Numpy and PyGame Libraries

• Study notes for the lectures are as follows

Numpy Library

• It is a Python library that operates with matrices
• Use "import numpy as np" to import it

PyGame

• It is a cross-platform set of Python modules designed for creating video games
• PyGame includes computer graphics and sound libraries

PyGame Library

• Use "import pygame" to import it
• Initialize using "pygame.init()"
• Create a display window with a specified width and height using "screen = pygame.display.set_mode((width, height))"
• Drawing a rectangle: "pygame.draw.rect(screen, color, pygame.Rect(x, y, width, height))", where screen is the surface to draw on, color is the color of the rectangle, and x, y are the coordinates of the top-left corner
• Update the full display Surface to the screen: "pygame.display.flip()"

Drawing in PyGame

• Drawing a line: "pygame.draw.line(surface, color, (startX, startY), (endX, endY), width)"
• Drawing a circle: "pygame.draw.circle(surface, color, (x, y), radius, width)"

PyGame Tutorial Links

• http://pygametutorials.wikidot.com/system:page-tags/tag/pygame
• http://gamedevelopment.tutsplus.com/tutorials/how-to-learn-pygame--cms-24184

Image Translation

• Achieved by adding a translation matrix, which involves adding tx to the x-coordinate and ty to the y-coordinate: q = p + t.

Image Scaling

• Used for zooming or making figures larger or smaller
• Scaling operation is based on the origin (0, 0) by default
• To scale according to a specific point, apply the same operation that's used for rotation.
• The scale matrix, s, is defined with sx and sy as scaling factors for x and y.

Image Rotation

• Some sets of points are rotated by multiplying each point vector by a rotate matrix r
• The point after the rotation is defined as rotated_point = r*p
• Points of polygons are rotated around the (0, 0) coordinates
• The rotation matrix consists of cosine and sine of the rotation angle a

Rotation Around a Specific Point

• Rotate around a specific center, the point should be subtracted by the center point
• Then the point is multiplied by the rotation matrix and the center must be added again. To achieve this sequence r_point = rotate.dot(p-center)+center

Image Shearing

• Achieved by multiplying a shear matrix to the point

Perspective Projection

• When viewed from a distance, objects appear smaller to the human eye than closer objects due to perspective
• Involves imagining the 2D projection as viewed through a camera viewfinder, influenced by camera position, orientation, and field of view

Projection on x, y plane

• Illustration of projecting 3D points onto a 2D plane, representing how 3D coordinates (Xe, Ye, Ze) are transformed to 2D coordinates (Xp, Yp) on a projection plane at -n or -f.

Projecting 3D Object onto 2D Image

• Formulae for projecting 3D points onto a 2D image plane are shown, involving camera parameters, point coordinates, and angles.

Graphics Processing Unit (GPU)

• GPU is a specialized electronic circuit designed for rapid image manipulation and memory alteration to render images for display
• Modern GPUs use transistors for calculations related to 3D computer graphics.
• Initially, GPUs accelerated texture mapping and rendering; now they also speed up geometric calculations like rotation and translation

CPU vs GPU

• CPUs perform operations faster and can handle complex operations in sequence
• GPUs are generally slower than CPUs and have a limited set of operations like matrix and vector multiplication, yet operate in parallel

OpenGL

• OpenGL is an API (application programming interface) designed to work with the GPU.
• It works with various programming languages and platforms, including Python, Java, Javascript, and Android

Direct3D

• Direct3D is the Microsoft equivalent of OpenGL.
• It can be used to create Windows and Xbox 3D games

Game Engines

• Software frameworks are designed for creating and developing video games for various platforms
• Includes a rendering engine for 2D or 3D graphics, a physics engine for collision detection and response, sound, scripting, animation, AI, networking, streaming, memory management, threading, localization support and scene graph

Unity3D

• Cross-platform game engine developed by Unity Technologies for video games on PC, consoles, mobile devices, and websites
• Unity technologies avail the complete engine for free, with all features, including less source code and premium support. Unity is known for its ability to target games to multiple platforms