Title: Theory / Unimportant / CS / Algo / Graphics / Fundamentals -Shirley Marschner{ / 10 Shading
Tags: récupéré MissingMedia examplesSwitchExample1 hasSeenConjDef

Smaller0: \(S\)'s color
Greater0: the cosine
Page: 234
Chapter: 10
Section: 1.1
Variables: \(S\) a surface
\(c\) a color
Name: Lambert's cosine law
Greater1: the angle between the surface normal
Connect Greater0: of

Name: Lambertian object
Definition: An object whose surface as the Lambert's property
Page: 233-234
Chapter: 10
Section: 1.0-1.1
Example: Matte object

Name: Matte surface
Definition: A surface whose color does not vary when the viewpoint vary
Page: 233
Chapter: 10
Section: 1

Name: Directional light
Definition: A light emitting ray in a single direction
Page: 234
Chapter: 10
Section: 1.1
Context: A light very far away from the source

Question: How to change the lightness of an object
Answer: Change light's intensity
Page: 234
Chapter: 10
Section: 1.1
Answer2: Change reflectance of the surface

Name: The diffuse reflectance
Definition: The fraction of light reflected by the surface.
Page: 234
Chapter: 10
Section: 1.1
Typ: An RGB color
Denoted by: \(c_r\)

Name: RGB intensity term
Page: 234
Chapter: 10
Section: 1.1
Notation: \(c_l\)
Typ: value in \([0,1]\)
Applied to3: A coefficient choosing the proportion of light reflected, independently of the color

Name: Two sided lightning
Definition: The color at \(c\) is [$]c_rc_l\abs{\mathbf{n\cdot l}}[/$]
Page: 234
Chapter: 10
Section: 1.1
Variables: \(l\) a directional light
\(S\) a surface
\(x\in S\)
\(n\) the normal of \(S\) at \(x\)
Applied to3: color of \(x\), assuming light coming from the two opposite direction

Name: The color of \(x\)
Definition: \(c_rc_l\max(0,n\cdot l)\)
Page: 234
Chapter: 10
Section: 1.1
Variables: \(l\) a directional light
\(S\) a surface
\(x\in S\)
\(n\) the normal of \(S\) at \(x\)
Notation: \(c\)

Question: How to avoid that, when \(n\) is away from \(l\), \(x\) is black
Answer: two sided lightning
Page: 234
Chapter: 10
Section: 1.1
Variables: \(l\) a directional light
\(S\) a surface
\(x\in S\)
\(n\) the normal of \(S\) at \(x\)
Answer2: add a light from the eye
Answer3: add an ambiant light
Answer4: add a constant before color multiplication

Question: Most real-world models are composed of
Answer: triangular meshes
Page: 262
Chapter: 12
Section: 1

Name: triangular meshes
Definition: A network of triangles that connect to one another through shared vertices and edges to form a single continuous surface.
Page: 262
Chapter: 12
Section: 1
Name2: triangle meshes
Intuition: triangular irregular network
Example4: TIN

Question: How to display a surface of triangular edges
Answer: Save surface display information at each vertices. Interpolate those data to draw the triangle
Page: 262
Chapter: 12
Section: 1

Name: The mesh topology
Definition: The way the triangles connect together, without regard for the vertex positions
Page: 262
Chapter: 12
Section: 1.1
Variables: \(S\) a triangular meshes

Name: A manifold mesh
Definition: Every edge is shared by exactly two triangles.
Page: 262
Chapter: 12
Section: 1.1
Definition2: Every vertex has a single, complete loop of triangles around it.
Conjdef: A mesh such that
Intuition: A mesh without gaps, separating inside from outside
Counterexample: for property 1
Counterexample2: for property 2

Name: An edge of \(M\)
Definition: A continuous sequence of edges, such that each edge only corresponds to a single triangle
Page: 262
Chapter: 12
Section: 1.1
Variables: \(M\) a mesh
Context: Mesh
Name2: A boundary of \(M\)

Name: A manifold with boundary
Definition: Every edge is used by either one or two triangles.
Page: 262
Chapter: 12
Section: 1.1
Definition2: Every vertex connects to a single edge-connected set of triangles.
Conjdef: A manifold mesh such that

Name: An orientation of \(M\)
Definition: A set of orientation for each triangles which are compatible
Page: 263
Chapter: 12
Section: 1.1
Variables: \(M\) a manifold mesh
Applied to3: Selecting a front and a back from the surface

Name: An orientation of \(T\)
Definition: Either the relation containing the pairs \((a_i,a_{i+1\mod 3})\) or the relation containing the pairs \((a_{i+1\mod 3},a_{i})\)
Page: 263
Chapter: 12
Section: 1.1
Variables: \(T=\{a_0,a_1,a_2\}\) a triangle
Applied to3: Choosing a front for the triangle

Name: Two triangles with consistent orientations
Definition: A pair \(T_1=(\{a_0,a_1,a_2\},R_1)\), \(T_2=(\{a_1,a_2,a_3\},R_2)\) of triangles with orientation such that \(R_1\) is disjoint from \(R_2\). That is, \((a_1,a_2)\) and \((a_2,a_1)\) each belong to a single of the \(R_i\)
Page: 266
Chapter: 12
Section: 1.1
Applied to3: Triangles with the same front face

Name: The front of \(T\)
Definition: The side of \(T\) such that the orientation is in counterclockwise order.
Page: 263
Chapter: 12
Section: 1.1
Variables: \(T=(\{a_0,a_1,a_2\},R)\) a triangle with an orientation
Context: Triangle orientation

Name: An orientable surface
Definition: A surface admitting a consistent orientation.
Page: 263
Chapter: 12
Section: 1.1
Example: A tetrahedron
Applied to: Mobius band

Name: A mobius band
Definition: A strip of paper, turned half a time and pasted to itself.
Page: 263
Chapter: 12
Section: 1.1
Typ: non orientable surface

Smaller0: \(S\) has a consistent orientation
Greater0: \(S\) edge are manifold
Page: 264
Chapter: 12
Section: 1.1
Variables: \(S\) a surface
Counterexample: Mobius band

Name: A manifold edge
Definition: An edge shared by at most 2 triangles
Page: 263
Chapter: 12
Section: 1.1
Variables: \(S\) a surface mesh