Lecture - Computer Graphics

7/29/2019 Lecture - Computer Graphics

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Visualization of Fluid Flows andFlow Diagnostics

Sourabh Bhat

University of Petroleum & Energy Studies

Computer Graphics



Computer Graphics

Computer Graphics Programming Evolution

1) Hardware – Direct register / video buffer

programming

2) OS (Win32, X, MacOS)

3) Graphics Standard (GKS, PHIGS, OpenGL)

4) Platform independent (Python, Java)

Evolution



Contents

• Example: Make a 2D Gaussian Plot

• Data Sampling

•

Graphic rendering – Light rendering model

• Texture mapping

•Transparency and blending

• Visualization pipeline

What are we going to study today?



Example2D Gaussian Function

3

1111

1111where

,22

RS

,- ,- D

,- y; ,- x ,

e y x f y x

Compact domain,

Continuous data

Continuous 3D surface in 3D space



Example

• Sampling:

– Nx = 30

– Ny = 30

– Uniform grid

in domain space

• Mapping:

– 3D surface is

mapped to set

of 4 vertex polygon

2D Gaussian Function



Example

• In 3D the quadriletral (3D polygon) is given by:

– V1 = <x, y, f(x, y)>

– V2 = <x + dx, y, f(x + dx, y)>

– V3 = <x + dx, y + dy, f(x + dx, y + dy)>

– V4 = <x, y + dy, f(x, y + dy)>

• These graphics primitives are rendered fast by

computers• The quad has uniform illumination or lighting

on its surface, so called flat shading

Quadrilateral in 3D space



Example

float X_min, X_max;

float Y_min, Y_max;

int N_x, N_y;

float dx = (X_max-X_min)/N_x;

float dy = (Y_max-Y_min)/N_y;

float f(float,float);

for (float x=X_min;x<=X_max-dy;x+=dx)

for (float y=Y_min;y<=Y_max-dy;y+=dy)

{

Quad q;

q.addPoint (x,y, f(x,y));q.addPoint (x+dx,y, f(x+dx,y));

q.addPoint (x+dx,y+dy, f(x+dx,y+dy));

q.addPoint (x,y+dy, f(x,y+dy));

}

Implementation



Rendering

• Computer graphic rendering generate a image

from 3D Scene, for a given data set

• Ingredients:

– A 3D scene

– A set of lights

– A viewpoint

• Determination of illumination of primitive

shapes?

Basics



Rendering

• Rendering methods decide the approximationof light effects

– Global illumination – Ray tracing (Accurate but

computationally expensive) – Local illumination – Relate illumination of a scene

point directly to the light-set and not any otherscene points (Phong Model)

• Phong local lighting model (OpenGL): Assumethat scene consist of opaque objects in voidspace, illuminate by point-like light source

Equations



Phong Local Lighting ModelEquation

))0,max()0,max((),,( V specdiff ambl C C C I p I



Phong Local Lighting Model

I(p,v,L): intensity of the scene point

Il: Intensity of the light

p: location of the scene point

V: direction vector from p to the viewpoint

L: direction vector from the light to p

n: surface normal at p

r: direction of the reflecting light

α: specular power α

Three components:

Camb: ambient lighting, overall effect of other objects, assuming to be constant

Cdiff : diffuse lighting, scattering of the surface, equal in all direction; plastic surface

Cspec: specular lighting, mirror-like surface

Equation

))0,max()0,max((),,( V specdiff ambl C C C I p I



Shading (Coloring)

• Flat shading:• Given a polygon surface (e.g., quadrilateral), flat shading

applies the lightening model once for the completepolygon, e.g., for the center point

•The whole polygon surface has the same light intensity

• The least expensive

• But visual artifact of the “faceted” surface

• Gouraud shading (or smooth shading):• Apply lightening model at every vertex of the polygon

• The intensity between the vertices are calculated usinginterpolation, thus yielding smooth variation

Primitive Shape



Shading (Coloring)Primitive Shape

Flat Shading Gouraud Shading



Shading (Coloring)

• Needs color definition

• Shading type (Flat or Gouraud)

•

Color distribution (Centroid color for Flat,vertex color for Gouraud)

Programming Example



Surface Normals

• Using gradient:

• Using normal averaging:

Formulae

)1,,

y

f

x

f (-n

N

pn j p j

)(

in



Texture

• Effectively simulate a wide range of appearance on the

surface of a rendered object

• Improve the realism of visualization

• Method: pre-define a texture image, mapping the polygon

vertex coordinates to texture coordinates, and then combine

the texture color with the polygon color

Mapping



Transparency & Blending

• Rendering translucent (or half-transparent) shape

• See multiple shapes at the same time

• e.g., the Gaussian surface and the underlying gridded

domain

Overlap objects in scene

• Blending method (rendering the transparent effect)

•

Source: the shape is being drawn• Destination: the frame buffer (currently displayed image)

• Source + Destination



Transparency & BlendingExample

The Gaussian Surface

The Grid



Transparency & Blending

• The blending output is a weighted

combination of the source and the destination• sf: source weight factor, [0,1]

• Also called alpha component

•df: destination weight factor, [0,1]

• sf and df: also called blending factors

Formulae

ndestinatiodf source sf dst **'



The Visualization Pipeline

float data[N_x,N_y]

Class Quad

)( 22

),f( y xe y x Continuous data

Discrete dataset

Geometric object

Displayed image

Data Acquisition

Data Mapping

Rendering



Quick Recap

• Data Sampling & Mapping

• Graphic rendering

– Light rendering model

• Texture mapping

• Transparency and blending

•

Visualization pipeline

Documents

Lecture - Computer Graphics