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Chapter 4 3D Graphics

4.1 3D computer graphics

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3D computer graphics are different from

2D computer graphics in that a three-dimensional

representation of geometric data is stored in

the computer for the purposes of performing

calculations and rendering 2D images. Sometimes

these images are later displayed in a

pre-rendered form, and sometimes they are

rendered in real-time. However, 3D computer

graphics rely on many of the same algorithms

as 2D computer graphics.

4.2 Creation of 3D computer graphics The

process of creating 3D computer graphics can be

sequentially divided into three basic phases

- Content creation (3D modeling,

texturing, animation) - Scene layout setup

- Rendering

- Content creation (modeling)
- The modeling stage could be described as

shaping individual objects that are later used in

the scene. There exist a number of modeling

techniques, including, but not limited to the

following - constructive solid geometry
- polygonal modeling
- subdivision surfaces
- implicit surfaces

Constructive Solid Geometry(CSG) is a

technique used in solid modeling. CSG is often,

but not always, a procedural modeling technique

used in 3D computer graphics and CAD.

Constructive solid geometry allows a modeler to

create a complex surface or object by

using Boolean operators to combine objects.

The simplest solid objects used for the

representation are called primitives. Typically

they are the objects of simple shape cuboids,

cylinders, prisms, pyramids, spheres, cones. The

set of allowable primitives is limited by each

software package.

Operations In modeling packages, basic

geometric objects such as the cube or 'box',

sphere or ellipse, and a number of other shapes

that can be described using a mathematical

formula, are commonly known as primitives.

These objects can typically be described

by a procedure which accepts some number of

parameters for example, a sphere may be

described by the coordinates of its center

point, along with a radius value.

These primitives can be combined into

compound objects using operations like

these Operations in constructive solid geometry

Boolean union The merger of two

objects into one.

Boolean difference The subtraction of

one object from another.

Boolean intersection The portion common

to both objects.

Applications of CSG

Polygonal modeling is an approach for

modeling objects by representing or approximating

their surfaces using polygons. Polygonal modeling

is well suited to scanline rendering and is

therefore the method of choice for real-time

computer graphics

The basic object used in mesh modeling is a

vertex, a point in three dimensional space. Two

vertices connected by a straight line become an

edge. Three vertices, connected to the each other

by three edges, define a triangle, which is the

simplest polygon in Euclidean space. More complex

polygons can be created out of multiple

triangles, or as a single object with more than 3

vertices.

Four sided polygons (generally referred to

as quads) and triangles are the most common

shapes used in polygonal modeling. A group of

polygons, connected to each other by shared

vertices, is generally referred to as an element.

Each of the polygons making up an element is

called a face.

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One of the more popular methods of

constructing meshes is box modeling, which uses

two simple tools The subdivide tool

splits faces and edges into smaller pieces by

adding new vertices. For example, a square would

be subdivided by adding one vertex in the center

and one on each edge, creating four smaller

squares.

The extrude tool is applied to a face or a

group of faces. It creates a new face of the same

size and shape which is connected to each of the

existing edges by a face. Thus, performing the

extrude operation on a square face would create a

cube connected to the surface at the location of

the face.

A subdivision surface, in the field of 3D

computer graphics, is a method of representing a

smooth surface via the specification of a coarser

piecewise linear polygon mesh. The smooth surface

can be calculated from the coarse mesh as the

limit of an iterative process of subdividing each

polygonal face into smaller faces that better

approximate the smooth surface.

A subdivision surface

An implicit surface, In mathematics and

computer graphics, an implicit surface is defined

as an isosurfacea level setof a function

f R3 ? R In other words, it is the

set of points in the 3d-space that satisfy the

equation f(x,y,z) constant

Scene layout setup Scene setup involves

arranging virtual objects, lights, cameras and

other entities on a scene which will later be

used to produce a still image or an animation. If

used for animation, this phase usually makes use

of a technique called "keyframing", which

facilitates creation of complicated movement in

the scene.

With the aid of keyframing, instead of

having to fix an object's position, rotation,

or scaling for each frame in an animation, one

needs only to set up some key frames between

which states in every frame are interpolated.

Lighting is an important aspect of scene

setup. As is the case in real-world scene

arrangement, lighting is a significant

contributing factor to the resulting aesthetic

and visual quality of the finished work.

Rendering Rendering is the final process of

creating the actual 2D image or animation from

the prepared scene. This can be compared to

taking a photo or filming the scene after the

setup is finished in real life. Rendering for

interactive media, such as games and simulations,

is calculated and displayed in real time, at

rates of approximately 20 to 120 frames per

second. Animations for non-interactive media,

such as video and film, are rendered much more

slowly.

