Acsc330 Computer Graphics Chapter 2 – Graphics Programming

2D as a special case of the 3D graphics

Using OpenGL for API

broad enough for PHICS, GKS, Java-3D & Direct X
Sierpinski gasket (an object that can be defined recursively and randomly)
A vertex – a location in space, rather than a point
A point in space is specified by a single vertex. Two vertices define a line segment. Three vertices can determine either a triangle or a circle. Four a quadrilateral etc.
Vertex function glVertex<sup>*

*,</sup> two or three characters of the form nt or ntv

n, number of dimensions (2, 3, or 4)

t, denotes data type, integer(i), float(f), double(d)

v, (if present) the variable are specified through a pointer to an array, rather than through

an argument list

Basic OpenGL types, GLfloat, Glint

#define Glfloat float
e.g. glVertex2i(GLint x_i, GLint y_i), 2D with integers

glVertex3f(GLfloat x, GLfloat y, GLfloat z), 3D using floating points

glVertex3fv(vertex), if an array is used, 3D

glBegin e.g. glBegin (GL_LINES);

. glVertex2f(x1, y1);

. glVertex2f(x2, y2);

. glEnd();

glEnd

• 
  Device-independent Graphics – in any coordinate system
  
• 
  World-coordinate systems (user’s coordinate system) or application or problem coordinate system
  
• 
  Physical-device coordinates or device coordinates
  

Simple but powerful

as a black box

Function calls Output

Data Input

1. 
   The primitive functions (low-level objects)
   

Attributes – ‘how’ (the way the primitives appear)

Attribute functions (e.g. colour, pattern, typeface)

3. 
   Description of the synthetic camera
   

3. 
   A set of transformation functions
   

6. 
   Control functions enable us to communicate with the window system (for a multiprocessing multiwindow environment)
   

7. 
   Inquiry functions
   

GLUT (GL Utility Toolkit)

• 
  Geometric primitives (points-GL_POINTS, line segments-GL_LINES, polygons, curves and surfaces)
  
• 
  Raster primitives (arrays of pixels) – lack geometric properties
  

Convex – all points on any line segment are inside the object

c is the number of the ASCII character

• 
  Can approximate a curved surface by a mesh of convex polygons – a tessellation
  

e.g. for a circle use a regular polygon of n sides.

for a sphere use a regular polyhedron

• 
  or, use the mathematical definitions of curved objects and then build graphics functions to implement those objects (e.g. quadratic surfaces, parametric polynomial curves and surfaces)
  

In OpenGL:

attribute – any property that determines how a geometric primitive is to be rendered.

(e.g. colour, thickness of a line, the pattern used to fill a polygon)
Colour

most interesting aspect

Three colour theory

Additive colour model (three primary colours mixed); red, green and blue - RGB

Colour gamut – range of colours

glIndexi(element);

which objects should appear on the screen

default viewing conditions exist

viewing rectangle of clipping rectangle (objects inside the rectangle are in the image; objects outside are clipped out and are not displayed)

orthographic view – orthographic projection (‘sees’ only those objects in the volume specified by viewing volume). Unlike a real camera, the orthographic projection can include objects behind the camera.

void glOrtho

model view and projection matrices

Interaction with the Window System

Window or screen window – a rectangular area of the display, the screen of a CRT

In OpenGL, window coordinates are 3D, whereas screen coordinates are 2D – measured in pixels

Many windows can be displayed on the CRT screen

Origin: OpenGl – bottom left; windowing information e.g. mouse position – top left  conversion is required from one coordinate system to the other

aspect ratio of a rectangle is the ration of the rectangle’s width to its height

distortion – a consequence of the default mode of operation, in which the entire clipping rectangle is mapped to the display window.

Viewport – a rectangular area of the display window. By default, it is the entire window, but it can be set to any smaller size in pixels – void glVIEWport

The Gasket Program

Polygons and Recursion

The 3D Gasket