Lien de la note Hackmd

Contexte

On a l’habitude de voir des models 3D virtuels

Conclusion: il est aise de concevoir et animer ses propres modeles 3D

FAUX !

Outils:

Blender
Maya

Formation de 3 a 5 ans dans les ecoles d’infographie.

Le cout/temp passe sur la 3D n’a jamais ete aussi elevve

Films animations/VFX
- Cout moyen par sequence VFX ($\lt10s$): 50k$
- Cout animation 3D $\gt$ cout dessin manuel
Jeu videos AAA
- 100M$
- 2 a 4 annees de dev

Les outils 3D se sont ameliores

Mais restent complexes et tres techniques (3 ans d’etude infographistes)

Creation 3D

La quantite et la qualite demande a augmente plus rapidement que les outils

Dessins/sculpture a la main restent plus efficace pour le prototypage/design

Equipe: Geometric & visual computing

Equipe informatique graphique et vision

Applications

Domaine d’applications typiques

Loisirs & creations artistiques
Modelisation & visualisation en Sciences Naturelles
Prototypage et fabrication

Notre “expertise”

Methode interactive pour l’aide a la creativite
Simulation visuelles
Analyses de formes et algorithmique

Aide: stages, emploi, poursuite en Informatique Graphique ?

Rem. IG: Domaine technique, R&D avancee

Lien fort sujets recherche et entreprise
Theses IG - sujets appliques qui interessent les industries

Si le domaine vous interesse:

AFIG

Plan du cours

Introduction et rappels d’Info Graphique
Warm-up systeme de particules
Animation descriptive
Animation physique
Animation de personnages

Evaluation

Un compte rendu de tp
- Collision de spheres, tissus, ou personnage articule
- $\simeq5$ pages
- Notre demarche, resultats et analyses

Computer graphics

Main subfields

Modeling
Animation
Rendering

Representing 3D shapes for Graphics Application

Computer graphics: mostly focus on representing surfaces
Scientific visualization: volume data

Surfaces

Two main rpz

Representation d’une sphere:

Difficulty of surface representation using function

C’est impossible, la forme est trop complexe

Objective of surface representation

Main idea: use piecewise approximation

Ideal surface representation

Approximate well any surface
Require few samples
Can be rendered efficiently (GPU)
Can be manipulated for modeling

Example of models:

Mesh-based
- Triangular meshes, polygonal meshes, subdivision surfaces
Polynomial
- Polynomial: bezier, spline NURBS
Implicit
- grid, skeleton based, RBF, MLS
Points sets

For projective/rasterization render pipeline: always render triangular meshes at the end

Pros	Cons
Simplest representation	Requires large number of saples: complex modeling
Fit to GPU Graphics render pipeline	Tangential discontinuities at edges

Mesh encoding

Example of 3D Mesh File

Affine transforms and 4D vectors/matrices

Perspective matrix

Perspective space: allows perspective projection expressed as a matrix.

Common constraints (in OpenGL):

Wrap the viewing volume (truncated cone with rectangulare basis called frutsum) ($z_{near},z_{far},\theta$) to a cube
- $\theta: view angle$
- $p=(x,y,z,1)\in$ frutsum $\Rightarrow p’=(x’,y’,z’,1)\in[-1,1]^30$

\[M=\begin{pmatrix} f&0&0&0\\ 0&f&0&0\\ 0&0&C&D\\ 0&0&-1&0 \end{pmatrix}\\ f=\frac{1}{\tan(\frac{\theta}{2})}\\ L = z_{near}-z_{far}\\ C= \frac{z_{far}+z_{near}}{L}\\ D= \frac{2z_{far}z_{near}}{L}\]

In practice

You must define $z_{near}, z_{far}$
$z_{far}-z_{near}$ should be as small as possible for max depth precsion

To which view space are mapped 3D world space points at $z_{near}, z_{far}$ ?

Fractals

Idea Recursively add self-similar details

Simple rule $\to$ complex shape
May look like complex natural details

Perlin noise

A widely used noise function

Creer une fonction pseudo-aleatoire continue

MAIS deterministe

On prend des echantillons a des valeurs entiere

Pour chaque on associe une tangente
Utilise une fonction de hash
- float hash(float n) {return fract(sin(n)*1e4);}

Fractal Perlin Noise

On somme la fonction avec elle-meme en changeant ses parametres

\[g(x)=\sum_{k=0}^N\alpha^kf(\omega^kx)\]

$f$: smooth Perlin noise function
$N$: number of Octave
$\alpha$: persistency
$\omega$: frequency gain

Usage

Material texture
- Ridge effect
- Marble effect
Animated textures
- Translation: $f(x,y+t)$
- Smooth evolution: $f(x,y,t)$
Moutain-looking terrain
- $z=f(x,y)$

Applications

In almost any complex shape

Exercice

Perlin Noise terrain

\[S(u,v)=\begin{cases} x(u,v)=u\\ x(u,v)=v\\ z(u,v)=hg(s(u+o), s(v+o)) \end{cases}\]

The perlin noise

\[g(u,v)=\sum_{k=0}^N\alpha^kf(2^ku,2^kv)\] \[N=9\\ \alpha=0.4\\ h=0.3\\ s=1\\ o=0\]

b: $N$ modifie
a: $s$ modifie
- Les montagnes du fond sont des “nouvelles” montagnes
- on voit plus loin
f: $o$ modifie
e: $h$ modifie

Animation

Reference surface function:

\[(u,v)\in[0,1]^2, f(u,v)=(u,v,0)\]

How to generate the following animations ?

