particles in a single solver step, and effect which is
+throughout the chain of particles in a single solver step, and effect which is
 dependent on the order in which constraints are solved. 
 
 In our hair simulation case, we solve the distance constraints by putting the
@@ -366,10 +366,10 @@ Section \ref{section:DistanceConstraint} \nameref{section:DistanceConstraint}.
 
 There are several ways of incorporating the stiffness parameter. The simplest
 -- and the way we chose to utilize -- is simply multiplying the $\Delta \b{p}$
-correction by the $k \in [0 \ldots 1]$ stiffness paramter. For multiple
+correction by the $k \in [0 \ldots 1]$ stiffness parameter. For multiple
 iteration loops of the solver, the effect of $k$ becomes non-linear. The
-reamining error after $n_s$ solver iterations is $\Delta \b{p}(1-k)^{n_s}$.
-\citet{MullerPBD} proposes to multiply the corrections not by $k$ directly, but
+remaining error after $n_s$ solver iterations is $\Delta \b{p}(1-k)^{n_s}$.
+\citet{MullerPBD} propose to multiply the corrections not by $k$ directly, but
 by $k' = 1 - (1-k)^{1/n_s}$. With this transformation, the error becomes $\Delta
 \b{p}(1-k')^{n_s} = \Delta\b{p}(1-k)$, and thus linearly dependent on $k$ and
 independent of $n_s$. The resulting stiffness is still dependent on the time
@@ -455,7 +455,7 @@ straight forward: we move both by $\b{p_1}$ and $\b{p_2}$ by $\Delta \b{p_1}$ an
 $\Delta \b{p_2}$ respectively.
 
 \subsection{Bending Constraint} \label{section:bendingConstraint}
-\citet{UmenhofferSimulation} uses the PBD technique to simulate cloth materials.
+\citet{UmenhofferSimulation} use the PBD technique to simulate cloth materials.
 They utilize the bending constraint to define the bending resistance of the
 material, giving it an extra stiffness. Their goal with the Bending Constraint
 is to keep an initial angle between adjacent triangles formed by particles. They
@@ -523,12 +523,12 @@ into the specifics we settled on for our hair simulation.
 
 The code is available at \url{http://git.sch.bme.hu/bobarna/brave-2}.
 
-\subsection{Datastructures}
+\subsection{Data Structures}
 
 The properties of particles introduced in chapter
-\ref{section:algorithmOverview}
-\nameref{section:algorithmOverview} got an additional color property. This is
-decision was made so hair with a gradient color could be simulated.
+\ref{section:algorithmOverview} \nameref{section:algorithmOverview} got an
+additional color property. This decision was made so hair with a gradient color
+could be simulated.
 
 \begin{verbatim}
     class Particle {
@@ -548,13 +548,13 @@ performance of operations and function calls.
 \subsection{Constraints}
 A \texttt{Constraint} class with an abstract \texttt{solve()} method was
 implemented, storing each derived constraint class \emph{(e.g.
-PositionConstraint, BendingConstraint)} in a heterogen
+PositionConstraint, BendingConstraint)} in a heterogeneous
 collection and calling each overriden \texttt{solve()} method when projecting
 the constraints in the iteration loop (line \lineRefSingle{16} of Algorithm
 \ref{alg:pbd}).
 
 This implementation proved to be not fast enough, lagging even with low particle
-counts. We could not discover the cause of this increased computing time, and
+counts. We could not discover the cause of this increased computational time, and
 decided to settle on another solution. Instead of the above mentioned, we
 store only the parameters that constraints operate on, and the simulation calls
 the relevant solve functions with these stored parameters.
@@ -596,7 +596,7 @@ 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
+strands in real time, although the limit of the real-time method can easily be
 surpassed when adding around a thousand strands each with more than 30
 particles.
 
@@ -609,10 +609,10 @@ desired aspects of the simulation.
 
 \subsection{Hair-hair Collisions}
 \label{subsec:future_work_collision}
-As it is computationally extensive to simulate each particle colliding with all
+As it is computationally expensive 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
+grid is outlined in the paper by \citet{PixarVolumetricHair}, which was also
 utilized in the \citet{FTLHair} paper for handling hair-hair collisions.
 Such a method could be used to dynamically generate collision constraints in
 line \lineRefSingle{13} of Algorithm~\ref{alg:pbd}.
@@ -704,11 +704,11 @@ asd
 \label{section:appendixOBJ}
 
 An OBJ reader utility was implemented as part of the project. As the OBJ file
-format \footnote{\url{http://paulbourke.net/dataformats/obj/}} describes a wide range
-of properties for objects, our OBJ reader handles only the subset of
-these description options -- those that are needed for the project. Not
-supported line types were simply ignored, still resulting in
-a successful file read if possible.
+format \footnote{\url{http://paulbourke.net/dataformats/obj/}} describes a wide
+range of properties for objects, our OBJ reader handles only the subset of these
+description options -- those that are needed for the project. Unsupported line
+types were simply ignored, still resulting in a successful file read if
+possible.
 
 \begin{table}[htb]
     \caption{Supported OBJ Data Types} 
@@ -760,7 +760,7 @@ face definitions of the above format.}}
 \subsection{Recording the simulation on-the-fly}
 A recording utility was made to work in tandem with the application. In essence,
 the rendered images are written into \texttt{bmp} or \texttt{png} files if the
-capturing is on. In the
+capturing is enabled. In the
 implementation\footnote{\url{https://git.sch.bme.hu/bobarna/brave-2}}, toggling
 the capturing is mapped to the \texttt{C} key.
 
@@ -777,7 +777,7 @@ the frame with left-padded zeroes.
 
 After the image files are written, the user can start the
 \texttt{make\_video.sh} script to assemble the \texttt{output.mp4} and delete
-all the rendered frames. This script uses the free and open-sorce ffmpeg command
+all the rendered frames. This script uses the free and open-source ffmpeg command
 line utility\footnote{\url{https://ffmpeg.org/}}
 
 

docs/spellcheck.sh

+#!/usr/bin/sh
+hunspell -d en_US -l documentation.tex