Non-real time rendering enables the

leveraging of limited processing power in order

to obtain higher image quality. Several

different, and often specialized, rendering

methods have been developed. These range from

the distinctly non-realistic wireframe rendering

through polygon-based rendering, to more

advanced techniques such as scanline rendering,

ray tracing, or radiosity. In general, different

methods are better suited for either

photo-realistic rendering, or real-time

rendering.

A rendered image can be understood in

terms of a number of visible features. Some

relate directly to particular algorithms and

techniques, while others are produced together.

shading how the color and brightness of

a surface varies with lighting

texture-mapping a method of applying

detail to surfaces bump-mapping a method of

simulating small-scale bumpiness on

surfaces reflection mirror-like or highly

glossy reflection

Reflection and shading models Popular

reflection rendering techniques in 3D computer

graphics include Flat shading A technique that

shades each polygon of an object based on the

polygon's "normal" and the position and intensity

of a light source. Gouraud shading Invented by

H. Gouraud in 1971, a fast and resource-conscious

vertex shading technique used to simulate

smoothly shaded surfaces.

Texture mapping A technique for simulating a

large amount of surface detail by mapping images

(textures) onto polygons. Phong shading

Invented by Bui Tuong Phong, used to simulate

specular highlights and smooth shaded surfaces.

Bump mapping Invented by Jim Blinn, a

normal-perturbation technique used to simulate

wrinkled surfaces. Cel shading A technique

used to imitate the look of hand-drawn animation.

Flat shading Flat shading is lighting

technique used in 3D computer graphics. It shades

each polygon of an object based on the angle

between the polygon's surface normal and the

direction of the light source, their respective

colors and the intensity of the light source. It

is usually used for high speed rendering where

more advanced shading techniques are too

computationally expensive.

The disadvantage of flat shading is that

it gives low-polygon models a faceted look.

Sometimes this look can be advantageous though,

such as in modeling boxy objects. Artists

sometimes use flat shading to look at the

polygons of a solid model they are creating. More

advanced and realistic lighting and shading

techniques include Gouraud shading and Phong

shading.

Gouraud shading is a method used in

computer graphics to simulate the differing

effects of light and color across the surface of

an object. In practice, Gouraud shading is used

to achieve smooth lighting on low-polygon

surfaces without the heavy computational

requirements of calculating lighting for each

pixel. Gouraud first published the technique in

1971. Gouraud shading is much less

processor-intensive than Phong shading, but does

not calculate all desirable lighting effects as

accurately.

Gouraud-shaded sphere - note the inaccuracies

towards the edges of the polygons.

Texture mapping is a method, invented by

Ed Catmull, of adding detail, surface texture, or

colour to a computer-generated graphic or 3D

model. A texture map is applied (mapped) to the

surface of a shape. This process is akin to

applying gift wrapping paper to a plain white

box.

In the right example, a texture map of the

Earth's coloration is applied to a sphere to

create the illusion of color detail that would

take very many additional polygons to realise

otherwise. This kind of coloration is the most

common application of texture mapping.

Phong shading is an interpolation method

in 3D computer graphics, using interpolation of

surface normals in rasterizing polygons, to get

better resolution of specular reflections such as

those generated by the Phong reflection model.

Phong shading is also commonly used to refer

to the reflection model or to the combination of

the reflection model and the interpolation

method. Phong shading provides a better

approximation to a point-by-point application of

an underlying reflection model by assuming a

smoothly varying surface normal vector.

Bump mapping is a computer graphics

technique where at each pixel, a perturbation to

the surface normal of the object being rendered

is looked up in a heightmap and applied before

the illumination calculation is done (see, for

instance, Phong shading). The result is a richer,

more detailed surface representation that more

closely resembles the details inherent in the

natural world. Normal mapping is the most

commonly used bump mapping technique, but there

are other alternatives, such as Parallax mapping.

A sphere without bump mapping.

The bump map that is applied to the image below.

This sphere is geometrically the same as the

first, but has a bump map applied. This changes

how it reacts to shading, giving it the

appearance of a bumpy texture resembling that of

an orange.

Cel shading animation also called

"cel-shading" or "toon shading" is a type of

non-photorealistic rendering designed to make

computer graphics appear to be hand-drawn.

Cel-shading is often used to mimic the style of a

comic book or cartoon. It is a somewhat recent

addition to computer graphics, most commonly

turning up in console video games. Though the end

result of cel-shading has a very simplistic feel

like that of hand-drawn animation, the process is

complex. The name comes from the clear sheets of

acetate, called cels, that are painted on for use

in traditional 2D animation.

Object with a basic cel-shader (AKA "toon

shader") and border detection.

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