# advanced computer graphics - Rendering

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February 5, 2015

1

ADVANCED COMPUTER GRAPHICS

Rendering

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The computer screen is a flat surface. When image data is stored in the

computer it is in the form of a data structure consisting of coordinate

points. a data structure of image points cannot be displayed directly onto

a flat computer screen.

In the same way that an engineer must use a rendering scheme in order

to represent a solid object onto the surface of the drawing paper, the

programmer must find a way of converting a data structure of coordinates

into an image on the computer monitor.

Introduction

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generating 2D images of a 3D world represented in a computer, building 2D images from 3D models ,Rendering is the conversion of a

scene into an image:

Scenes are composed of models in three-dimensional space, Models

are composed of primitives supported by the rendering system, Models

entered by hand or created by a program, The image is drawn on

monitor, printed on laser printer, or written to a raster in memory or a

file.

Rendering

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Classically, "model" to scene" to image" conversion broken into finer steps, called the graphics pipeline. The basic forward projection

pipeline looks like:

Rendering

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Each stage refines the scene, converting primitives in modeling space to

primitives in device space, where they are converted to pixels

(rasterized).

Rendering

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Three conceptual stages of the pipeline:

Application (executed on the CPU) Geometry Rasterizer

Rendering Pipeline

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The APPLICATION stage

Executed on the CPU, Means that the programmer decides what

happens

Most important task: send rendering primitives (e.g. triangles) to the

graphics hardware

The GEOMETRY stage

geometrical operations on the input data (e.g. triangles) Allows:

Move objects (matrix multiplication) Move the camera (matrix multiplication) Compute lighting at vertices of triangle Project onto screen (3D to 2D) Clipping (avoid triangles outside screen) Map to window

Rendering Pipeline

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The RASTERIZER stage

Main task: take output from GEOMETRY and turn into visible pixels

on screen

Also, add textures and various other per-pixel operations

Rendering Pipeline

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Coordinate Transformation

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Coordinate Transformation

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Coordinate Transformation

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Coordinate Transformation

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A common interpretation of the rendering process is to consider it as a

series of transformations that take the object from the coordinate

system in which it is encoded, into the coordinate system of the

display surface. This process, sometimes referred to as the rendering

pipeline, is described as a series of spaces through which the object

transform from database to screen.

A waterfall model of the rendering pipeline is shown

Coordinate Transformation

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Local Space

Objects are usually easier to model if they are conveniently positioned in the

coordinate plane. For example, when we place the bottom-left vertex of a

cube at the origin of the coordinate system, the coordinates are all positive

values

Coordinate Transformation

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World Space

The coordinate system of the scene is called the world space, or world

coordinate system.

Objects modeled in local space usually have to be transformed into

world space at the time they are placed in a scene. For example, a

particular scene may require a cube placed so that its left-bottom vertex

is at coordinates x = 2, y = 3, z = 0. The process requires applying a

translation transformation to the cube as it was originally defined in local

space. Furthermore, lighting conditions are usually defined in world

space. Once the light sources are specified and located, then shading

and other rendering transformations can be applied to the polygons so

as to determine how the object appears under the current illumination.

Surface attributes of the object, such as texture and color, may affect

the shading process. Figure shows the world space transformation of a

cube under unspecified illumination conditions and with undefined texture

and color attributes.

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Coordinate Transformation

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A vector space is a mathematical structure that

is defined by a given number of linearly

independent vectors, also called base vectors

(for example in Figure, there are three base

vectors);

Every model in the game lives in its own Model

Space and if you want them to be in any spatial

relation (like if you want to put a teapot over a

table) you need to transform them into a

common space (which is what is often called

World Space).

Coordinate Transformation

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Now let's say that we start with an active space, call it Space A, that

contains a teapot. We now want to apply a transformation that moves

everything in Space A into a new position; but if we move Space A we then

need to define a new "active" space to represent the transformed Space

A. Let's call the new active space Space B

Coordinate Transformation

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The first step when we want to render a 3D scene is to put all the models

in the same space, the World Space. Since every object will be in its own

position and orientation in the world, every one has a different Model to

World transformation matrix.

Three teapots each one in its own model space

Coordinate Transformation

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Three teapots set in World Space

Coordinate Transformation

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With all the objects at the right place we now need to project them to the screen. This is usually done in two steps. The first step moves all the

object in another space called the View Space. The second step performs

the actual projection using the projection matrix. This last step is a bit

different from the others and we will see it in detail in a moment.

Why do we need a View Space? The View Space is an auxiliary space that we use to simplify the math and keep everything elegant and

encoded into matrices. The idea is that we need to render to a camera,

which implies projecting all the vertices onto the camera screen that can

be arbitrarily oriented in space.

Coordinate Transformation

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Now, if you imagine you want to put the camera in World Space you would use

a transformation matrix that is located where the camera is and is oriented so

that the Z axis is looking to the camera target.

two teapots and a camera in

World Space

everything is transformed into View

Space (World Space is represented

only to help visualize the

transformation)

Coordinate Transformation

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The scene is now in the most friendly space possible for a projection, the

View Space. All we have to do now is to project it onto the imaginary screen

of the camera. Before flattening the image, we still have to move into

another, final space, the Projection Space. This space is a cuboid which

dimensions are between -1 and 1 for every axis. This space is very handy

for clipping (anything outside the 1:-1 range is outside the camera view

area) and simplifies the flattening operation (we just need to drop the z

value to get a flat image).

Coordinate Transformation

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Projection Space obtained from the teapot

in previous Figure

Coordinate Transformation

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Eye Space

The eye space, or camera coordinate system, introduces the

necessary transformations to improve rendering to any desired

degree. Perspective transformations requires knowledge of the

camera position and the projection plane.

Backface Elimination or Culling

One of the most important rendering problems that must be solved at

this stage of the pipeline is the elimination of the polygonal faces

that are not visible from the eye position, In the simplest case,

entire polygons that are not visible are removed at this time.

This operation is known as culling.

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A solid object composed of polygonal surfaces that completely enclose

its volume is called a polyhedron. the polygons whose normals point

away from the eye or camera can be assumed to be blocked by other,

closer polygons, and are thus invisible.

A single mathematical test can be used to determine if a polygonal face

is visible.

The geometric normal to the polygonal face is compared with a vector

from the polygon to the camera or eye position. This is called the line-of-

sight vector. If the resulting angle is greater than 90 degrees, then the

polygonal surface faces away from the camera and can be culled. Figure

shows the use of polygonal surface and line-of-sight vectors in culling.

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Once the position of the camera

is determined in the scene, it is

possible to perform the backface

elimination.

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Screen space is defined in terms of the viewport. The final transformation

in the rendering pipeline consists of eliminating those elements of the eye

space that fall outside the boundaries of the screen space. This

transformation is known as clipping.

The perspective and clipping transformations are applied as the image

reaches the last stage of the rendering pipeline.

Screen Space

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Types of rendering

a. Wireframe

b. Smooth shading

c. Ray tracing

d. Radiosity

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