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UNIVERSITY OF THE SOUTHERN CARIBBEAN
ROYAL ROAD, MARACAS, ST. JOSEPH.
Assignment 2
An Assignment
Presented in Partial Fulfilment
of the Requirements for the course
CPTR441 : Computer Graphics
Instructor: Mr. Connell Hunte
By: Onishea Thomas
Date: , 2020
Approval...........................
Throughout history, humans have been proven to be visual creatures, from drawings in caves located in Indonesia to sculptures and photography. It is proven that over or approximately 30% of the brain is dedicated to visual processing. Computer graphics is the next step in the era of technology that innovates visual information and imagery as according to Eck and Smith (2018), “Computer graphics refers to anything involved in the creation or manipulation of images on a computer, including animated images.”
Computer graphics has revolutionized industries such as Entertainment industry not only with cartoons but with realism, art and design industries, Industrial design and much more. Computer graphics is a vast area in computer science with concepts such as Geometrical Transformations, Viewing in Three Dimensions and Lighting and Illumination. Geometrical Transformations is when the object solely is transformed relative to the coordinate system or background (javatpoint , n.d.). Javatpoint (n.d.) states the mathematical statement of this viewpoint is defined by geometric transformations applied to each point of the object. For instance it is moving a car against a scenic background which is kept fixed. The common types of geometrical transformations are Translation, reflection, rotation and scaling. To give an idea how these transformations operate the car would be the object used to describe these transformations.Translation is when the car is slid in any direction, while reflection is when the car flipped over a line. When the car is enlarged or reduced it is Scaling but is a Rotation if the car is rotated a certain degree around a point. These transformations can be used on any object. Geometrical Transformations in the field of computer graphics is one of the most important tools to set proper objects into 2D or 3D space. Therefore 2D geometrical transformations consist of translation, rotation scaling and shear. Lin et al (1995) states Translations is a common requirement to move a picture or 2D object to a new position like before where the car slid in any direction and would be calculated by the equation x1 = x + tx while Y1 = y + ty. Scaling transformation is used to change the size of the object. Origin (0,0) scaling is achieved by multiplying the coordinates of a point by x- and y scale factors expression is x1 = x x sx while y1 = y x sy. If |sx| and |sy| are both more than, the object size would increase and in order to reduce the size |sx| and |sy| must be less than. If the scaling transformation is symmetric or uniformed in which the x-and y- scale factors are the same (sx = sy) the car would expand by the same amount in each axis direction. For asymmetrical or non - formal scaling transformations the x- and y-scale factors are not equal (sx≠ sy). The car would change its size by different amounts in the x- and y-axis directions. (sx < 0) is if the scale factor in x is negative which causes the car to reflect in the y-axis. Similarly, (sy< 0) then the car is reflected in the x-axis. Rotation is used to orientate objects and the equation is x1 = x x cos0 - Y x sin0 while y1 = y x sin0 + y x cos0. A shear transformation distorts the shape of an object and the equation is x1 = x + hx x y while y1 = y + hx x x. 2D Transformations derived an expression for new coordinates of a point after transformation and the Matrix representation of the expressions. To obtain square matrices an additional row was added to the matrix and an additional coordinate while homogeneous coordinates is adding a third coordinate to every
interaction of light from all surfaces in a scene for instance shadows, refractions and inter-object reflections while Direct illuminations is an emission at light sources and scattering at surfaces. Ambient light contribution has a very similar approximation of global illumination, assumed to be a constant and has no direction. Diffuse light is reflected when Illumination surface receives a light source and reflects equally in all directions and is based on Lambert’s Law (Cosine law dot product). Specular Lighting reflection is strongest near mirror angle. Spectacular light is bright in mirror or metals direction and depends on viewer position relative to mirror direction. Specular light is calculated in the Phong Model.
References Computer Graphics Introduction of Transformation - javatpoint. (n.d.). Retrieved from https://www.javatpoint.com/computer-graphics-introduction-of-transformations#:~:text=Geometric Transformation: The object itself,each point of the object.&text=This effect is attained through the application of coordinate transformations. Eck, D. (2016). Introduction to Computer Graphics. David J. Eck.
1) Geometrical Transformations which includes,
● 2D Transformations
● Homogeneous Coordinates
● 2D Matrix Transformations
● Composition of Transformations
● 3D Matrix Transformations
2) Viewing in Three Dimensions
● Perspective Projection
● Parallel Projection
● Arbitrary 3D Views
● Mathematics of Planar Projections
3) Lighting and Illumination
● Ambient Lighting
● Diffuse Lighting
● Specular Lighting
● Multiple Light Sources
