geometric modellin

8/2/2019 Geometric Modellin

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I N T R O D U C T I O N T O C O M P U T E R G R A P H I CS

credits: van Dam,R. Hwa September 6-8, 2011 OpenGL 1/54

Geometric Modeling;The Graphics Framework;Introduction to OpenGL


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Recap

CG markets: entertainment and science same tools (hw & sw), different apps come talk to me about a Directed Study

CG paradigms: sample-based graphics (pixels, image

processing)

geometry-based graphics Geometric modeling

primitives decomposition of a model


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Decomposition of a GeometricModel

Divide and Conquer Hierarchy of geometrical components Reduction to primitives (e.g., spheres,

cubes, etc.) Simple vs. not-so-simple elements (nail

vs. screw)

Head

Shaft

Point

composition decomposition


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Hierarchical (Tree) Diagram ofNail

Object to be modeled is (visually) analyzed, andthen decomposed into collections of primitiveshapes.

Tree diagram provides visual method ofexpressing composed of relationships of model

Such diagrams are part of 3D program interfaces(e.g., 3D Studio MAX, Maya)

As data structure to be rendered, it is called ascenegraph

Nail

Head

(cylinder)

Body

root node

leaf nodes

Shaft

(cylinder)

Point

(cone)

tree diagram


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Composition of a GeometricModel

Primitives created in decomposition processmust be assembled to create final object.Done with affine transformations, T, R, S(as in above example).

Other composition operators exist (e.g.,Constructive Solid Geometry CSG -- usesBoolean operators).

Primitives

in their ownmodeling

coordinate system

Composition

in world (root)coordinate

system

Translate

Translate and Scale

Translate and Rotate


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2D Primitives

Line

X

Y

Polyline

X

Y

Polygon

X

Y

Circle

X

Y


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Curves

Piecewise linear approximation

Splines: higher-order polynomials piecewise curvilinear approximation

French Curves Draftmans Spline

Mathematical Splines

Natural Cubic Spline:

(duck)


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Example 3D PrimitivesPolyhedron

Sphere

Polyline

Patch

(spline boundary curve)


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What Kind of Math do We Need?Cartesian Coordinates

Typically modeling space is floating point,screen space is integer

NB:Often, screen coordinates are measured top tobottom, based on raster scan

(0,0)

x, y Cartesian gridInteger Grid


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Conceptual Framework forInteractive Graphics

Graphics library/package (e.g., OpenGL) isintermediary between application and displayhardware (Graphics System)

Application program maps application objects toviews (images) of those objects by calling ongraphics library

This hardware and software framework is morethan 4 decades old but is still useful, indeeddominant

Applicationprogram

GraphicsLibrary(GL)

GraphicsSystem

applicationmodel

(objects)


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2D Hw/Sw Topics

a) Display Hardware: Raster scan vs. Vector

b) Color Tables

indirect specification of (pseudo) color color correction, simple types of animation

c) BitBlt/RasterOp for operating on blocks ofpixels


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a) Graphics Display Hardware Vector (calligraphic, stroke, random-scan)

still used in some plotters

Raster (TV, bitmap, pixmap), used in displays andlaser printers

Ideal Drawing Vector Drawing

Raster

Outline primitives Filled primitives


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2D Raster Architecture

Raster displays store images (pixmaps, orbitmaps) in a frame buffer, also known asbitmapbuffer, or refresh buffer

The frame bufferis a chunk of memory locatedeither in separate hardware (VRAM) or in CPUsmain memory (DRAM)

The frame buffercan be accessed directly,through memory operations

Video controller draws all scan-lines at consistent> 60 Hz; separates update rate of the frame buffer and

refresh rate of the display contains Color-Table

DisplayFrame buffer


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b) Color Tables: 1-bit vs. n-bit

Display

2n intensities or colors


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Image Display SystemLook-up Table

Any specific 2n colors may be inadequate (n may be as lowas 16 in low-end systems)

Look-up table allows 2n colors out of 224 colors to be usedin one image, some other 2n in another image

