Win Viewing

7/30/2019 Win Viewing

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Window toViewport Mapping


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Acknowledgements

Some of the material for the slides were adapted fromRick Parent

Some of the images were taken from Hearn, Baker, and Carithers, Computer Graphics with

OpenGL


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Figure 3-1 The transformation sequence from modeling coordinates to device coordinates for athree-dimensional scene. Object shapes can be individually defined in modeling-coordinate referencesystems. Then the shapes are positioned within the world-coordinate scene. Next, world-coordinatespecifications are transformed through the viewing pipeline to viewing and projection coordinates andthen to normalized coordinates. At the final step, individual device drivers transfer the normalized-coordinate representation of the scene to the output devices for display.


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Coordinate Systems

Four Cartesian co-ordinates systems in computer Graphics.

1. Modeling co-ordinates

2. World co-ordinates

3. Normalized device co-ordinates

4. Device co-ordinates

Modeling coordinate is also known as local coordinate.

Ex: where individual object in a scene within separate coordinate referenceframes.

Each object has an origin (0,0)So the part of the objects are placed with reference to the objects origin.

In term of scale it is user defined, so, coordinate values can be any size.


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Coordinate Systems

World Coordinate

The world coordinate system describes the relative positionsand orientations of every generated objects.

The scene has an origin (0,0).

The object in the scene are placed with reference to the scenesorigin.

World co-ordinate scale may be the same as the modeling co-ordinate scale or it may be different.

However, the coordinates values can be any size (similar toMC)


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Coordinate Systems

Normalized Device Coordinate

Output devices have their own co-ordinates.

Co-ordinates values:

The x and y axis range from 0 to 1 All the x and y co-ordinates are floating point numbers in the

range of 0 to 1

This makes the system independent of the various devices

coordinates. This is handled internally by graphic system without user

awareness.


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Coordinate Systems

Device Coordinates

Specific co-ordinates used by a device.

Pixels on a monitor

Points on a laser printer.

mm on a plotter.

The transformation based on the individual device is handledby computer system without user concern.


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Coordinate Systems

World Coordinate System - This is object space or the space inwhich the application model is defined.

Screen Coordinate System - The space in which the image isdisplayed.

World Window (or clipping) - This is the rectangle in the world

defining the region that is to be displayed. Interface Window - The window opened on the raster graphics

screen in which the image will be displayed. Viewport - The rectangular portion of the interface window that

defines where the image will actually appear (usually the entire

interface window but in some cases modified to be a portion of theinterface window). Viewing Transformation - The process of mapping a world

window in World Coordinates to the Viewport.


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World Coordinate System

Application specific difficult to workdirectly in screen coordinates

20 feet

10 feet


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Screen Coordinate System

- 2D Regular Cartesian Grid- Origin (0,0) at lower left

corner (OpenGL convention)- Horizontal axis xVertical axis y

- Pixels are defined at the grid

intersections- This coordinate system is definedrelative to the display window origin(OpenGL: the lower left cornerof the window)

(0,0)

y

x

(2,2)


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Define a world window


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World Window

World window a rectangular region in theworld that is to be displayed

Define by

W_L, W_R, W_B, W_T

W_L W_R

W_B

W_T

Use OpenGL command:gluOrtho2D(left,right,bottom, top)glOrtho(left,right, bottom, top,near, far)


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Viewport

The rectangular region in the screen for displayingthe graphical objects defined in the world window

Defined in the screen coordinate system

V_L V_R

V_B

V_T

glViewport(int left, int bottom,int (right-left),

int (top-bottom));
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To draw in world coordinate system

Two tasks need to be done

Define a rectangularworld window(call an OpenGL function)

Define a viewport (call an OpenGL function)

Perform window to viewport mapping(OpenGL internals will do this for you)


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Window to viewport mapping

Window-to-Viewport mapping is the process ofmapping or transforming a two-dimensional,world-coordinate scene to device coordinates. In

particular, objects inside the world or clippingwindow are mapped to the viewport. Theviewport is displayed in the interface window onthe screen. In other words, the clipping window is

used to select the part of the scene that is to bedisplayed. The viewport then positions the sceneon the output device.


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The objects in the world window will then

be drawn onto the viewport

(x,y)

(Sx, Sy)

World windowviewport


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How to calculate (sx, sy) from (x,y)?

