Interactive Computer Graphics

• Interactive computer graphics allows users to control a picture and make changes to the produced image
• Interactive computer graphics requires two-way communication between the computer and the user
• The user sends commands with an input device to change the image

Advantages of Interactive Graphics

• Higher Quality
• More precise results or products
• Greater Productivity
• Lower analysis and design cost
• Enhanced ability to understand data and perceive trends

Representative Uses

• Computer graphics is widely used in industry, business, government, education, entertainment, and homes
• User-friendliness enhances the success and popularity of systems
• Graphical interfaces facilitate attractive and easy interaction between users and computers
• Used for 2D and 3D graphics of mathematical, physical, and economic functions
• Graphics can be used to create histograms, bars, and pie charts useful for decision making
• Desktop publishing on personal computers allows graphics for creation and dissemination of information
• Organizations use in-house document creation and dissemination
• Desktop publishing allows users to create documents with text, tables, graphs, and scanned images for office automation
• Computer-aided drafting utilizes graphics to design electrical, mechanical, electromechanical, and electronic devices
• Examples include automobile bodies, building structures, airplanes, very large-scale integrated chips, optical systems, and computer networks
• Graphics in simulation make mathematic models and mechanical systems more realistic for study
• Animation software supported by interactive graphics has proven useful in production of animated movies and cartoons
• Computer graphics tools allow users to create artistic pictures that express messages and attract attention, useful in advertising

Conceptual Framework for Interactive Graphics

• Graphics Library: Sits between the application and display hardware; includes graphics library / API
• Application Program: Maps all application objects to images by invoking graphics functions/calls
• Graphics System: An interface that interacts between the Graphics library and Hardware
• Modifications to images are the result of user interaction

Scan Converting a Straight Line

• A straight line can be defined by two endpoints and an equation
• Equation of the line is used to determine the x and y coordinates of all the points that lie between the two endpoints.
• Using the equation of a straight line, y = mx + b, values of y can be found by incrementing x from x1 to x2
• By scan-converting these calculated x, y values, we can represent the line as a sequence of pixels

Algorithm for drawing a line using the equation of a line

• Step 1: Start Algorithm
• Step 2: Declare variables x1, x2, y1,y2, dx, dy, m, b.
• Step 3: Input values for x1, x2, y1, y2. (x1, y1) are the coordinates of the starting point, and (x2, y2) are coordinates of the ending point.
• Step 4: Calculate dx = x2 - x1
• Step 5: Calculate dy = y2 - y1
• Step 6: Calculate slope m
• Step 7: Calculate y-intercept b = y1 - m * x1
• Step 8: Set(x, y) equal to the starting point, identify the lowest point and initialize xend to largest value of x.
• If dx < 0: x = x2, y = y2, xend = x1
• If dx > 0: x = x1, y = y1, xend = x2
• Step 9: Stop if x = xend
• Step 10: Plot a point at current (x, y) coordinates
• Step 11: Increment the value of x, x = x+1
• Step 12: Compute next value of y from equation y = mx + b
• Step 13: Go to Step 9.

Circle Scan Conversion

• A circle is an eight-way symmetric figure
• The shape of the circle is uniform in all quadrants i.e. the 8 octants the make the circle.
• If the calculation of the points in one octant is completed, the other seven points can be determined using the concept of eight-way symmetry.
• Circle drawing considers the circle centered at the origin, where all octants have the same values but just need to be reversed
• If a point on the circle is P1(x, y), then the other seven points can be easily found due to symmetry
• Only a 45-degree arc has to be calculated because the whole circle can be easily computed with that information.
• The putpixel function is used for eight points on the circle to draw it
• putpixel (x, y, color), putpixel (x, -y, color), putpixel (-x, y, color), putpixel (-x, -y, color), putpixel (y, x, color), putpixel (y, -x, color), putpixel (-y, x, color), putpixel (-y, -x, color)
• Example: If point (2, 7) is on the circle, so are (2, -7), (-2, -7), (-2, 7), (7, 2), (-7, 2), (-7, -2), (7, -2)
• The seven points are calculated using reflection, which is accomplished by reversing the x and y coordinates

Circle Definitions

• Polynomial Method
• Polar Coordinates

Ellipse Scan Conversion

• An ellipse is a symmetric figure but uses four-way symmetry instead of eight-way symmetry like a circle