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C++ > Computer Graphics Code Examples

Implement Graham Scan Algorithm to Find the Convex Hull

/* Implement Graham Scan Algorithm to Find the Convex Hull This is a C++ Program to implement Graham Scan algorithm. Graham's scan is a method of computing the convex hull of a finite set of points in the plane with time complexity O(n log n). */ // A C++ program to find convex hull of a set of points for explanation of orientation() #include <iostream> #include <stack> #include <stdlib.h> using namespace std; struct Point { int x; int y; }; Point p0; // A utility function to find next to top in a stack Point nextToTop(stack<Point> &S) { Point p = S.top(); S.pop(); Point res = S.top(); S.push(p); return res; } // A utility function to swap two points int swap(Point &p1, Point &p2) { Point temp = p1; p1 = p2; p2 = temp; } // A utility function to return square of distance between p1 and p2 int dist(Point p1, Point p2) { return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y); } int orientation(Point p, Point q, Point r) { int val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y); if (val == 0) return 0; // colinear return (val > 0) ? 1 : 2; // clock or counterclock wise } // A function used by library function qsort() to sort an array of points with respect to the first point int compare(const void *vp1, const void *vp2) { Point *p1 = (Point *) vp1; Point *p2 = (Point *) vp2; // Find orientation int o = orientation(p0, *p1, *p2); if (o == 0) return (dist(p0, *p2) >= dist(p0, *p1)) ? -1 : 1; return (o == 2) ? -1 : 1; } // Prints convex hull of a set of n points. void convexHull(Point points[], int n) { // Find the bottommost point int ymin = points[0].y, min = 0; for (int i = 1; i < n; i++) { int y = points[i].y; // Pick the bottom-most or chose the left most point in case of tie if ((y < ymin) || (ymin == y && points[i].x < points[min].x)) ymin = points[i].y, min = i; } // Place the bottom-most point at first position swap(points[0], points[min]); // Sort n-1 points with respect to the first point. A point p1 comes before p2 in sorted ouput if p2 has larger polar angle (in counterclockwise direction) than p1 p0 = points[0]; qsort(&points[1], n - 1, sizeof(Point), compare); // Create an empty stack and push first three points to it. stack<Point> S; S.push(points[0]); S.push(points[1]); S.push(points[2]); // Process remaining n-3 points for (int i = 3; i < n; i++) { // Keep removing top while the angle formed by points next-to-top, top, and points[i] makes a non-left turn while (orientation(nextToTop(S), S.top(), points[i]) != 2) S.pop(); S.push(points[i]); } // Now stack has the output points, print contents of stack while (!S.empty()) { Point p = S.top(); cout << "(" << p.x << ", " << p.y << ")" << endl; S.pop(); } } // Driver program to test above functions int main() { Point points[] = { { 0, 3 }, { 1, 1 }, { 2, 2 }, { 4, 4 }, { 0, 0 }, { 1, 2 }, { 3, 1 }, { 3, 3 } }; int n = sizeof(points) / sizeof(points[0]); cout << "The points in the convex hull are: \n"; convexHull(points, n); return 0; }

LIFO stack. Stacks are a type of container adaptor, specifically designed to operate in a LIFO context (last-in first-out), where elements are inserted and extracted only from one end of the container. stacks are implemented as container adaptors, which are classes that use an encapsulated object of a specific container class as its underlying container, providing a specific set of member functions to access its elements. Elements are pushed/popped from the "back" of the specific container, which is known as the top of the stack.

Consider a situation, when we have two persons with the same name, jhon, in the same class. Whenever we need to differentiate them definitely we would have to use some additional information along with their name, like either the area, if they live in different area or their mother's or father's name, etc. Same situation can arise in your C++ applications. For example, you might be writing some code that has a function called xyz() and there is another library available which is also having same function xyz(). Now the compiler has no way of knowing which version of xyz() function you are referring to within your code.

An array is defined as the collection of similar type of data items stored at contiguous memory locations. Arrays are the derived data type in C++ programming language which can store the primitive type of data such as int, char, double, float, etc. It also has the capability to store the collection of derived data types, such as pointers, structure, etc. The array is the simplest data structure where each data element can be randomly accessed by using its index number. C++ array is beneficial if you have to store similar elements. For example, if we want to store the marks of a student in 6 subjects, then we don't need to define different variables for the marks in the different subject. Instead of that, we can define an array which can store the marks in each subject at the contiguous memory locations.

Test whether container is empty. Returns whether the stack is empty: i.e. whether its size is zero. stack::empty() function is an inbuilt function in C++ STL, which is defined in <stack>header file. empty() is used to check whether the associated container is empty or not and return true or false accordingly. This member function effectively calls member empty of the underlying container object. No parameter passed. Function returns true if the underlying container's size is 0, false otherwise.

In C++, classes and structs are blueprints that are used to create the instance of a class. Structs are used for lightweight objects such as Rectangle, color, Point, etc. Unlike class, structs in C++ are value type than reference type. It is useful if you have data that is not intended to be modified after creation of struct. C++ Structure is a collection of different data types. It is similar to the class that holds different types of data. A structure is declared by preceding the struct keyword followed by the identifier(structure name). Inside the curly braces, we can declare the member variables of different types.

