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					@ -35,27 +35,27 @@ Ever been jump-scared by this sight in an FPS? Why are things rendered like that
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In order to display a scene (like a murder scene), 
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					In order to display a scene (like a murder scene), 
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we need to have a way of **representing** the **surface** of the composing objects (like corpses) in computer-memory.
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					we need to have a way of **representing** the **surface** of the composing objects (like corpses) in computer memory.
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We only care about the **surface** since we won't be seeing the insides anyways---Not that we want to.
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					We only care about the **surface** since we won't be seeing the insides anyway---Not that we want to.
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At this stage, we only care about the **shape** or the **geometry** of the **surface**.
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					At this stage, we only care about the **shape** or the **geometry** of the **surface**.
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Texturing, lighting and all the sweet gory details comes at a much later stage once all the **geometry** have been processed.
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					Texturing, lighting, and all the sweet gory details come at a much later stage once all the **geometry** has been processed.
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But how do we represent surfaces in computer-memory?
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					But how do we represent surfaces in computer memory?
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## Vertices
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					## Vertices
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There are several ways to **represent** the surfaces of 3d objects for a computer to understand.
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					There are several ways to **represent** the surfaces of 3d objects for a computer to understand.
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For instance, **NURB surfaces** are great for representing **curves**
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					For instance, **NURB surfaces** are great for representing **curves**, and it's all about the
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and it's all about the **high-precision** needed to do **CAD**.
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					**high precision** needed to do **CAD**. We could also do **ray-tracing** using fancy equations for
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We could also do **ray-tracing** using fancy equations for rendering **photo-realistic** images.
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					rendering **photo-realistic** images.
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These are all great--ignoring the fact that they would take an eternity to process...
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					These are all great--ignoring the fact that they would take an eternity to process...
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But what we need is a **performant** approach that can do this for an entire scene with
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					But what we need is a **performant** approach that can do this for an entire scene with
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hundereds of thousands of objects (like a lot of corpses) in under a small fraction of a second. What we need is **polygonal modeling**.
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					hundreds of thousands of objects (like a lot of corpses) in under a small fraction of a second. What we need is **polygonal modeling**.
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**Polygonal modeling** enables us to do an exciting thing called **real-time rendering**. The idea is that we only need an
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					**Polygonal modeling** enables us to do an exciting thing called **real-time rendering**. The idea is that we only need an
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**approximation** of a surface to render it **realisticly-enough** for us to have some fun killing time!
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					**approximation** of a surface to render it **realistically enough** for us to have some fun killing time!
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We can achieve this approximation using a collection of **triangles**, **lines** and **dots** (primitives),
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					We can achieve this approximation using a collection of **triangles**, **lines**, and **dots** (primitives),
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which themselves are composed of a series of **vertices** (points in space).
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					which themselves are composed of a series of **vertices** (points in space).
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<Image 
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					<Image 
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					@ -63,20 +63,19 @@ which themselves are composed of a series of **vertices** (points in space).
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/> 
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					/> 
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A **vertex** is simply a point in space.
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					A **vertex** is simply a point in space.
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Once we get enough of these **points**, we can conncet them to form **primitives** such as **triangles**, **lines** and **dots**.
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					Once we get enough of these **points**, we can connect them to form **primitives** such as **triangles**, **lines**, and **dots**.
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And once we connect enough of these **primitives** together, they form a **model** or a **mesh** (that we need for our corpse).
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					And once we connect enough of these **primitives** together, they form a **model** or a **mesh** (that we need for our corpse).
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With some interesting models put together, we can compose a **scene** (like a murder scene :D).
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					With some interesting models put together, we can compose a **scene** (like a murder scene :D).
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<Image 
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					<Image 
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    paths={["/images/bunny.png"]} 
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					    paths={["/images/bunny.jpg"]} 
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/> 
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					/> 
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But let's not get ahead of ourselves. The primary type of **primitive** that we care about during **polygonal modeling**
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					But let's not get ahead of ourselves. The primary type of **primitive** that we care about during **polygonal modeling**
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is a **triangle**. But why not squares or polygons with variable number of edges?
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					is a **triangle**. But why not squares or polygons with a variable number of edges?
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## Why Triangles?
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					## Why Triangles?
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In **Euclidean geometry**, triangles are always **planar** (they exist only in one plane), 
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					In **Euclidean geometry**, triangles are always **planar** (they exist only in one plane), 
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any polygon composed of more than 3 points may break this rule, but why does polygons residing in one plane so important 
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					any polygon composed of more than 3 points may break this rule, but why does polygons residing in one plane so important 
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to us?
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					to us?
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					@ -86,28 +85,26 @@ to us?
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/> 
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					/> 
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When a polygon exists only in one plane, we can safely imply that **only one face** of it can be visible
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					When a polygon exists only in one plane, we can safely imply that **only one face** of it can be visible
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at any one time, this enables us to utilize a huge optimization technique called **back-face culling**.
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					at any one time; this enables us to utilize a huge optimization technique called **back-face culling**.
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Which means we avoid wasting a ton of **precious processing time** on the polygons that 
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					Which means we avoid wasting a ton of **precious processing time** on the polygons that 
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we know won't be visible to us. We can safely **cull** the **back-faces** since we won't
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					we know won't be visible to us. We can safely **cull** the **back-faces** since we won't
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be seeing the **back** of a polygon when it's in the context of a closed off model. 
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					be seeing the **back** of a polygon when it's in the context of a closed-off model. 
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We figure this by simply using the **winding-order** of the triangle to determine whether we're looking at the
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					We figure this out by simply using the **winding order** of the triangle to determine whether we're looking at the
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back of the triangle or the front of it.
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					back of the triangle or the front of it.
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Normal surface
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					Normal surface
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					Triangles also have a very small **memory footprint**; for instance, when using the **triangle-strip** topology (more on this very soon), for each additional triangle after the first one, only **one extra vertex** is needed.
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Triangles also have very small **memory footprint**, for instance when using the **triangle-strip** topology (more on this very soon), for each additional triangle after the first one, only **one extra vertex** is needed.
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					The most important attribute, in my opinion, is the **algorithmic simplicity**.
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					Any polygon or shape can be composed from a **set of triangles**; for instance, a rectangle is 
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					simply **two coplanar triangles**.
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The most important attribute however (in my opinion) is the **algorithmic simplicity**.
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					Also, it is becoming a common practice in computer science to break down
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Any polygon or shape can be composed from a **set of triangle**, for instance a rectangle is 
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simply **two co-planar triangles**.
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It is becoming an increasingly more common practice in computer science to break down
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hard problems into simpler, smaller problems. This will be more convincing when we cover the **rasterization** stage :)
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					hard problems into simpler, smaller problems. This will be more convincing when we cover the **rasterization** stage :)
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Bonus point: present day **hardwares** and **algorithms** have become **extremely efficient** at processing 
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					Bonus point: present-day **hardware** and **algorithms** have become **extremely efficient** at processing 
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triangles (sorting, rendering, etc) after eons of evolving around them.
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					triangles (sorting, rendering, etc) after eons of evolving around them.
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