SMA 103: ANALYTICAL GEOMETRY

Institution KENYATTA UNIVERSITY
Course BACHELOR OF MATHEMAT...
Year 1st Year
Semester Unknown
Posted By stephen oyake rabilo
File Type pdf
Pages 71 Pages
File Size 1.45 MB
Views 9119
Downloads 2
Price: Buy Now whatsapp Buy via whatsapp
  • whatsapp
  • facebook
  • twitter

Description

In this chapter, the Cartesian coordinate system is introduced. The distance between points, midpoints, perpendicular/parallel lines and angles between two lines are covered. The general and point slope form of the equation of the straight line are also covered. 1.2 Lesson Learning Outcomes By the end of this lesson, you should be able to; 1.2.1 Carry out operations on the Straight Line. 1.2.1 The Straight Line In this work the geometrical problems considered are those that are presented on two dimensional plane only and it is therefore important at this point to discuss the plane. Consider any plane with a point denoted by O, which we call the point of reference or the origin. Let line X be horizontal and pass through O and line Y be vertical and pass through O. The horizontal line X is referred to as the x-axis and the vertical line Y is the y-axis. Distance measured from the y-axis is referred to as an abscissa and it is positive if measured to the right and negative if measured to the left. A vertical distance from the x-axis is called a y-ordinate and it is positive if measured above the x-axis and negative if measured below the x-axis. Any point on the plane can described by its abscissa and its ordinate as P(x, y), for any point P. The symbol (x, y) represents the coordinates of the point, where x is the abscissa and y the ordinate and it is also referred to as the Cartesian coordinates of P.
Below is the document preview.

No preview available
Lesson 5 Computer Animation - Skinning Trending!
Skinning is the process of attaching a renderable skin to an underlying articulated skeleton. There are several approaches to skinning with varying degrees of realism and complexity. Our main focus will be on the smooth skinning algorithm, which is both fast and reasonably effective, and has been used extensively in real time and pre-rendered animation. The smooth skinning algorithm goes by many other names in the literature, such as blended skinning, multimatrix skinning, linear blend skinning, skeletal subspace deformation (SSD), and sometimes just skinning. This chapter will explain the smooth skinning algorithm in detail and provide additional information about the offline creation and binding process. Binding refers to the initial attachment of the skin to the underlying skeleton and assigning any necessary information to the vertices. Smooth skinning, while fast and straightforward, does have its limitations, and so alternative techniques are also briefly introduced and referenced, including a variety of deformation techniques and some more elaborate anatomically based approaches that simulate muscle and skin deformations
No pages found 7305 Views 0 Downloads 223.91 KB
Lesson 6 Computer Animation - KeyFrame Animation Trending!
Generalized coordinates In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration. Example is a vector to specify the posture of the body q=(q1 ,q2 ,q3 ,q4 ,q5 , q6 , q7 ,... ,qn) Usually, the first three numbers: location of the root the next three numbers: orientation of root The rest: the joint angles of the body
No pages found 5385 Views 0 Downloads 122.79 KB
Lesson 7 Computer Animation - Facial Animation Trending!
Facial Anination deals with the simulation of the different facial expresions a character can make. Inorder to simulate conversation, visible emotional expressions(e.g Saddness, Happines), we need to understand the different mechanisims and muscle structures that the face uses to accurately represent the emotion / visemes. generally the facial expressions and visemes in animation relies on three different appoaches: • Muscle-based models • Capture real human data • Expression Cloning
No pages found 4902 Views 1 Downloads 2.36 MB
Lesson 8 Computer Animation - Data Driven Facial Animation Trending!
Data based facial animation The generation of facial animation data can be approached in different ways: 1. marker-based motion capture on points or marks on the face of a performer 2. markerless motion capture techniques using different type of cameras 3. audio-driven techniques 4. key frame animation
No pages found 5140 Views 0 Downloads 257.74 KB
Lesson 9 Computer Animation - MOTION CAPTURE AND PHYSICALLY BASED ANIMATION OF CHARACTERS Trending!
There are three methods • Create them manually • Use real human / animal motions • Use physically based simulation Using Real Human (Animal) Motion • Real human (animal) motion is realistic • Much faster and cheaper than manually producing the data We use the motion capture device (Mocap) • There are four major types of Mocaps – Optical – Magnetic – Inertial trackers
No pages found 7690 Views 1 Downloads 603.79 KB
Lesson 10 Computer Animation - MOTION CAPTURE AND PHYSICALLY BASED ANIMATION OF CHARACTERS Trending!
Motion tracking or motion capture started as a photogrammetric analysis tool in biomechanics research in the 1970s and 1980s, and expanded into education, training, sports and recently computer animation for television, cinema, and video games as the technology matured. A performer wears markers near each joint to identify the motion by the positions or angles between the markers. Acoustic, inertial, LED, magnetic or reflective markers, or combinations of any of these, are tracked, optimally at least two times the frequency rate of the desired motion, to submillimeter positions. The resolution of the system is important in both the spatial resolution and temporal resolution as motion blur causes almost the same problems as low resolution.
No pages found 6894 Views 1 Downloads 585.08 KB
labour law notes Trending!
The purpose of this simplified labour law class notes is to enable the student to pass his or her labour law exam paper with ease.
98 Pages 5869 Views 0 Downloads 727.16 KB
Family law notes Trending!
Family law may refer to law that govern a man and a woman who share common household.
91 Pages 8252 Views 1 Downloads 411.04 KB
Family law 2 notes Trending!
Family refer to a man and a woman sharing common household
15 Pages 8618 Views 0 Downloads 166.79 KB
company law notes
Company law refers to the laws that govern the formation and winding up of a company under certain company's act.
117 Pages 567 Views 0 Downloads 731.85 KB