2D transformations are important operations in computer graphics that allow modifying the position, size, and orientation of objects in a 2D plane. There are several types of 2D transformations including translation, rotation, scaling, and more. Transformations are represented using matrix math for efficient application of sequential transformations. Key techniques include homogeneous coordinates to allow different types of transformations to be combined into a single matrix operation.
3D transformations in computer graphics include translation, scaling, and rotation of 3D objects. Translation moves an object by adding translation offsets to the x, y, and z coordinates. Scaling enlarges or shrinks an object by multiplying the coordinates by scaling factors. Rotation rotates an object by applying rotation matrices to change the orientation. Reflection mirrors an object across planes by flipping the sign of coordinates on one axis. These transformations are used to manipulate 3D objects in computer graphics and animation.
Projection is the process of mapping a 3D object onto a 2D plane. There are two main types of projection: parallel projection, where lines project parallel to each other, and perspective projection, where lines converge to a point. Parallel projection includes oblique projection, where lines hit the plane at a non-90 degree angle, and orthographic projection, where lines hit perpendicular. Orthographic projection can be multiview projection showing top, side and front views, or axonometric projection where the object is rotated for multiple views.
2D transformations are important operations in computer graphics that allow modifying the position, size, and orientation of objects in a 2D plane. There are several types of 2D transformations including translation, rotation, scaling, and more. Transformations are represented using matrix math for efficient application of sequential transformations. Key techniques include homogeneous coordinates to allow different types of transformations to be combined into a single matrix operation.
3D transformations in computer graphics include translation, scaling, and rotation of 3D objects. Translation moves an object by adding translation offsets to the x, y, and z coordinates. Scaling enlarges or shrinks an object by multiplying the coordinates by scaling factors. Rotation rotates an object by applying rotation matrices to change the orientation. Reflection mirrors an object across planes by flipping the sign of coordinates on one axis. These transformations are used to manipulate 3D objects in computer graphics and animation.
Projection is the process of mapping a 3D object onto a 2D plane. There are two main types of projection: parallel projection, where lines project parallel to each other, and perspective projection, where lines converge to a point. Parallel projection includes oblique projection, where lines hit the plane at a non-90 degree angle, and orthographic projection, where lines hit perpendicular. Orthographic projection can be multiview projection showing top, side and front views, or axonometric projection where the object is rotated for multiple views.
2D transformations are used in computer graphics to modify and reposition graphics. The key 2D transformation techniques are translation, rotation, scaling, reflection, and shearing. Translation moves an object by adding offsets to its coordinates. Rotation modifies an object's position by applying rotational matrices. Scaling enlarges or shrinks an object by multiplying its coordinates. Reflection mirrors an object across an axis by inverting one coordinate. Shearing skews an object by adding its coordinates. Homogeneous coordinates allow representing transformations using matrix multiplications.
The document describes two algorithms for drawing lines on a graph:
1. The DDA (Digital Differential Analyzer) line drawing algorithm which calculates the slope of the line and uses incremental steps to determine each new pixel coordinate.
2. Bresenham's line drawing algorithm which uses a decision parameter to determine whether the next pixel is directly above/below or diagonal to the current pixel in order to draw lines with integer coordinates.
Fragmentation refers to the inefficient use of memory space. Internal fragmentation is the wasted space within each allocated memory block due to rounding up to the next allocation size. External fragmentation occurs when various unused memory holes are scattered throughout the memory space. The sample code demonstrates how to calculate internal and external fragmentation by allocating memory to processes and tracking the remaining free space.
The document discusses three file allocation strategies - sequential, indexed, and linked allocation. It provides descriptions of each strategy and includes sample code to demonstrate how they work. Sequential allocation stores files sequentially in contiguous disk blocks. Indexed allocation stores files in random blocks, maintaining an index to link file blocks. Linked allocation stores files non-contiguously, with each block containing a pointer to the next block in the file.
The Banker's algorithm is a deadlock avoidance algorithm that checks if a system is in a safe state when resources are requested. It models the allocation of resources to processes as a bank lending money to customers. The algorithm uses data structures like Available, Max, Allocation, and Need to represent the available resources, maximum requested resources, allocated resources, and remaining needed resources for each process. It iterates through processes to see if their remaining needs can be met by available resources while maintaining a safe state.