Help Dimension of the Perlin noise ? Which parameter $(u,v,t-\text{time})$ ?

a: axe $z$ qui change
- $f(u,v)=(u,v,p(u+t))$
- Faux! $u+t$ nous fait deplacer dans les $t$ negatifs
- $f(u,v)=(u,v,p(u-t))$
b: $f(u,v)=(u,v,p(u+t, v))$
c: piege !
- On a le droit au bruit de Perlin 3D
- $(u,v,p(u,v,t))$

Quand on a des textures animees a partir de bruit de Perlin, il y a une dimension supplementaire: le temps

d: similaire a la c
e: $f(u,v)=(u,v,p(u-t)+up(u,v,t))$
- Multiplication par $u$ car le bruit est plus important a la fin
v: on ne change pas que $z$ cette fois
- $f(u,v)=(u+p(u,v,t),v+p(u,v,t), p(u,v,t))$

Geometry processing libraries

Development libraries

LibIGL
CGAL
GeoGram

Viewer (+lib)

Graphite
Meshlab

Software

Blender

Useful CG programming library

Useful libs

Eigen
GLM
Assimpl
DevIL

Minimalistic GUI

ImGui
NanoGui
AnTweakBar

Full framework

Particle system

Definition Element at a given position + extra parameters (mass, life time, etc)

On appelle un systeme de particules en oppositionL

Rigid bodies - Solid objects with static shape
Deformable bodies - Continuum material that can deforms

Pros	Cons
Lightweight rpz	Simple model from physics point of view
Generic flexible model (spatial deformation, no connectivity, etc)

Particles systems in History

One of the first animated model in CG

Example of particle system

Free fall of sphere under gravity

Geometrical rpz of each particle: sphere
Equation of motion $p(t)=\frac{1}{2}gt^2+v_0t+p_0$
Initial position and speed may be placed at random position
Each particle may have a different life time

What are the parameters used for $p_0$ and $v_0$ in this example ?

\[p_0=(0,0,0)\\ v_0=(\sin(), 1,\cos())\]

Si on a un $\sin$ du temps, on aurait des particules emises suivant un cercle

Genre comme ca

Or, nos particules ne suivent pas ce cerlce, elles suivent un nombre aleatoire $\theta$:

$v_0=(\sin(\theta), 1,\cos(\theta))$

Par exemple, $\theta\in[-\pi,\pi]$

Bouncing spheres

What is the equation of motion (taking into account the bouncing) ?

Considere a particle emited at time $t=0$
At what time $t_i$, the particle touch the floor ?
What is the new speed after impact ?
What is the complete equation of trajectory ?

\[t_i=\\ p(t)=\frac{1}{2}gt^2+v_0t\\ p_g(t_i)=0\\ \begin{aligned} \frac{1}{2}g_yt_i^2+v_{og}t_i=0&\Rightarrow\frac{1}{2}g_yt_i=-v_{oy}\\ &\Rightarrow=-2\frac{v_{oy}}{g_y} \end{aligned}\\ p(t_i)\quad v(t_i)\to\begin{pmatrix} V_x\\ -V_y\\ V_z \end{pmatrix}\\ p_2(t)=\frac{1}{2}g(t-t_i)^2+v'(t_i)(t-t_i)+p(t_i)\]

General motions

Motion equation is not restricted to physics-based equations

What are the parameters associated to each particle ?
What are the corresponding equations of motions ?

On dirait que les bulles sortantes bougent en forme de cercle

\[\text{rand}\to[0,1]\\ p_0=(?,0,?)\]

Comment faisons-nous pour recreer le cercle ?

On randomise $x$ et $y$ entre $-1$ et $1$ Or ca nous fais un carre et on veut un cercle On tire au hasard 2 rayons $r_1$ et $r_2$

$\sqrt{r_1^2+r_2^2}\gt R\\ \begin{cases} R\cos(\theta)\\ R\sin(\theta) \end{cases}$ Avec:

$r_1, r_2\in[0,R]$

On a donc $p_0,v_0,R,C$

$p(t) = p_0+v_0(t-t_0)+\begin{pmatrix} r\cos(\theta t-t_0+\gamma)\\ r\sin(\theta t-t_0+\gamma)\\ 0 \end{pmatrix}$ Avec:

$\gamma$: un offset aleatoire

Billboards, impostors, sprites

Particle can be displayed as small images/thumbnails

In practice:

Each particle is displayed as a quadrangle
A texture is mappe on the quad

The texture can contains transparency

Usage

Large use of billboard for complex models

vegetation, fire, etc.

Example

Use case in production

Le seigneur des anneaux

Comment on ete fait ces chevaux liquides ? Comment a ete filme la scene ?

Il n’y a que des vrais chevaux sur la scene Pour l’eau, les chevaux ont ete fait a partir d’emission de particules

Zoom sur une chute d’eau

La base des tetes de chevaux

Couches de particules emisent a partir des tetes

Ensemble final

La riviere

Les vrais chevaux, qui ne meurent pas

Faux chevaux et cavaliers modelises pour etre emporte par la riviere

AN3D: Bases du rendu graphique

Contexte

Creation 3D

Equipe: Geometric & visual computing

Applications

Aide: stages, emploi, poursuite en Informatique Graphique ?

Plan du cours

Evaluation

Computer graphics

Main subfields

Representing 3D shapes for Graphics Application

Surfaces

Two main rpz

Difficulty of surface representation using function

Objective of surface representation

Mesh encoding

Example of 3D Mesh File

Affine transforms and 4D vectors/matrices

Perspective matrix

Fractals

Perlin noise

Fractal Perlin Noise

Usage

Applications

Exercice

Perlin Noise terrain

Animation

Geometry processing libraries

Useful CG programming library

Particle system

Particles systems in History

Example of particle system

Bouncing spheres

General motions

Billboards, impostors, sprites

Usage

Example

Use case in production

Further Reading

AN3D: Interpolate position

IMED2: TP3

IMED2: Project