224 = approx. 16.7 million, exceeds eyes ability todiscriminate (somewhere between 7-10 million)

Color table is resource managed (usually) by windowmanager


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Color LookUp Table Operation

Pixel value is indexed to color look up table (CLUT)where color is stored. Here we use only 12 bits(4bits per color) for clarity typically, 24 bits areused

CLUT look-up done at video rates In 24-bit true color systems, 3 x 8 bits for R, G,

B; each color has its own 8-bit CLUT (0-255)

CLUT allows variety of effects fast image changes: change table rather than

stored image multiple images: select or composite/blend

animation hack


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c) BitBlt/RasterOp (1/3) Logically operate on each pixel in

rectangular source and destinationregions in same or different pixmaps to

achieve dynamics, e.g., to move/scrollwindows on screen

RasterOp (Source, Destination) Destination

In some implementations S and D neednot be same size

pixmap stored inframe buffer


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BitBlt/RasterOp (2/3) AND (S,D): S can mask out pixels in D OR (S,D): S is non-destructively added to D;

used for painting, transparent and kernedcharacters (where characters extend beyond their

boxes)

Heres how you can use them:Lets say you want to add some game sprites to background

0 (black) AND anything is 0, 1 (white) AND anything is anything

AND =

1. Mask out with black

0 OR anything is anything

OR =

2. Add sprites in


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More BitBlt/RasterOp (3/3) Replace (S,D): S destructively replaces D, i.e., is

deleted and copied on top of D (also called Move); usedfor making opaque characters, icons, scroll

Copy (S,D) as above, but S is not deleted XOR (S,D) S selectively inverts D; used in 1-bit systems

for cheap cursors:

Note: effects in color systems for all but replace may beweird

S XOR (S XOR D) = D 0 = W, 1 = B

S D D

S D D

XOR

XOR


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Recap

Geometry-based paradigm (modeldecomposition, scenegraphs)

The Graphics Framework 2D hw/sw select topics

display hw: vector vs. raster; the frame-buffer, the video controller, the display

color-tables BitBlt operation

Applicationprogram

GraphicsLibrary(GL)

GraphicsSystem


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Next: the Graphics Library

Application

model

Application

program

GraphicsLibrary

(GL)

Graphics

System


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Graphics Library examples: OpenGL, DirectX, X3D provides representations and support for:

primitives attributes

color line style

material properties for 3D

lights transformations

immediate mode vs. retained mode immediate mode: no stored representation,

package holds only attribute state, andapplication must completely draw each frame;simple to use but slow; requires at least one

function call for every vertex to be drawn. retained mode: library compiles and displays

from scenegraph; give the library a pointer to abunch of Vertex data and tell it to render fromthere


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I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S

credits: van Dam, R. Hwa September 6, 2011 OpenGL 23/54

What is OpenGL?

The OpenGraphics Library 3-D graphics API specificationa software interface to graphics hardware1 raster graphics library

pass in vertices, normals, and otherscene data

get pixels out industry standard

supported across many platforms Mac OS, Windows, Linux, iPhone,

PSP specification publicly available

1 The OpenGL Graphics System: A Specification Version 3.0


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OpenGL Architecture (1/2)

OpenGL uses a client-server model client sends commands to the server server interprets, processes commands note: client and server usually on the same

computer, but need not be your program = client OpenGL = server

example interaction:program OpenGL

begin trianglenormal (0, 0, -1)

vertex (-1, 1, -1, 1)vertex (1, -1, -1, 1)

vertex (-1, -1, -1, 1)

end triangle


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OpenGL Architecture (2/2)

OpenGL is state-full and procedural the current OpenGL state (collectively called a

context) contains data describing how rendering

should proceed

ex: current color, lights, textures, etc state does not change until explicitly set

once some state is set, it remains in effect until changed considering we are working with hardware, this makes

some sense want to have precise control

procedural model usually accessed through a plain C API NOT object-oriented at all (though this changes gradually

in OpenGL 3.1 and beyond)

can be cumbersome if you are used to workingwith object-oriented systems

one line can affect how all subsequent code executes sometimes difficult to encapsulate functionality have to be mindful of default state as well


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OpenGL vs. Direct3D

Direct3D is Microsofts low-level 3D graphics API and plays a similar role toOpenGL in the graphics pipeline.

