SMA 103: ANALYTICAL GEOMETRY
| Institution | KENYATTA UNIVERSITY |
| Course | BACHELOR OF MATHEMAT... |
| Year | 1st Year |
| Semester | Unknown |
| Posted By | stephen oyake rabilo |
| File Type | |
| Pages | 71 Pages |
| File Size | 1.45 MB |
| Views | 9119 |
| Downloads | 2 |
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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.
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Lesson 5 Computer Animation - Skinning
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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
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Lesson 6 Computer Animation - KeyFrame Animation
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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
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Lesson 7 Computer Animation - Facial Animation
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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
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Lesson 8 Computer Animation - Data Driven Facial Animation
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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
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Lesson 9 Computer Animation - MOTION CAPTURE AND PHYSICALLY BASED ANIMATION OF CHARACTERS
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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
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Lesson 10 Computer Animation - MOTION CAPTURE AND PHYSICALLY BASED ANIMATION OF CHARACTERS
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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.
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labour law notes
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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.
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