(x,y)

(Sx, Sy)


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First thing to remember you dont need todo it by yourself. OpenGL will do it for you

You just need to define the viewport (withglViewport()), and the world window (withgluOrtho2D())

But we will look under the hood


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Also, one thing to remember

A practical OpenGL issue

Before calling gluOrtho2D(), you need to havethe following two lines of code

glMatrixMode(GL_PROJECTION);

glLoadIdentity();gluOrtho2D(Left, Right, Bottom, Top);


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Things that are given:

The world window (W_L, W_R, W_B, W_T) The viewport (V_L, V_R, V_B, V_T)

A point (x,y) in the world coordinate system

Calculate the corresponding point (sx, sy) inthe screen coordinate system


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(x,y) (sx,sy)

(x W_L) / (W_R W_L) = (sx V_L) / (V_R V_L)

(y - W_B) / (W_T W_B) = (sy V_B) / (V_T V_B)

sx = x * (V_R-V_L)/(W_R-W_L) - W_L * (V_R V_L)/(W_R-W_L) + V_L

sy = y * (V_T-V_B)/(W_T-W_B) W_B * (V_T-V_B)/(W_T-W_B) + V_B


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Some practical issues

How to set up an appropriate world window

automatically? How to zoom in the picture?

How to set up an appropriate viewport, so

that the picture is not going to be distorted?


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World window setup

The basic idea is to see all the objects in the

world This can just be your initial view, and the user

can change it later

How to achieve it?


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World window set up

Find the world coordinates extent that willcover the entire scene

min X max X

min Y

max Y


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Zoom into the picture

Shrink your world window call gluOrtho2D() with a new range

Viewport


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Non-distorted viewport setup

Distortion happens when

World window and display window havedifferent aspect ratios

Aspect ratio?

R = W / H


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Compare aspect ratios

World window

Aspect Ratio = R

Display window

Aspect Ratio = W / H

W

H

R > W / H


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Match aspect ratios

World window

Aspect Ratio = R

Display window


W

H

R > W / H

R ?


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Match aspect ratios

World window

Aspect Ratio = R

Display window


W

H

R > W / H

R W/R

glViewport(0, 0, W, W/R)


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Compare aspect ratios

World window

Aspect Ratio = R

Display window


W

H

R < W / H


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Match aspect ratios

World window

Aspect Ratio = R

Display window


W

H

R < W / H

?


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Match aspect ratios

World window

Aspect Ratio = R

Display window


W

H

H * R

R < W / H glViewport(0, 0, H*R, H)


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When to call glViewport() ?

Initialization

Default: same as the window size

When the user resizes the display window

Two places:


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Resize (Reshape) window

Void main(int argc, char** argv){

glutDisplayFunc(display);glutReshapeFunc(resize);

glutKeyboardFunc(key);

}

void resize () a functionprovided by you. It will becalled when the windowchanges size.


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Resize (reshape) window

Void resize(int W, int H){

glViewport(0,0,W, H);}

This is done by default in GLUT

You can use the call to makesure the aspect ratio isfixed that we just discussed.


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An Example

#include

void drawSquare(void)

{

glBegin(GL_POLYGON); //initiates polygon and starts list of vertices

glVertex3f(5,5,0); //defines vertex at position x=5, y=5, z=0




glEnd(); //terminates the list of vertices for polygon

} void display(void)

{

glClear(GL_COLOR_BUFFER_BIT); //clears window to prepare it for drawing

//sets the Red, Green, Blue float values to full green for the color in//which to drawglColor3f(0.0, 1.0, 0.0);

//specifies a 100x100 viewport in pixels whose lower-left corner is at//(100, 0)measured from the origin of the window

glViewport(100, 0, 100, 100);

drawSquare();

glFlush(); /forces any buffered OpenGL commands to execute

}


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An Example

int main(int argc, char **argv)

{

/*initializes the OpenGL utilities toolkit,taking as parameters the arguments from the main

function*/

glutInit(&argc, argv);

/* the buffering mode, the color, and the depth mode, for display */

glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH);/*specifies the initial top-left corner of the window as 100x100 in pixels*/

glutInitWindowPosition(100,100);/*specifies the initial height and width of the window as 200x200 in pixels*/

glutInitWindowSize(200,200);/*creates a window on the display with title "square"*/

glutCreateWindow("square");

/*sets the Red, Green, Blue, Alpha clear color to full red to use when clearing the color buffer */

glClearColor(1.0, 0.0, 0.0, 0.0);

/*specifies that the projection matrix will be the matrix affected by subsequent transformations*/

glMatrixMode(GL_PROJECTION);


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An Example

/*sets the current transformation matrix (the projection matrix) to an

identity matrix */

glLoadIdentity();

//defines orthographic two-dimensional viewing

glOrtho(0.0, 10.0, 0.0, 10.0, -1.0, 1.0);

/*registers display() as the call back function to redraw the window */glutDisplayFunc(display);/*causes the program to enter an event-processing loop*/

glutMainLoop();

return 0;

}

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