Though the APIs feel somewhat different, at the end of the day, they providebasically the same functionality.

Differences OpenGL is a specification with several free implementations on different

platforms, while Direct3D is a proprietary API written by Microsoft.

Direct3D exposes the programmer to the graphics hardware much morethan OpenGL does. While OpenGL certainly supports hardware

acceleration, it generally tries to abstract away details of dealing with the

hardware. Direct3D on the other hand, allows much more fine-grainedcontrol but sacrifices some ease of use to do so.

For Windows users, D3Ds tight coupling with windows has itsadvantages

Development environment is standardized and robust. D3D development istightly integrated with Visual Studio and other powerful tools Direct3D provides a much more object-oriented API than GL. Still, many would argue Direct3D is clunkier and harder to use than

OpenGL.

Overall, OpenGL is more widely used than Direct3D due to its simplicityand availability on a wider range of platforms. (both used in the games

industry, however OpenGL used also w/out fail in scivis.)


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OpenGL, GLU, and GLUT

OpenGL (Graphics Library) offers a platform-independent software

interface with graphics hardware

supports basic geometric primitives (points,lines, polygons)

sets up an environment for graphicalprogramming

May be useful to think of it as a statemachine

GLU (OpenGL Utility Library) higher-level features (e.g. curved surfaces)

built out of basic OpenGL functions

GLUT (OpenGL Utility Toolkit) separate library by Mark Kilgard, platform

independent

hides details about basic window operationsand context creation

a simple framework for writing OpenGLapplications independent of any particularplatform


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Anatomy of an OpenGL program

#include #include int main(int argc, char **argv) {

glutInit( &argc, argv );

glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGB);glutInitWindowSize(400, 300);glutInitWindowPosition(0,0);glutCreateWindow("GLUT Skeleton");

//initialize callbacks here//

my_setup();

glutMainLoop();

return(0);}


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Single vs. Double Buffering

Use two buffers (two chunks of memory) Draw always on the back buffer When done drawing, swap buffers


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glutInitDisplayMode()





my_setup();

glutMainLoop();return(0);

} GLUT_DOUBLE, GLUT_SINGLE GLUT_RGB, GLUT_RGBA, GLUT_INDEX GLUT_DEPTH


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glutInitWindow*()





my_setup();


}


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glutCreateWindow()





my_setup();


} glutCreateWindow merely requests a window


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Anatomy of an OpenGL program





my_setup();

glutMainLoop();

return(0);}


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glutMainLoop()

Event-Driven Programming Interactive graphics program are typically

event-driven

Main program goes into a loop, waitingfor things to happen e.g., keyboard, mouse inputs, etc. when an interesting event occurs, callback

function returns control to program

The events can be user-input generated (mouse, keyboard etc) system-generated (window creation,

overlapping-window removed etc)


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Callbacks

OpenGL handles events through themechanism of callbacks:

associate events with procedures procedure gets called-backwhenever its associated event takesplace

Every OpenGL program must handlethe display event


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Common Callbacks

Input events: glutMouseFunc glutKeyboardFunc

System events: glutDisplayFunc (!!!) glutReshapeFunc glutTimerFunc glutIdleFunc

Example: setting up callbacksglutDisplayFunc( my_display);

glutIdleFunc( my_idle );


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Example my_display()

void my_display(void) {

//insert your drawing code always here

glClear(GL_COLOR_BUFFER_BIT) ;

glColor3f(0,0,1) ;

glBegin(GL_POLYGON);glVertex2f(-0.25, 0.75);glVertex2f(0.95, 0.75);glVertex2f(0.95, -0.55);glVertex2f(-0.25, -0.55);

glEnd();

glutSwapBuffers();

return ;}


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The Callback for Displaying

my_displaygets called: at initial creation of the window when window becomes unobstructed when the program requests it

glutPostRedisplay()