Remove top element. Removes the element on top of the stack, effectively reducing its size by one. The C++ function std::stack::pop() removes top element from the stack and reduces size of stack by one. This function calls destructor on removed element. The element removed is the latest element inserted into the stack, whose value can be retrieved by calling member stack::top. This calls the removed element's destructor. This member function effectively calls the member function pop_back of the underlying container object.

#include is a way of including a standard or user-defined file in the program and is mostly written at the beginning of any C/C++ program. This directive is read by the preprocessor and orders it to insert the content of a user-defined or system header file into the following program. These files are mainly imported from an outside source into the current program. The process of importing such files that might be system-defined or user-defined is known as File Inclusion. This type of preprocessor directive tells the compiler to include a file in the source code program.

Check whether eofbit is set. Returns true if the eofbit error state flag is set for the stream. This flag is set by all standard input operations when the End-of-File is reached in the sequence associated with the stream. Note that the value returned by this function depends on the last operation performed on the stream (and not on the next). Operations that attempt to read at the End-of-File fail, and thus both the eofbit and the failbit end up set. This function can be used to check whether the failure is due to reaching the End-of-File or to some other reason.

A program shall contain a global function named main, which is the designated start of the program in hosted environment. main() function is the entry point of any C++ program. It is the point at which execution of program is started. When a C++ program is executed, the execution control goes directly to the main() function. Every C++ program have a main() function.

In while loop, condition is evaluated first and if it returns true then the statements inside while loop execute, this happens repeatedly until the condition returns false. When condition returns false, the control comes out of loop and jumps to the next statement in the program after while loop. The important point to note when using while loop is that we need to use increment or decrement statement inside while loop so that the loop variable gets changed on each iteration, and at some point condition returns false. This way we can end the execution of while loop otherwise the loop would execute indefinitely. A while loop that never stops is said to be the infinite while loop, when we give the condition in such a way so that it never returns false, then the loops becomes infinite and repeats itself indefinitely.

Access next element. Returns a reference to the top element in the stack. stack::top() function is an inbuilt function in C++ STL, which is defined in <stack> header file. top() is used to access the element at the top of the stack container. In a stack, the top element is the element that is inserted at the last or most recently inserted element. Since stacks are last-in first-out containers, the top element is the last element inserted into the stack. This member function effectively calls member back of the underlying container object. No parameter is required.

Insert element. Inserts a new element at the top of the stack, above its current top element. The content of this new element is initialized to a copy of val. This member function effectively calls the member function push_back of the underlying container object. C++ Stack push () function is used for adding new elements at the top of the stack. If we have an array of type stack and by using the push() function we can insert new elements in the stack. The elements are inserted at the top of the stack. The element which is inserted most initially is deleted at the end and vice versa as stacks follow LIFO principle.

In computer programming, loops are used to repeat a block of code. For example, when you are displaying number from 1 to 100 you may want set the value of a variable to 1 and display it 100 times, increasing its value by 1 on each loop iteration. When you know exactly how many times you want to loop through a block of code, use the for loop instead of a while loop. A for loop is a repetition control structure that allows you to efficiently write a loop that needs to execute a specific number of times.

In computer programming, we use the if statement to run a block code only when a certain condition is met. An if statement can be followed by an optional else statement, which executes when the boolean expression is false. There are three forms of if...else statements in C++: • if statement, • if...else statement, • if...else if...else statement, The if statement evaluates the condition inside the parentheses ( ). If the condition evaluates to true, the code inside the body of if is executed. If the condition evaluates to false, the code inside the body of if is skipped.

The sizeof() is an operator that evaluates the size of data type, constants, variable. It is a compile-time operator as it returns the size of any variable or a constant at the compilation time. The size, which is calculated by the sizeof() operator, is the amount of RAM occupied in the computer. The sizeof is a keyword, but it is a compile-time operator that determines the size, in bytes, of a variable or data type. The sizeof operator can be used to get the size of classes, structures, unions and any other user defined data type. The data_type can be the data type of the data, variables, constants, unions, structures, or any other user-defined data type.

Logical Operators are used to compare and connect two or more expressions or variables, such that the value of the expression is completely dependent on the original expression or value or variable. We use logical operators to check whether an expression is true or false. If the expression is true, it returns 1 whereas if the expression is false, it returns 0. Assume variable A holds 1 and variable B holds 0:

Sort elements of array. Sorts the num elements of the array pointed to by base, each element size bytes long, using the compar function to determine the order. The sorting algorithm used by this function compares pairs of elements by calling the specified compar function with pointers to them as argument. The function does not return any value, but modifies the content of the array pointed to by base reordering its elements as defined by compar. The order of equivalent elements is undefined.

You'll learn to print the number entered by a user using C++ cout statement. This program asks user to enter a number. When enters an 'integer', it is stored in variable number using

C++ Program demonstrates the Removal of All the nodes which don't lie in any Path with Sum greater than or equal to K. Create a new 'Binary Tree node' with given data. Truncates

This technique can only calculate power if the exponent is a 'positive integer'. To find power of a number, you can use pow() function. C++ program calculates the power of any number