Computer Graphics (Diploma IT, VDU)

Ellipse Generation Algorithm (Midpoint Ellipse Algorithm) - Detailed Explanation and Implementation in C The Midpoint Ellipse Algorithm is used to draw an ellipse on a pixel-based display. It is a generalization of the midpoint circle algorithm. Unlike circles, ellipses have two different radii: one for the x-axis (horizontal radius) and one for the y-axis (vertical radius). This algorithm uses integer-based arithmetic and exploits the symmetry of the ellipse to reduce computations. Mathematical Background of an Ellipse An ellipse is defined as a set of points ( x , y ) (x, y) such that: x 2 a 2 + y 2 b 2 = 1 Where: ( x c , y c ) (xc, yc) : Center of the ellipse a a a : Length of the semi-major axis (horizontal radius) b b b : Length of the semi-minor axis (vertical radius) Concept Behind Midpoint Ellipse Algorithm Ellipse Symmetry: Since the ellipse is symmetric about both x-axis and y-axis, it is sufficient to calculate points in only one quadrant and then refl...

  Midpoint Circle Generation Algorithm (Explanation and Implementation in C) The Midpoint Circle Generation Algorithm is an efficient algorithm used in computer graphics to draw a circle using only integer arithmetic. This algorithm exploits the symmetry of circles to reduce the number of calculations needed. It calculates points in one octant and then reflects these points to draw the entire circle. Concept and Explanation of Midpoint Circle Algorithm: Given a center point ( x c , y c ) and a radius r r , the goal is to draw a circle using pixel-based plotting. Since a circle is symmetric, it is enough to calculate points in one octant (the 45-degree segment of the circle) and then reflect these points to the other seven octants. The algorithm calculates points along the circumference of the circle using a decision parameter  p , which is updated incrementally based on whether the next pixel is closer to the ideal circle path. Steps of the Midpoint Circle Algorithm: ...

  Bresenham’s Line Drawing Algorithm and Implementation in C Language The Bresenham’s Line Drawing Algorithm is an efficient method to draw a straight line between two given points on a pixel-based screen. Unlike the Digital Differential Analyzer (DDA) algorithm, which uses floating-point arithmetic, Bresenham’s algorithm uses only integer arithmetic , making it faster and more suitable for real-time applications. Concept Behind Bresenham's Algorithm Given two points ( x 1 , y 1 ) and ( x 2 , y 2 ) , the task is to draw a line between these points by determining which pixels on a screen should be illuminated. To achieve this, Bresenham’s algorithm uses a decision parameter that helps decide which pixel to plot at each step while incrementally traversing from the starting point to the endpoint. How Bresenham’s Algorithm Works Calculate dx and dy: d x = x 2 − x 1 d y = y 2 − y 1 These values represent the differences between the x and y coordinates. Set up the...

Detailed Explanation of the DDA Algorithm: The Digital Differential Analyzer (DDA) algorithm is one of the simplest algorithms used in computer graphics to draw a straight line between two points. It works by interpolating values in small steps between the starting and ending coordinates, incrementing either the x-coordinate, y-coordinate, or both, depending on the slope of the line. This algorithm is based on the idea of incremental calculations to approximate the continuous line. Steps in the DDA Algorithm: Let’s assume we want to draw a line between two given points, (x1,y1)) and (x2,y2). The DDA algorithm proceeds as follows: Calculate dx and dy: dx=x2−x1 dy=y2−y1 These values represent the change in the x and y coordinates from the starting point to the endpoint. Determine the number of steps required: The number of steps is based on the larger of the absolute values of dx and dy: steps=max⁡( ∣ dx ∣ , ∣ dy ∣ ) This ensu...