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A Simple Display Function


glClear(GL_COLOR_BUFFER_BIT) ;glColor3f(0,0,1) ;

glBegin(GL_POLYGON);glVertex2f(-0.1, 0.7);glVertex2f(0.9, 0.7);glVertex2f(0.9, -0.3);glVertex2f(-0.1, -0.3);

glEnd();

glutSwapBuffers();return ;

}


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What Goes Between glBeginand glEnd Specification of mode

GL_POINTS GL_LINES, GL_LINE_STRIP,

GL_LINE_LOOP

GL_POLYGON GL_TRIANGLES, GL_TRIANGLE_STRIP,

GL_TRIANGLE_FAN

GL_QUADS, GL_QUADS_STRIP Declaration of vertices

glVertex{2|3|4}{i|f|d}[v] integer, float, or double

Attributes Color Point size

Line width, style Patterns for filled polygons


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How does the output change

with respect to different modes?


glClear(GL_COLOR_BUFFER_BIT) ;

glColor3f(0,0,1) ;

glBegin(??);glVertex2f( 0.0, 0.9);glVertex2f(-0.5,-0.9);glVertex2f( 0.9, 0.2);

glVertex2f(-0.9, 0.2);glVertex2f( 0.5,-0.9);

glEnd();


}


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Mouse Inputs

Associate mouse events with my_mouseprocedure:glutMouseFunc(my_mouse)

Write your own code inside my-mouse:void my_mouse(int button, int state, int

x, int y)

where button can take these values:

GLUT_LEFT_BUTTON,GLUT_MIDDLE_BUTTON,GLUT_RIGHT_BUTTON

state:GLUT_UP, GLUT_DOWN

x, y: position in window (in pixels) with origin at

upper left


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Drawing Space


glBegin(GL_POLYGON);glVertex2f(-0.1, 0.7);

glVertex2f(0.9, 0.7);glVertex2f(0.9, -0.3);glVertex2f(-0.1, -0.3);

glEnd();


}

void glut_setup(void) {

glutInitWindowSize(400,100);

glutInitWindowPosition(0,0);

glutDisplayFunc(my_display);

return ;

}

What is the expected image output?


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Viewport

Defines where in the window todisplay the image

Uses within window coordinatesystem (pixel unit; origin at lower

left corner)

OpenGL default: set to be theentire window

default window reshape: setviewport to whole window


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Adding-in a Viewport Function

Define callback: my_reshape(w,h) Otherwise, viewport will be set to whole window

again

In the function my_reshape call:glViewport(origin_x,origin_y,

width,height); note that origin is at the lower left corner


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Define User-Friendly

Coordinate System More intuitive instead of square in the interval

of [-1,1]

Graphics system does the mapping in OpenGL, this is done with theprojection

matrix

glMatrixMode (GL_PROJECTION);

glLoadIdentity();

gluOrtho2D(left,right,bottom,top);


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Changes of Co-OrdinatesglBegin(GL_POLYGON);

glVertex2i(1,2);glVertex2i(7,2);

glVertex2i(4,10);glEnd();

gluOrtho2D(2,8,5,12);

glViewPort(0,0,500,300);

glutInitWindowSize(800,500);

glutInitWindowPosition(0,0);


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Bonus: Operating on the FrameBuffer

Steps:1.Allocate space for pixel array

1 x width x height x sizeof(pixel) array of pixels(grayscale image) or

3 x width x height sizeof(pixel) array (RGBimage) or

4 x width x height array sizeof(pixel) (RGBAimage) etc

2.Initialize array with original image values

3.Perform desired operations on pixel array

4.Write array to Frame Buffer:

glRasterPos( x, y ) specify x, y position wherewe want to write some pixels

glDrawPixels( , *pixel_array) write a blockof pixels to the frame buffer

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