Priority scheduling assigns priorities to processes and executes the highest priority process first. If processes have equal priorities, they are executed in first come first served order. The example document shows how priority scheduling works by assigning priorities from 1 to 5 to five processes, then calculating their waiting times and turnaround times based on executing the highest priority processes first. Round robin scheduling assigns a fixed time quantum to each process, preempting and resuming processes to ensure all get CPU time and avoid starvation. The example shows how time is divided between processes using a 2ms time quantum.
CPU scheduling is the process by which the CPU selects which process to execute next from among processes in memory that are ready to execute. The CPU scheduler selects processes from the ready queue to execute. The goal of CPU scheduling is to maximize CPU utilization and throughput while minimizing waiting time and response time. Common CPU scheduling algorithms include first come first serve (FCF) which services processes in the order they arrive, and shortest job first (SJF) which selects the process with the shortest estimated run time to execute next.
Implementation of checking the validity of an arithmetic expression, conversion from infix to postfix form, evaluation of a postfix expression (C code)
An array is a collection of homogeneous data items stored in successive memory locations. It allows storing multiple elements of the same type using a single name. Elements in an array can be accessed using the array name and index number. Common operations on arrays include storing/retrieving elements, searching for a particular element or largest/smallest element, and calculating sum of elements based on certain criteria like even/odd indexing. Arrays can also be modified by inserting or deleting elements.
A two dimensional array is an array that has two dimensions like rows and columns. The total number of elements in a two dimensional array is calculated by multiplying the number of rows and columns. A two dimensional array can be accessed using two indices like A[i][j] where i represents the row and j represents the column. Common operations on two dimensional arrays include storing and retrieving elements, finding the sum of boundary elements, finding the sum of diagonal elements, adding, subtracting and multiplying two dimensional arrays.
A stack is a linear data structure that follows the LIFO (last in, first out) principle. Elements are added to the top of the stack and removed from the top. A pointer called the top pointer tracks the top element of the stack during push and pop operations. The push operation adds an element to the top of the stack, while the pop operation removes the top element. A stack can be implemented using either an array or linked list. The document then provides algorithms and sample code for implementing stack operations like push and pop on an array-based stack.
Queue is a linear data structure that follows the FIFO (first-in, first-out) principle. Elements are added to the rear of the queue and removed from the front. A queue can be implemented using an array or linked list, with front and rear pointers indicating the first and last elements. To add an element, the rear pointer is incremented and the element is inserted at that position. To remove an element, it is accessed via the front pointer before incrementing the front pointer. This allows efficient O(1) insertion and removal of elements from the queue.
The document discusses two searching algorithms - linear search and binary search. Linear search sequentially compares the target element to each element in the array, while binary search uses a divide and conquer approach to quickly hone in on the target element in a sorted array. Both algorithms are demonstrated with pseudocode and examples.
Sorting involves ordering or arranging a collection of elements according to a specific order. There are different sorting algorithms that can sort data in ascending or descending order, including bubble sort, selection sort, and insertion sort. Sorting algorithms can also be categorized as internal sorting, which sorts all data within memory, or external sorting, which sorts data that cannot all fit into memory at once.
Linked lists are data structures that store data in scattered locations in memory. Each data item or node contains a data part that holds the actual data and a link part that points to the next node. The nodes are linked together using these links. A linked list requires an external pointer to point to the first node. Operations like traversing, searching, inserting and deleting nodes can be performed on linked lists by manipulating these node links.
Given a set of positive integers and a target sum S, the sum of subset problem is to determine if there exists a subset of the integers whose sum equals S. The algorithm uses a two dimensional table t, where t[i,j] is true if there is a subset that sums to j using the first i elements of the set. It iterates through the elements, setting t[i,j] to true if t[i-1,j] is already true or t[i-1,j-w[i]] is true, where w[i] is the current element. It returns t[n,m] which indicates if a subset summing to S exists.
Quicksort is a sorting algorithm that uses a divide and conquer approach. It works by selecting a pivot element and partitioning the array around the pivot so that elements less than the pivot are to its left and greater elements are to its right. It then recursively applies this process to the subarrays until each contains a single element, at which point the array is fully sorted. The example demonstrates quicksort sorting an array from 0 to 7.