fix: preserve authored casing in note suites

trees/ag-000I.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\card{Definition}{Signed distance function \citewiki{sdf}{Signed_distance_function}}{
+\card{Definition}{signed distance function \citewiki{sdf}{Signed_distance_function}}{
 
 \p{
 Let #{\Omega} be a subset of a [metric space](https://en.wikipedia.org/wiki/Metric_space) #{X} with metric #{d}, and #{\partial \Omega} be its boundary. The distance between a point #{\point{p}} of #{X} and the subset #{\partial \Omega} of #{X} is defined as usual as

trees/ag-000J.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\card{Convention}{Sign}{
+\card{Convention}{sign}{
 \p{Simply put, SDFs are the minimum possible distance from a point to an implicit surface defined by #{f(\point{p})=0}.}
 
 \p{The convention adopted in this note is that the #{+} and #{-} signs indicate whether the point is outside or inside the surface, respectively, so that when a ray marches towards the surface from the outside, the distance is positive, becomes smaller when approaching the surface.

trees/ag-000K.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere
 
-\refdeft{Implicit surface}{sec. 1}{hart1996sphere}{
+\refdeft{implicit surface}{sec. 1}{hart1996sphere}{
 \p{If an SDF #{f} is a continuous mapping, the subset #{\Omega}  can be implicitly described as the [locus](https://en.wikipedia.org/wiki/Locus_(mathematics)) of points
 
 ##{ \Omega = \{ p : f(p) \le 0 \} }

trees/ag-000R.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere
 
-\refdeft{Point-to-set distance}{def. 1}{hart1996sphere}{
+\refdeft{point-to-set distance}{def. 1}{hart1996sphere}{
 \p{
 The \newvocab{point-to-set distance} defines the distance from a point #{\point{x} \in \mathbb{R}^3} to a set #{A \subset \mathbb{R}^3} as the distance from #{x} to the closest point in #{A},
 

trees/ag-000S.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray
 
-\refdeft{Signed distance bound}{def. 2}{hart1996sphere}{
+\refdeft{signed distance bound}{def. 2}{hart1996sphere}{
 \p{
 A function #{f: \mathbb{R}^3 \rightarrow \mathbb{R}} is a \newvocab{signed distance bound} of its implicit surface #{f^{-1}(0)} if and only if
 

trees/ag-000V.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray
 
-\refdeft{Ray equation}{sec. 1.1 eq. 3}{gillespie2024ray}{
+\refdeft{ray equation}{sec. 1.1 eq. 3}{gillespie2024ray}{
 \p{
 A \vocab{ray} anchored at origin #{\boldsymbol{r}_o} in the direction of the unit vector #{\boldsymbol{r}_d} can be parametrically defined as a \newvocab{ray equation}
 

trees/ag-000W.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray
 
-\refdeft{Ray intersection}{sec. 1.1 eq. 4}{gillespie2024ray}{
+\refdeft{ray intersection}{sec. 1.1 eq. 4}{gillespie2024ray}{
 \p{Plugging the \vocab{ray equation} #{r: \mathbb{R} \rightarrow \mathbb{R}^n} into the function #{f: \mathbb{R}^n \rightarrow \mathbb{R}} that defines the implicit surface produces the composite real function #{F: \mathbb{R} \rightarrow \mathbb{R}} where #{F=f \circ \boldsymbol{r}} such that the \vocab{solution}s to
 
 ##{

trees/ag-000X.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\refdeft{Implicit surface}{sec. 1}{winchenbach2024lipschitz}{
+\refdeft{implicit surface}{sec. 1}{winchenbach2024lipschitz}{
 \p{Let #{\Omega} be a subset of a [topological space](https://en.wikipedia.org/wiki/Topological_space) #{X}, and #{\partial \Omega} be its [boundary](https://en.wikipedia.org/wiki/Boundary_(topology)).
 }
 

trees/ag-000Y.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Level set \citewiki{level-set}{https://en.wikipedia.org/wiki/Level_set}}{
+\card{Definition}{level set \citewiki{level-set}{https://en.wikipedia.org/wiki/Level_set}}{
 A \newvocab{level set} of a real-valued function #{f} (a.k.a. an iso-contour of a scalar field in 3D)
 
 ##{L_c(f)=\left\{\point{x} \mid \forall \point{x} \in X, f(\point{x})=c  \right\} }

trees/ag-0018.tree

@@ -26,7 +26,7 @@
 \def\eps{\varepsilon}
 \def\tmax{t_{\max}}
 
-\card{Algorithm}{Ray marching (naïve)}{
+\card{Algorithm}{ray marching (naïve)}{
 \minialg{
 % \begin{algorithm*}{Ray marching (naive)}{}
 \alg/input{$\ro \in \RR^3$, ray origin}

trees/ag-0019.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Example}{Ray marching (naïve)}{
+\card{Example}{ray marching (naïve)}{
 
 \p{The following renders a scene with a unit sphere at the origin, the camera at #{(0,0,8)} and looking at the origin, through a screen of height 1.0, centered at 5.0 from the camera.
 }

trees/ag-001A.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Ray}{
+\card{Definition}{ray}{
 \p{A \newvocab{ray} is a half-line that starts at a point and extends indefinitely in one direction.
 }
 

trees/ag-001B.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Ray marching (naïve)}{
+\card{Definition}{ray marching (naïve)}{
 \p{The \newvocab{ray marching (naïve)} algorithm is to march a ray by a \em{fixed step size}, check if a \vocab{ray intersection} occurs at each step, until the ray reaches a maximum distance or step count.
 }
 

trees/ag-001C.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Ray marching}{
+\card{Definition}{ray marching}{
 \p{To render a scene, the \newvocab{Ray marching} algorithm marches a ray from an origin towards a direction. At each step, the algorithm marches a short (possibly changing) distance and checks if a \vocab{ray intersection} occurs. This process continues until a \em{stopping condition} is met. The information obtained from the ray intersection is then used to determine the color of a pixel on the screen.
 }
 }

trees/ag-001D.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Example}{Ray-marching for different types of rays}{
+\card{Example}{ray-marching for different types of rays}{
 
 \p{A \vocab{view ray} has the origin at the camera, the direction is determined by the pixel on the screen that it passes through. It may intersect with a surface in the scene, and the information obtained from the intersection is used to determine the color of the corresponding pixel on the screen.}
 

trees/ag-001E.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Remark}{Ray-casting/ray-tracing/ray-marching}{
+\card{Remark}{ray-casting/ray-tracing/ray-marching}{
 \p{The \newvocab{ray-casting}/\newvocab{ray-tracing}/\newvocab{ray-marching} algorithms simply apply one of the multitude of root finding methods to solve the \vocab{ray intersection} equation.
 }
 

trees/ag-001I.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\refdeft{Sphere tracing}{sec. 2.3, eq. 12}{hart1996sphere}{
+\refdeft{sphere tracing}{sec. 2.3, eq. 12}{hart1996sphere}{
 \p{The \newvocab{sphere tracing} algorithm is to march a ray by an adaptive safe step size, which is the absolute value of the \vocab{signed distance bound} calculated by #{F/\lambda} per \ref{ag-000T}, the rest is the same as \vocabk{ray marching (naïve)}{ag-001B}.
 }
 

trees/ca-000P.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\note{basics: from groups to modules}{
+\note{Basics: from groups to modules}{
 \transclude{ca-000O}
 \transclude{ca-000Q}
 \transclude{ca-000R}

trees/ca-0013.tree

@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\note{algebras}{
+\note{Algebras}{
 \transclude{ca-0014}
 \transclude{ca-0015}
 \transclude{ca-0016}

trees/uts-000C.tree

@@ -21,15 +21,15 @@
 
 \put\transclude/numbered{false}
 
-\block{disclaimer}{
+\block{Disclaimer}{
   \p{This is a manual translation of a portion of \em{Chapitre 9 Formes sesquilinéaires et formes quadratiques} of Bourbaki's \em{Éléments de Mathématique} \citek{bourbaki2007algebra} from French to English.}
 
   \p{Such a translation is not available eleswhere, to the best of our knowledge. We claim no rights to the original text, and all mistakes in the translation are our own. The translation is for educational purposes only.}
 
   \p{So far, we have only translated the portion that is related to Clifford algebras, namely \em{§ 9. Clifford Algebra}. The translation is still in progress.}
 }
 
-\block{editorial remarks}{
+\block{Editorial remarks}{
   \p{We always keep the original notation, and the numbering of equations, definitions, propositions, sections etc.}
 
   \p{Equation labels are placed on the right side of the equations unlike the original text where they are placed on the left side.}